Deliverable 4.5 Parametric assessment and optimized design …niker.eu/assets/Files/Download/D4.5 -...

NEW INTEGRATED KNOWLEDGE BASED

APPROACHES TO THE PROTECTION OF CULTURAL

HERITAGE FROM EARTHQUAKE-INDUCED RISK

NIKER

Grant Agreement n° 244123

Deliverable 4.5

Parametric assessment and optimized design procedures for vertical elements

Due date: February 2012

Submission date: April 2012

Issued by: BAM

WORKPACKAGE 4: Optimization of design for vertical elements

Partners: UNIPD, UMINHO, UPC, ENA

Leader: BAM

PROJECT N°: 244123

ACRONYM: NIKER

TITLE: New integrated knowledge based approaches to the protection

of cultural heritage from earthquake-induced risk

COORDINATOR: Università di Padova (Italy)

START DATE: 01 January 2010 DURATION: 36 months

INSTRUMENT: Collaborative Project

Small or medium scale focused research project

THEME: Environment (including Climate Change)

Dissemination level: PP Rev: FIN

NEW INTEGRATED KNOWLEDGE BASED APPROACHES TO THE PROTECTION OF CULTURAL HERITAGE FROM EARTHQUAKE-INDUCED RISK

NIKER Grant Agreement n°

244123

Optimization of design for vertical elements D4.5 i

TABLE OF CONTENTS

1 INTRODUCTION ........................................................................................................................ 3

1.1 Description and objectives of the work package ................................................................ 3

1.2 Objective and structure of the deliverable ......................................................................... 3

2 GENERAL OVERVIEW OF THE ASSESSMENTS CARRIED OUT ........................................... 4

2.1 Introduction ....................................................................................................................... 4

2.2 Parametric modelling of walls ........................................................................................... 5

3 WORK PROGRAM AND RESULTS OF UNIPD ........................................................................ 7

3.1 Numerical modelling of stone masonry. Parametric assessment ...................................... 7

3.1.1 Introduction ................................................................................................................... 7

3.1.2 Model description .......................................................................................................... 7

3.1.3 Parameters.................................................................................................................... 8

3.1.4 Results .......................................................................................................................... 9

3.1.5 Conclusions ................................................................................................................. 18

3.2 Analytical prediction of compressive strength for three-leaf masonry specimens ............ 19

3.2.1 Introduction ................................................................................................................. 19

3.2.2 Existing models for prediction of the compressive strength of three-leaf masonry before grouting .................................................................................................................................. 19

3.2.3 Existing models for prediction of the compressive strength of three-leaf masonry after grouting .................................................................................................................................. 19

3.2.4 Experimental data used for the new calibration of the prediction model ....................... 20

3.2.5 Calibration of the analytical model for the prediction of compressive strength of non-injected masonry walls ........................................................................................................... 23

3.2.6 Calibration of the analytical model for the prediction of compressive strength of injected masonry walls ........................................................................................................................ 23

3.2.7 Conclusive Remarks ................................................................................................... 30

4 WORK PROGRAM AND RESULTS OF UMINHO ................................................................... 32

4.1 Half-timbered walls parametric assessment .................................................................... 32

4.1.1 Introduction ................................................................................................................. 32

4.1.2 Parametric assessment ............................................................................................... 32

4.1.3 Results ........................................................................................................................ 33

4.1.4 Conclusions ................................................................................................................. 34

4.2 Rammed earth parametric assessment........................................................................... 34

4.2.1 Introduction ................................................................................................................. 34

4.2.2 Layer thickness ........................................................................................................... 36

4.2.3 Compressive strength ................................................................................................. 36



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Optimization of design for vertical elements D4.5 ii

4.2.4 Tensile strength ........................................................................................................... 37

4.2.5 Fracture energy in tension ........................................................................................... 37

4.2.6 Interface parameters ................................................................................................... 38

4.2.7 Conclusions ................................................................................................................. 38

5 WORK PROGRAM AND RESULTS OF UPC .......................................................................... 39

5.1 Introduction ..................................................................................................................... 39

5.1.1 Overview ..................................................................................................................... 39

5.1.2 Model description ........................................................................................................ 39

5.1.3 Modelling of strengthening techniques ........................................................................ 40

5.1.4 Initial material properties ............................................................................................. 40

5.2 Model calibration and initial results ................................................................................. 41

5.3 Parametric investigation .................................................................................................. 41

5.3.1 Overview. Object of parametrization and variables considered. ................................... 41

5.3.2 Boundary conditions - amount of vertical restraint ....................................................... 41

5.3.3 Masonry compressive strength .................................................................................... 43

5.3.4 Vertical pre-stress ....................................................................................................... 44

5.3.5 Amount of reinforcement steel ..................................................................................... 45

5.3.6 Young’s modulus of units ............................................................................................ 46

5.4 Conclusions .................................................................................................................... 47

6 WORK PROGRAM AND RESULTS OF ENA .......................................................................... 48

6.1 Introduction ..................................................................................................................... 48

6.2 Parametric assessment .................................................................................................. 48

6.2.1 Model description ........................................................................................................ 48

6.2.2 Parameters.................................................................................................................. 51

6.3 Results ........................................................................................................................... 51

6.4 Conclusions .................................................................................................................... 54

7 REFERENCES ......................................................................................................................... 55



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Optimization of design for vertical elements D4.5 3

1 INTRODUCTION

1.1 DESCRIPTION AND OBJECTIVES OF THE WORK PACKAGE

One of the main aims of NIKER project is to develop and validate intervention technologies that are based on the use of traditional and innovative materials, to be applied to various types of structural elements. In particular, WP4 focuses on vertical elements, as walls. During WP4, the envisaged intervention techniques have been tested and numerically modelled with the final aim of establishing design procedures that optimize their use on existing buildings.

Hence, the goals of WP4 are:

• Definition of adequate and feasible intervention methods for vertical structural elements related to the catalogue and requirements described in WP3;

• Definition and improvement of laboratory procedures for evaluating the intervention methods and specifications for laboratory specimens;

• To carry out the necessary tests to characterise the experimental behaviour of original and strengthened masonry ans massive walls in order to obtain information on the systems performance and the main constitutive laws relevant for modelling;

• To numerically simulate the experimental behaviour and perform parametric assessment to define critical mechanical parameters or define optimised design procedures.

1.2 OBJECTIVE AND STRUCTURE OF THE DELIVERABLE

This report is aimed at validate reliable models representative of the mechanical behaviour of vertical element through the parametric studies of numerical models improved in D4.4.

The goal is to define critcal mechanical parameters by studying the effect of selected variables on the behaviour of structural vertical components. In this study improved numerical models (see D4.41) and the constitutive laws derived in WP4.1 are used to simulate the observed experimental behaviour.

The different kinds of approaches implemented in D4.4 are mainly focussed on the two main categories of analytical and numerical (FEM, linear or non-linear) analyses. Input data from WP 3.1 and WP 4.1 concerning material characterization and the effect of intervention techniques are used to perform the numerical simulations and to evaluate them in relation to the damage database. The processing of this data serves the purposes of validation and calibration. Output data is fed into WP 8 and WP 10.

The parametric modelling is based on specific studies on elements at different levels carried out in D4.4. The deliverable contains a general overview of the parametric modelling activities, followed by single chapters, where the results obtained from each partner are discussed. In total 4 partners are involved in the composition of D4.5 (UNIPD, UMINHO, UPC and ENA).

1 Deliverable 4.4: Report about the accuracy and reliability of the numerical simulations on vertical elements, Submitted in

March 2012.



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2 GENERAL OVERVIEW OF THE ASSESSMENTS CARRIED OUT

2.1 INTRODUCTION

Parametric modelling is a crucial step in the definition of parameters and procedures that can optimize both design and assessment of structures. There are numerous computational methods and tools currently available to perform such analyses. They are supported by different theories and strategies with different levels of complexity, computation time and cost. A complex analysis is not always synonym of a better result and the choice of a method over another depends mostly on the purpose of the analysis. To achieve suitable reliability and to improve accuracy, models were calibrated on experimental test results. The effect of selected variables on the behaviour of the structural vertical components is presented.

The project allowed exchanging expertise among partners, which contributed to the modelling of their own but also of others experimental tests. A scheme of the contributions to this deliverable for the various constructive elements is given in Tab. 2.1 and 2.2.

The results reported in this deliverable will flow into the guidelines elaborated in WP10, which will provide the potential users (designer, architects, engineers, construction companies, bodies responsible of building maintenance) with tailored design guidelines and easy-to-use summary tables in order to ensure the appropriate and correct use of the intended techniques.

Table 2.2.1 - Tests performed in WP 4.1 (D4.3).

Material group Material D4.3 - Testing D4.4 - Modelling

Partner Experiment carried out Partner Activity

Stone masonry walls

Stone masonry (non-grouted and grouted)

UNIPD

Compressive strength In-plane cyclic shear test Diagonal compression/ shear strength

UNIPD

Analytical modelling. Calibration of a hysteretic model based on in-plane shear-compression tests and simulation of the in-plane cyclic behaviour. FEM modelling. Calibration of global behaviour (in-plane strength and deformability).

Stone masonry wall ENA Compressive strength ENA

Analytical formulation law of effective behaviour of the self-consistent method for the wall stone Calibration of numerical model based on compression tests simulation.

Half timbered walls

Half timbered walls UMINHO Shear bond strength In-plane cyclic shear test

UMINHO FEM Non-linear model on orthotropic properties for timber.

Fired clay bricks masonry walls

Clay bricks walls (unreinforced and reinforced) ITAM In-plane cyclic shear test UPC

FEM Non linear Simulation of experiments for estimation of capacity.

Earthen masonry or monolithic

walls

Earth block masonry

Rammed earth (unreinforced and reinforced)

BAM

Compressive strength Diagonal compression/ shear strength In-plane cyclic shear test

ZRS / UMINHO

Non-linear model of rammed earth simulating the experimental compression and shear behaviour.

Earth block masonry and cob (unreinforced)

BAM Compressive strength Diagonal compression/ shear strength

ZRS

Non-linear model of earth block masonry, rammed earth and cob simulating their experimental compression behaviour.

CEB masonry ENA Compressive strength ENA Analytical formulation law of effective behaviour of the earth material in linear elasticity.



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Table 2.2 - Parametric modelling performed for D4.5, based on previous work presented in Tab. 2.1 (D.4.3 and D4.4).

Partner Object of parameterization and

optimization Type of

modelling Variables Outputs

UNIPD

Three-leaf stone masonry walls tested under shear-compression,

Unstrengthened and strengthened with grout injection

Scale 1:1 and 2:3

FEM non linear continuum damage model

Slenderness ratio,

vertical pre-compression level,

Scale,

Material properties.

Maximum resistance (horizontal stress)

Displacement capacity (drift for ultimate state and drift for maximum resistance)

Damage pattern and damage progression

UMINHO

Shear behaviour of rammed earth walls:

Mechanical (compressive strength, tensile strength, fracture energy in tension, interfaces cohesion and friction)

Geometrical properties (compaction layers thickness)

FEM (macro- and micro-modelling)

Compaction layers thickness

Compressive strength

Tensile strength

Fracture energy in tension

Interfaces cohesion and friction

Shear strength

Half-timbered walls:

Vertical pre-compression level

Anisotropic properties of timber

Non-linear properties of timber-timber and timber-infill interfaces

Type of material and geometrical properties of strengthening

FEM

Values of strength and fracture energy of timber

Stiffness of interface elements

Values of cohesion

Friction angle

Fracture energy of interfaces

Thickness of strengthening steel plates and steel properties of bolts

Stresses and damage distribution

Efficiency of strengthening technique adopted

Capacity of walls in terms of ductility and ultimate strength

UPC

Shear walls under distributed vertical load and concentrated in-plane horizontal load

Three sets of materials: adobe brick with clay mortar, dry brick with cement mortar and solid brick with cement mortar

Simulation of reinforcement: diagonal steel wires and polymer geo-net

Simplified FEM micro-modelling of masonry shear walls

Boundary conditions (degree of vertical fixicity at top)

Compressive strength of masonry composite

Young’s modulus of units

Vertical load

Amount of steel reinforcement

Capacity and stiffness of plain and reinforced walls.

Efficiency of reinforcement method for given load and boundary conditions and material properties

ENA

Numerically simulate of earth/adobe and local stone walls.

The earth wall is made out of CEB and earth mortar

The stone wall is made out of local Stone and lime-mortar

Analytical: quasi-static analysis

FEM: non-linear dynamic analysis

Height, thickness and length Optimized ratios of the three dimensions

2.2 PARAMETRIC MODELLING OF WALLS

Parametric modelling of walls is strongly aimed to reproduce the prevailing failure mechanisms and a sequence of damage formation on the panels consistent with those observed experimentally (reported in D4.3). FEM are devoted to the clarification of stress-strain distributions in elements, and to the calibration of constitutive curves on the basis of the results of the experimental campaigns. Analytical and FE models are proposed for the parametric studies.

FEM non linear continuum damage model and simplified analytical model are adopted by UNIPD for parametric analysis of three-leaf stone masonry walls tested under shear-compression. Unstrengthened and strengthened (with grout injection) samples are considered at different scales (1:1 and 2:3). The study is aimed to investigate the maximum resistance in term of horizontal



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stress and the displacement capacity taking into account different variables (slenderness ratio, vertical pre-compression level, different scale, material properties).

The parametric studies performed by UMINHO are focused on half timbered wall and rammed earth walls. In the first case the parameters that are being studied are the vertical pre-compression level, the bolts diameter and the thickness of the steel plates adopted in the strengthening techniques (this task is currently being developed) and different boundary conditions for the constraining of the top of the wall (this task still has to be approached) in order to study their influence on the global behaviour of half-timbered walls in terms of ultimate capacity and ductility, as well as failure modes of the walls. For rammed earth walls a parametric analysis followed the calibration of the FEM models simulating the tests on rammed earth wallets carried by BAM-ZRS. Two approaches were followed: macro- and micro-modelling. The micro-modelling approach consisted of a multi-layered model with Mohr-Coulomb failure criteria at the interfaces between compaction layers, which aimed to simulate possible failure through them. The models calibrated according to both approaches were included in the parametric analysis.

The parametric study performed by UPC is focused on the results obtained by cyclic test performed by ITAM on adobe units, dry brick solid bricks masonry (reinforced and non-reinforced). A simplified FEM micro-modelling of masonry shear walls is adopted taking into account smeared cracking for units combined with plasticity model for interfaces. The study is aimed to investigate the capacity and stiffness of plain and reinforced walls and the efficiency of reinforcement method for given load and boundary conditions and material properties

Parametric study of experimental behaviour of earth/adobe and local stone walls is performed by ENA with the main aims of obtaining the resistance of the wall the Young’s modulus and the percentage of deformation limit. To determine the optimal dimensions of a mud wall two approaches are adopted: the first based on the calculation of the applied forces is a quasi-static analysis of the mud wall behaviour. The second based on the calculation of displacement of the wall under the effect of the seismic action, is non-linear dynamic analysis performed using ANSYS computer software.



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3 WORK PROGRAM AND RESULTS OF UNIPD

3.1 NUMERICAL MODELLING OF STONE MASONRY. PARAMETRIC ASSESSMENT

3.1.1 Introduction

A parametric study was performed considering the calibrated material behaviour laws in D4.4, with the scope of assessing the influence of the vertical pre-compression, slenderness ratio and material resistance on the global behaviour of the different typologies of masonry panels and in particular on the maximum resistance, displacement capacity and failure modes of the masonry panels.

3.1.2 Model description

For the parametrical analysis it was used homogeneous and isotropic material using the non-linear continuum damage model, (Faria et al., 1998), described in D4.4. The finite element software Cast3M (CEA 1990) was used. The same macro-modelling strategy as in the case of shear-compression numerical analysis, D4.4, was followed with plane stress models and eight-node elements with Gauss integration scheme (QUA8).

The translational degrees of freedom (Ux, Uy) at the base of the model were constrained while the initial vertical pre-compression was applied to the nodes of the top surface of the top reinforced concrete beam; the horizontal displacement laws were applied also on the same beam, in similar way like in the real experimental procedure. The parametric study was performed considering the material behaviour laws defined based on the shear-compression tests of D4.4 and they are presented in Table 3.1.

Figure 3.1 - Finite element model of slenderness = 1.2: mesh, boundary conditions and applied loads on the numerical simulation of the shear-compression tests used for parametrical analysis.

'0

Masonry (8 node elements - QUA8)

RC Beam (8 node elements - QUA8)

Application of the horizontal displacement law

Base boundary conditions (Ux and Uy blocked)

x

y

'0

Masonry (8 node elements - QUA8)

RC Beam (8 node elements - QUA8)

Application of the horizontal displacement law

Base boundary conditions (Ux and Uy blocked)

x

y



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Table 3.1 - Parameter values from the calibration process based on the shear-compression tests (D4.4) used for para-metrical analysis.

Parameters 1:1 (UR) 1:1 (R) 2:3 (UR) 2:3 (R)

YOUN Elastic modulus [N/m2] 3.3∙10

9 5.0∙10

9 3.0∙10

9 4.7∙10

9

NU Poisson ratio [-] 0.19 0.12 0.19 0.12

RHO Density [kg/m3] 2200 2500 2200 2500

GVAL Tensile fracture energy [J] 50 50 50 50

FTUL Tensile stress [N/m2] 0.05∙10

6 0.17∙10

6 0.06∙10

6 0.15∙10

6

REDC Drop factor for peak tensile stress [-] 0 0 0 0

FC01 Elastic limit compressive stress [N/m2] -0.85∙10

6 -1.5∙10

6 -0.5∙10

6 -1.5∙10

6

RT45 Equi-biaxial Compressive Ratio [-] 1 1 1 1

FCU1 Compressive peak stress [N/m2] -2.6∙10

6 -6.5∙10

6 -3.5∙10

6 -6.6∙10

6

EXTU Ultimate limit strain [-] -0.02 -0.025 -0.02 -0.025

EXTP Reference strain for plastic parameter [-] -0.0009 -0.0008 -0.00075 -0.0017

STRP Reference stress for plastic parameter [-] -1.5∙106 -2.8∙10

6 -1.45∙10

6 -3.9∙10

6

EXT1 Fitting point 1 - Strain [-] -0.0009 -0.0008 -0.00075 -0.0017

STR1 Fitting point 1 - Stress[N/m2] -1.5∙10

6 -2.8∙10

6 -1.45∙10

6 -3.9∙10

6

EXT2 Fitting point 2 - Strain [-] -0.01 -0.016 -0.021 -0.023

STR2 Fitting point 2 - Stress [N/m2] -2.4∙10

6 -4.7∙10

6 -1.8∙10

6 -4.4∙10

6

NCRI Tensile softening criteria [-] 1 1 1 1

3.1.3 Parameters

This study aimed at assessing the influence of the vertical pre-compression level and specimen slenderness on the maximum horizontal load (Hmax), on the displacement capacity (drift for ultimate state - ψδu - and displacement for maximum load - ψHmax) and on the sequence of failure mechanisms and correspondent prevailing failure mechanisms, for each type of masonry condition.

A total of 10 different vertical pre-compression levels were considered, (10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, 90% of the maximum compressive resistance). The parametric analyses was carried out for 6 different slenderness (h/l) ratios for each type of panels; 0.5, 0.75, 1.0, 1.2, 1.5 and 2.0 for the scale 1:1 and 0.5, 0.8, 1.0, 1.25, 1.55 and 2.0 for the scale 2:3. The parametric analysis matrix is given in Table 3.2.

Table 3.2 - Parametric analysis matrix.

σ'0 (% of σmax)

Slenderness ratio (h/l)

1:1 2:3

0.5 0.75 1.0 1.2 1.5 2.0 0.5 0.8 1.0 1.25 1.55 2.0

10% • • • • • • • • • • • •

20% • • • • • • • • • • • •

30% • • • • • • • • • • • •

40% • • • • • • • • • • • •

50% • • • • • • • • • • • •

60% • • • • • • • • • • • •

70% • • • • • • • • • • • •

80% • • • • • • • • • • • •



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90% • • • • • • • • • • • •

3.1.4 Results

Maximum resistance

Figure 3.2 presents the variation of the maximum horizontal stress for the different considered pre-compression levels and slenderness ratios, for each type of panels. The red dashed line represents the slenderness of the tested panels and the blue triangles the experimental results.

(a) 1:1 UR (b) 1:1 R

(c) 2:3 UR (d) 2:3 R

Figure 3.2 - Parametric shear-compression analysis - σHmax.

When comparing the unreinforced and reinforced masonry, it is observed that, in general, for the different pre-compression levels and slenderness ratios, with the injection procedure the panels present an average increase in strength, (approximately 250% for the scale 1:1 and 210% for the scale 2:3). The value of Hmax obviously depends on the applied pre-compression level, slenderness, and thus failure mode as it is shown in Figure 3.2.

Displacement capacity

In Figure 3.3 it is presented the variation of the drift for ultimate state (ψδu) for the different considered pre-compression levels and slenderness ratio, for each type of panels, and in Figure 3.4 the same analysis is presented but now for the drift correspondent to the maximum resistance (ψHmax).

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Ho

rizo

nta

l st

ress

(N

/mm

2)

σ'0 (% σmax)

Sl = 0.50

Sl = 0.75

Sl = 1.00

Sl = 1.20

Sl = 1.50

Sl = 2.00

Experimental Data (Sl = 1.20)

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

2.00

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Ho

rizo

nta

l st

ress

(N

/mm

2)

σ'0 (% σmax)

Sl = 0.50

Sl = 0.75

Sl = 1.00

Sl = 1.20

Sl = 1.50

Sl = 2.00


0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Ho

rizo

nta

l st

ress

(N

/mm

2)

σ'0 (% σmax)

Sl = 0.50

Sl = 0.80

Sl = 1.00

Sl = 1.25

Sl = 1.55

Sl = 2.00


0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

2.00

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Ho

rizo

nta

l st

ress

(N

/mm

2)

σ'0 (% σmax)

Sl = 0.50

Sl = 0.80

Sl = 1.00

Sl = 1.25

Sl = 1.55

Sl = 2.00




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1:1 UR 1:1 R

2:3 UR 2:3 R

Figure 3.3 - Parametric shear-compression analysis - ψδu.

1:1 UR 1:1 R

2:3 UR 2:3 R

Figure 3.4 - Parametric shear-compression analysis - ψHmax.

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

ψδ

u[%

]

σ'0 (% σmax)

Sl = 0.5

Sl = 0.75

Sl = 1.0

Sl = 1.2

Sl = 1.5

Sl = 2.0

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

ψδ

u[%

]

σ'0 (% σmax)

Sl = 0.5

Sl = 0.75

Sl = 1.0

Sl = 1.2

Sl = 1.5

Sl = 2.0

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

ψδ

u[%

]

σ'0 (% σmax)

Sl = 0.5

Sl = 0.8

Sl = 1.0

Sl = 1.25

Sl = 1.55

Sl = 2.0

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

ψδ

u[%

]

σ'0 (% σmax)

Sl = 0.5

Sl = 0.8

Sl = 1.0

Sl = 1.25

Sl = 1.55

Sl = 2.0

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

ψH

ma

x[%

]

σ'0 (% σmax)

Sl = 0.5

Sl = 0.75

Sl = 1.0

Sl = 1.2

Sl = 1.5

Sl = 2.0

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

ψH

ma

x[%

]

σ'0 (% σmax)

Sl = 0.5

Sl = 0.75

Sl = 1.0

Sl = 1.2

Sl = 1.5

Sl = 2.0

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

ψH

ma

x[%

]

σ'0 (% σmax)

Sl = 0.5

Sl = 0.8

Sl = 1.0

Sl = 1.25

Sl = 1.55

Sl = 2.0

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

ψH

ma

x[%

]

σ'0 (% σmax)

Sl = 0.5

Sl = 0.8

Sl = 1.0

Sl = 1.25

Sl = 1.55

Sl = 2.0



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For both reinforced and unreinforced specimens there is a decrease of ψδu (≈20% for the reinforced and ≈25% for the unreinforced) with the increase of the pre-compression level for all the considered slenderness ratios. The highest percentual decrease happens for low levels of pre-compression (from 10 to 20%.σmax and from 20 to 30%.σmax), for these same intervals there is an increase of ψHmax, followed by a subsequent decrease.

When comparing the unreinforced and reinforced it is observed that, in general, for the different pre-compression levels and slenderness ratios, the scale 1:1 in average present an increase of approximately 110% on ψδu and ψHmax, while for the scale 2:3 the average increase in ψδu and ψHmax is of approximately 150%.

Summary of results

The behaviour in terms of drift at ultimate limit state and maximum load depend on the prevailing failure modes of the considered masonry types. Different failure modes (pure and mix) affect the behaviour of the panels depending on its slenderness, applied pre-compression levels and material resistance. The variation of the prevailing failure modes with the variation of the pre-compression level, for the different masonry and slenderness ratio can be observed from the Hmax vs. ψδu curves, that resulted from this parametric study, Figure 3.5. Also helpful to the comprehension of the behaviour is the Hmax vs. ψHmax curves, Figure 3.6.

The curves presented in Figure 3.5 and Figure 3.6 give an idea of the type of failure, maximum resistance and displacement capacity that this type of structural elements may present under unreinforced and reinforced conditions and for a wide range of slenderness ratios and pre-compression loads. However, when analysing the parametric results, it has to be taken into consideration the error between the experimental and numerical results presented in D4.4, in particular in what concerns the displacement capacity.

The dots represent the performance of each numerically analyzed panel in terms of maximum resistance Hmax and drift at ultimate limit state ψδu (Figure 3.5) or for maximum load ψHmax (Figure 3.6), for pre-compression levels ranging from 10% (point on the right of each curve) to 90% (point on the left of each curve) of σmax. Each curve corresponds to a difference slenderness ratio.

1:1 UR 1:1 R

0

100

200

300

400

500

600

700

800

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Hm

ax

(kN

)

ψδu [%]

Sl = 0.5

Sl = 0.75

Sl = 1.0

Sl = 1.2

Sl = 1.5

Sl = 2.0

0

200

400

600

800

1000

1200

1400

1600

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Hm

ax

(kN

)

ψδu [%]

Sl = 0.5

Sl = 0.75

Sl = 1.0

Sl = 1.2

Sl = 1.5

Sl = 2.0



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2:3 UR 2:3 R

Figure 3.5 - Parametric shear-compression analysis - Panels Hmax vs. ψδu curves.

1:1 UR 1:1 R

2:3 UR 2:3 R

Figure 3.6 - Parametric shear-compression analysis - Hmax vs. ψHmax.

Panels with low slenderness ratio (sl = 0.5) present a more fragile behaviour characterized by lower displacements for ultimate state, this because failure is in general governed by shear. However, for this low slenderness ratio when high pre-compression levels are applied failure occurs due to crushing, on the other hand, with the decrease of the pre-load shear behaviour prevails.

For all analysed types of masonry, as the slenderness ratio increases the behaviour becomes more ductile (high displacements for ultimate state). For the analysis performed with a high slenderness ratio (sl = 2.0), failure was in general governed by flexural behaviour. However, for high pre-compression values, crushing failure prevails and for low of pre-compression values, particularly in reinforced panels, rocking mechanism prevails.

Furthermore, from Figure 3.5 and Figure 3.6 it is noticeable the transition of the dominant failure modes with the variation of the pre-compression load, within the same slenderness ratio, in

0

100

200

300

400

500

600

700

800

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Hm

ax

(kN

)

ψδu [%]

Sl = 0.5

Sl = 0.8

Sl = 1.0

Sl = 1.25

Sl = 1.55

Sl = 2.0

0

200

400

600

800

1000

1200

1400

1600

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Hm

ax

(kN

)

ψδu [%]

Sl = 0.5

Sl = 0.8

Sl = 1.0

Sl = 1.25

Sl = 1.55

Sl = 2.0

0

100

200

300

400

500

600

700

800

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2

Hm

ax

(kN

)

ψHmax [%]

Sl = 0.5

Sl = 0.75

Sl = 1.0

Sl = 1.2

Sl = 1.5

Sl = 2.0

0

200

400

600

800

1000

1200

1400

1600

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2

Hm

ax

(kN

)

ψHmax [%]

Sl = 0.5

Sl = 0.75

Sl = 1.0

Sl = 1.2

Sl = 1.5

Sl = 2.0

0

100

200

300

400

500

600

700

800

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2

Hm

ax

(kN

)

ψHmax [%]

Sl = 0.5

Sl = 0.8

Sl = 1.0

Sl = 1.25

Sl = 1.55

Sl = 2.0

0

200

400

600

800

1000

1200

1400

1600

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2

Hm

ax

(kN

)

ψHmax [%]

Sl = 0.5

Sl = 0.8

Sl = 1.0

Sl = 1.25

Sl = 1.55

Sl = 2.0



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particular, when the curves bend sharply (≈30 to 50%.σmax). Before reaching these transition points, depending on the pre-compression level, slenderness ratio and material strength, failure can be influenced by mix behaviour such as the mix flexural/shear behaviour illustrated in damage pattern figures in D4.4 and in Figure 3.7 a, or the mix shear/crushing behaviour illustrated in Figure 3.7b.

40%.σmax 70%.σmax

0

d+ d

+ d

- 1

(a) (b)

Figure 3.7 - Damage pattern at δu for 2:3 reinforced panels with slenderness equal to 1.0. (a) 40%.σmax. (b) 70%.σmax.

3.1.4.1 Validation of the numerical approach and of the existing analytical formulations

In this section, are validated the failure fields determined through the (i) analytical expressions presented in equations Eq. 3.1 to Eq. 3.3 and the ones resulting from the (ii) numerical parametric analyses shown in the previous section. It is analysed if these are capable of correctly represent the shear-compression tests experimental results and observed failure modes. The analytical formulations, presented below, were normally applied for the strength prediction of masonry typology made of bricks. Further calibration was performed for three-leaf stone masonry, such as the formulation for the prediction of the shear mechanism which was proposed by Turnsek and Cacovic (1971) and then refined by Turnsek and Sheppard (1980).

t

t

Hfb

f 0

max

'1

Shear failure mechanism Eq. 3.1

l

h.6.

'1 max

max

0

Compression failure mechanism Eq. 3.2

l

h.2.

'' max

2

max

0

max

0

Flexural failure mechanism Eq. 3.3

where σ’0 is the average compression stress due to the vertical load and b is the shear distribution factor, that can be defined as following:



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5.15.1

11

5.1

1

l

hif

l

hif

bl

hb

Eq. 3.4

where h and l are the height and the length of the masonry wall, as proposed in (Benedetti and Tomaževic, 1984) and as also found in recent codes (PCM, 2003); τHmax is the nominal average shear stress at maximum resistance (horizontal load divided by the horizontal cross sectional area), as proposed in (Bernardini, et al., 1982). From the representation of the shear-compression experimental results, Table 3.3, over (i) the analytical curves adjusted base on the experimentally obtained mechanical parameters and (ii) the results of the parametric analysis, Figure 3.8 - Figure 3.11, it is possible to conclude that, in general, a good agreement was found between the experimental data and both approaches, particularly in the case of the injected panels, in both scales, mainly due to the monolithic behaviour of the three-leaf walls avoiding the out-of-plane failure and the separation of outer layers, characteristic of multi-leaf stone masonries. However, the injection cannot completely prevent the buckling of external leaves that occurs close to the failure, after the in-plane mechanisms occur, and causing the collapse of the specimen, although it is delayed.

Table 3.3 - Experimental horizontal stress values from the in-plane shear-compression experimental campaign.

Specimens Vertical Load [N/mm2] Condition and scale Experimental Horizontal Stress [N/mm

2]

C1 1.00 UR (1:1) 0.15

C2 1.25 0.15

C3 0.75 0.23

C4 0.5 0.21

C5 1.00 R(1:1) 0.34

C6 1.50 0.42

C7 1.25 0.43

C8 2.00 0.52

E1 0.50 UR(2:3) 0.13

E2 1.00 0.20

E3 0.75 0.25

E4 1.25 0.28

E5 1.25 R(2:3) 0.33

E6 1.00 0.39

E7 1.50 0.39

E8 2.00 0.44



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(a) Sl = 0.5 (b) Sl = 0.75

(c) Sl = 1.0 (d) Sl = 1.2

(e) Sl = 1.5 (f) Sl = 2.0

Figure 3.8 - Comparison between the analytical formulations, the numerical parametrical study and the experimental values for 1:1 UR panels.

(a) Sl = 0.5 (b) Sl = 0.75

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00

Ho

rizo

nta

l st

ress

[N

/mm

2]

σ'0 [N/mm2]

Flexural Failure

Shear Failure

Crushing Failure

Numerical Analysis (Sl = 0.5)

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00

Ho

rizo

nta

l st

ress

[N

/mm

2]

σ'0 [N/mm2]

Flexural Failure

Shear Failure

Crushing Failure


0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00

Ho

riz

on

tal

stre

ss [

N/m

m2]

σ'0 [N/mm2]

Flexural Failure

Shear Failure

Crushing Failure


0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00

Ho

rizo

nta

l st

ress

[N

/mm

2]

σ'0 [N/mm2]

Flexural Failure

Shear Failure

Crushing Failure


Experimental Data

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00

Ho

rizo

nta

l st

ress

[N

/mm

2]

σ'0 [N/mm2]

Flexural Failure

Shear Failure

Crushing Failure


0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00

Ho

rizo

nta

l st

ress

[N

/mm

2]

σ'0 [N/mm2]

Flexural Failure

Shear Failure

Crushing Failure


0.00

0.25

0.50

0.75

1.00

1.25

1.50

1.75

2.00

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00

Ho

rizo

nta

l st

ress

[N

/mm

2]

σ'0 [N/mm2]

Flexural Failure

Shear Failure

Crushing Failure


0.00

0.25

0.50

0.75

1.00

1.25

1.50

1.75

2.00

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00

Ho

rizo

nta

l st

ress

[N

/mm

2]

σ'0 [N/mm2]

Flexural Failure

Shear Failure

Crushing Failure

Numerical analysis (Sl = 0.75)



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(c) Sl = 1.0 (d) Sl = 1.2

(e) Sl = 1.5 (f) Sl = 2.0

Figure 3.9 - Comparison between the analytical formulations, the numerical parametrical study and the experimental values for 1:1 R panels.

(a) Sl = 0.5 (b) Sl = 0.8

(c) Sl = 1.0 (d) Sl = 1.25

0.00

0.25

0.50

0.75

1.00

1.25

1.50

1.75

2.00

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00

Ho

rizo

nta

l st

ress

[N

/mm

2]

σ'0 [N/mm2]

Flexural Failure

Shear Failure

Crushing Failure


0.00

0.25

0.50

0.75

1.00

1.25

1.50

1.75

2.00

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00

Ho

rizo

nta

l st

ress

[N

/mm

2]

σ'0 [N/mm2]

Flexural Failure

Shear Failure

Crushing Failure


Experimental Data

0.00

0.25

0.50

0.75

1.00

1.25

1.50

1.75

2.00

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00

Ho

rizo

nta

l st

ress

[N

/mm

2]

σ'0 [N/mm2]

Flexural Failure

Shear Failure

Crushing Failure


0.00

0.25

0.50

0.75

1.00

1.25

1.50

1.75

2.00

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00

Ho

rizo

nta

l st

ress

[N

/mm

2]

σ'0 [N/mm2]

Flexural Failure

Shear Failure

Crushing Failure


0.00

0.20

0.40

0.60

0.80

1.00

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00

Ho

rizo

nta

l st

ress

[N

/mm

2]

σ'0 [N/mm2]

Flexural Failure

Shear Failure

Crushing Failure


0.00

0.20

0.40

0.60

0.80

1.00

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00

Ho

rizo

nta

l st

ress

[N

/mm

2]

σ'0 [N/mm2]

Flexural Failure

Shear Failure

Crushing Failure


0.00

0.20

0.40

0.60

0.80

1.00

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00

Ho

rizo

nta

l st

ress

[N

/mm

2]

σ'0 [N/mm2]

Flexural Failure

Shear Failure

Crushing Failure


0.00

0.20

0.40

0.60

0.80

1.00

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00

Ho

rizo

nta

l st

ress

[N

/mm

2]

σ'0 [N/mm2]

Flexural Failure

Shear Failure

Crushing Failure


Experimental Data



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(e) Sl = 1.55 (f) Sl = 2.0

Figure 3.10 - Comparison between the analytical formulations, the numerical parametrical study and the experimental values for 2:3 UR panels.

(a) Sl = 0.5 (b) Sl = 0.8

(c) Sl = 1.0 (d) Sl = 1.25

0.00

0.20

0.40

0.60

0.80

1.00

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00

Ho

rizo

nta

l st

ress

[N

/mm

2]

σ'0 [N/mm2]

Flexural Failure

Shear Failure

Crushing Failure


0.00

0.20

0.40

0.60

0.80

1.00

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00

Ho

rizo

nta

l st

ress

[N

/mm

2]

σ'0 [N/mm2]

Flexural Failure

Shear Failure

Crushing Failure


0.00

0.25

0.50

0.75

1.00

1.25

1.50

1.75

2.00

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00

Ho

rizo

nta

l st

ress

[N

/mm

2]

σ'0 [N/mm2]

Flexural Failure

Shear Failure

Crushing Failure


0.00

0.25

0.50

0.75

1.00

1.25

1.50

1.75

2.00

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00

Ho

rizo

nta

l st

ress

[N

/mm

2]

σ'0 [N/mm2]

Flexural Failure

Shear Failure

Crushing Failure


0.00

0.25

0.50

0.75

1.00

1.25

1.50

1.75

2.00

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00

Ho

rizo

nta

l st

ress

[N

/mm

2]

σ'0 [N/mm2]

Flexural Failure

Shear Failure

Crushing Failure


0.00

0.25

0.50

0.75

1.00

1.25

1.50

1.75

2.00

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00

Ho

rizo

nta

l st

ress

[N

/mm

2]

σ'0 [N/mm2]

Flexural Failure

Shear Failure

Crushing Failure


Experimental Data



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(e) Sl = 1.55 (f) Sl = 2.0

Figure 3.11 - Comparison between the analytical formulations, the numerical parametrical study and the experimental values for 2:3 R panels.

Both the analytical formulations and the behaviour model applied to the numerical simulations consider a homogeneous isotropic material, explaining the general good agreement between these two approaches, in particular for the reinforced panels in both scales and slenderness (h/l) ratios higher than 1. If the lower limitation for the definition of shear distribution factor (b≥0.5) in function of the slenderness, is not considered for the analytical model (Turnsek and Cacovic, 1971), a very good agreement is found between the numerical and analytical approaches also for slenderness values lower than 1, Figure 3.12. Further experimental tests on panels with slenderness lower than 1 are necessary in order to proper define the limitations of both numerical and analytical approaches.

(b = 0.5) (b = 1.0)

Figure 3.12 - Comparison between the analytical formulations, the numerical parametric analysis and the experimental values for the 2:3 unreinforced panels (slenderness = 0.5).

3.1.5 Conclusions

Parametric study showed how a panel’s performance under combined shear and compression depend on pre-compression loads, slenderness and strength of the material. It was also shown the type of failure, maximum resistance and displacement capacity that this type of structural elements may present under unreinforced and reinforced conditions and for a wide range of slenderness ratios and pre-compression loads. However, when analysing the parametric results it has to be taken into consideration the error between the experimental and numerical results obtained on the calibration of the model based on the shear-compression tests, in particular in what concerns the displacement capacity.

Both the analytical formulations and the behaviour model applied on the numerical parametric simulations consider a homogeneous isotropic material, explaining the general good agreement

0.00

0.25

0.50

0.75

1.00

1.25

1.50

1.75

2.00

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00

Ho

rizo

nta

l st

ress

[N

/mm

2]

σ'0 [N/mm2]

Flexural Failure

Shear Failure

Crushing Failure


0.00

0.25

0.50

0.75

1.00

1.25

1.50

1.75

2.00

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00

Ho

rizo

nta

l st

ress

[N

/mm

2]

σ'0 [N/mm2]

Flexural Failure

Shear Failure

Crushing Failure


0.00

0.20

0.40

0.60

0.80

1.00

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00

Ho

rizo

nta

l st

ress

[N

/mm

2]

σ'0 [N/mm2]

Flexural Failure

Shear Failure

Toe Crushing Failure


0.00

0.20

0.40

0.60

0.80

1.00

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00

Ho

rizo

nta

l st

ress

[N

/mm

2]

σ'0 [N/mm2]

Flexural Failure

Shear Failure

Toe Crushing Failure




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between these two approaches. Furthermore, both approaches allowed a good representation of the shear-compression tests experimental results and observed failure modes.

3.2 ANALYTICAL PREDICTION OF COMPRESSIVE STRENGTH FOR THREE-LEAF MASONRY SPECIMENS

3.2.1 Introduction

In this chapter the estimation, using analytical models, of the compressive strength of three-leaf stone masonry, before and after consolidation with grout injections, is presented. For this, the experimental results from previous campaigns are used in addition to those of the experimental campaign carried out within the scope of the present project (D4.3).

The effect that the reduced scale has on the compressive strength of three-leaf panels is also taken into account in the new formulations.

3.2.2 Existing models for prediction of the compressive strength of three-leaf ma-sonry before grouting

According to the analytical model proposed by Egermann (1993), the compressive strength of masonry before grouting is calculated as the weighted sum of the compressive strength of the external and internal leaves, Eq. 3.5. In this, the simplifying hypotheses of (i) elastic behaviour of the layers, (ii) plane connection among them and (iii) transverse strains negligible were considered.

0inf,infinf

,0, .... fV

Vf

V

Vf

w

kextext

w

extwc

Eq. 3.5

In Eq. 3.5, Vext/Vw and Vinf/Vw are the volumetric ratios of external layers and internal core to the entire wall, fwc,0 is the compressive strength of the unstrengthened wall, fext,k is the strength of the external layers, finf,0 is the compressive strength of the infill and θext and θinf are empirical corrective factors for taking into account the influence of the mutual interaction between the external layers and the internal core in the global behaviour of the wall.

Vintzileou and Tassios (1995) derived formula for the estimation of the compressive strength of the non-injected masonry, based on Egermann (1993), assuming that the compressive strength of the original wall (before the intervention) is mainly due to the external layers, so that the internal core is negligible. Therefore, the following Eq. 3.6 is derived:

cext

w

extwc f

V

Vf ,0, .

Eq. 3.6

Tassios in (2004) was able to predict in a rather satisfactory way the compressive strengths measured by Valluzzi (2000), Toumbakari (2002) and Vintzileou and Tassios (1995). Taking into account the available experimental data, the use of a partial safety factor γrd equal to 1.5 was proposed to calculate the compressive strength values adequate for design.

3.2.3 Existing models for prediction of the compressive strength of three-leaf ma-sonry after grouting

In Vintzileou and Tassios (1995) a simple formula was developed, based on the assumption that (i) grouting does not affect significantly the mechanical properties of the external leaves, where their initial compressive strength is only re-instated, and that (ii) grouting substantialy improves the mechanical properties of the infill. Therefore, the strength enhancement of the infill was taken proportional to the square root of the compressive strength of the grout, as an indicator of its



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tensile strength. The contribution of the strengthened infill material to the compressive strength of the masonry is proportional to the ratio Vinf/Vw (Vinf denotes to the volume of infill in the total volume Vw of the wall). Thus, the following formula was derived:

0,

,inf0,, ..25.11.

wc

cgr

w

wcswcf

f

V

Vff

Eq. 3.7

In (Vintzileou, 2007) this formula was applied to the available experimental results and it was found that it overestimated the compressive strength of grouted masonry. However, if a γrd value equal to 1.35 is applied, the formula yields safe values for the design of grouted three-leaf masonry.

Valluzzi et al. (2004) recalibrated Eq. 3.7, on the basis of the results collectable from the literature and systematic testing of cylinders made of filling material grouted with hydraulic lime based grouts, thus obtaining Eq. 3.9. This new formulation considered an empirical formula based on the results by Valluzzi et al. (2004) and Vintzileou and Tassios (1995) for the prediction of the compressive strength of the grouted infill material, as follows:

18.1

,,inf, .31.0 cgrscyls fff

Eq. 3.8

0,

inf,inf0,, .1.

wc

s

w

wcswcf

f

V

Vff

Eq. 3.9

Eq. 3.7 showed a very good agreement when applied to walls injected with low-strength grouts (about fgr ≤ 4-5 MPa), whereas in the case of high-strength grouts (about fgr ≥ 14-15 MPa), it leads to rougher estimations than the (Eq. 3.9). Eq. 3.9 seems to overestimate the compressive strength of grouted three-leaf masonry in most cases and, therefore a γrd value equal to 1.80 should be applied to the predicted values, (Vintzileou, 2007).

Vintzileou (2007) then correlated the compressive strength of the grouted infill material and the tensile strength of the grout by evaluating the available results from testing cylinders made of filling material before and after grouting with either ternary or hydraulic lime based grout. Thus the following expression, Eq. 3.10, was derived:

tgrs ff ,inf, .50.060.1

Eq. 3.10

where fgr,t denotes the tensile strength of the grout due to bending. However, taking into account the fact that for the time being there is no established method for testing the tensile strength of grouts and mortars and that it is a property sensitive to numerous parameters, it seems more appropriate to base the estimation of the compressive strength of the grouted masonry on the compressive strength of the grout.

3.2.4 Experimental data used for the new calibration of the prediction model

Based on the above described approaches an attempt is made to apply to calibrate the existing formulae for non-injected and injected masonry panels on the available experimental results including the current results obtained by grouting using natural hydraulic lime (NHL).

The data available and suitable for the evaluation of the existing models and the re-calibration of a new one are very scarce for hydraulic-lime based grouts. The data used for this research is given in Table 3.4, referring to the following materials: cement grouts, (Miltiadou, 1990 and Vintzileou and Tassios, 1995), ternary grouts and cement grouts, (Toumbakari, 2002), hydraulic lime products, (Valluzzi, 2000, Valluzzi et al., 2004, Mazzon, 2010 and current experiment), ternary



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grouts (cement, lime, pozzolan) and natural hydraulic lime, (Kalagri et al., 2010 and Vintzileou and Miltiadou-Fezans, 2008). It’s important to mention that in the experiments performed by Vintzileou and Miltiadou-Fezans (2008), Mazzon (2010) and part of the current experiment, the walls tested were built in reduced scale 2:3, allowing us to obtain more information about the effect of the reduced scale.

Table 3.4 - Mechanical characteristics of grouts used to inject three-leaf masonry specimens and compressive resistance of the cylinders simulating the injected inner core.

Experimental campaign Grout designation Mechanical properties Cylinders

fgr,c(1)

[N/mm2] fgr,t

[2] [N/mm

2] fcyl,s [N/mm

2]

(Miltiadou, 1990 and Vintzileou and Tassios, 1995)

Mix A (F1) - Cement Grout 30.0 2.50 13.4 (1:1)

Mix B (F3) - Cement Grout 13.0 1.40 9.50 (1:1)

(Toumbakari, 2002) 13b0 - Ternary grout 7.3 1.7 -

13b10 - Ternary grout 9.0 1.1 -

Cb0 - Cement grout 19.5 1.5 -

(Valluzzi, 2000 and Valluzzi et al., 2004) FEN X-B 3.23 0.35 0.81 (1:1)

FEN X-A+F0.5 5.10 - 2.07 (1:1)

FEN X-A+F0.5 3.35 - 1.71 (1:1)

FEN X-A +R0.55 3.21 - 1.43 (1:1)

FEN X-A +FR0.55 3.65 - 1.38 (1:1)

(Mazzon, 2010) NHL FENIX-B 12.80 3.80 2.12 (2:3)

Experimental Campaign Grout Designation Mechanical Properties Cylinders

fgr,c[1]

[N/mm2] fgr,t

[2] [N/mm

2] fcyl,s [N/mm

2]

(Kalagri et al., 2010 and Vintzileou and Miltiadou-Fezans, 2008)

G1 - Ternary grout 10.6 3.13 3.24 (2:3)

G2 (NHL St Astier) + Superplasticizer

6.36 3.87 2.79 (2:3)

G3 (NHL St Astier) 6.00 2.70 3.27 (2:3)

G4 (NHL Chaux Blanche) 6.72 1.05 3.29 (2:3)

G5 (NHL Calx Romana) 2.90 1.08 2.74 (2:3)

G6 (NHL Albaria Calce Albazzana)

2.49 0.65 2.28 (2:3)

G7 NHL Unilit B Fluid 0 2.53 0.98 2.01 (2:3)

Current experiment NHL FENIX-B 12.48 2.75 3.40 (1:1)

NHL FENIX-B 3.52 (2:3) [1]

Compressive strength of grout at the age of testing masonry specimens.

[2] Flexural strength of grout at the age of testing masonry specimens.

Table 3.5 - Properties of the panels used for the prediction of fwc,s and model calibration.

Panel Dimensions (lxtxh) [cm]

fgr,c [N/mm2] fcyl,s

[N/mm2]

Vinf/Vw

[-] fwc,0

[N/mm2]

fwc,s

[N/mm2]

fwc,s/fwc,0 [-]

Ewc,0

[N/mm2]

Ewc,s

[N/mm2]

(Vintzileou and Tassios, 1995)

1[4]

60x40x120 30 13.4 0.35 2.10 3.10 1.48 7000 6250

2 60x40x120 - - 0.35 1.30 - - 2706 -

3[4]

60x40x120 30 13.4 0.35 2.40 4.30 1.80 5000 5971



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4 60x40x120 30 13.4 0.35 1.60 - - 4442 -

5 60x40x120 30 13.4 0.35 1.70 4.20 2.47 5670 7778

6 60x40x120 13 9.50 0.35 1.35 4.05 3.00 5625 8438

7 60x40x120 30 13.4 0.35 - 3.70 - - 15431

8 60x40x120 13 9.50 0.35 - 3.00 - - 3333

(Toumbakari, 2002)

BC1 60x40x120 7.3 - 0.35 - 5.04 - - 2238.2

BC2 60x40x120 9.0 - 0.35 2.41 3.15 1.31 730 1564.9

BC3 60x40x120 19.5 - 0.35 2.09 2.91 1.39 1018 1404.8

BC4 60x40x120 7.3 - 0.35 2.18 3.00 1.38 1098 1040.4

BC5 60x40x120 7.3 - 0.35 2.28 3.86 1.69 1145 1170.2

SC1[4]

60x40x120 9.0 - 0.35 2.02 3.25 1.61 720 1622.2

SC2 60x40x120 19.5 - 0.35 2.09 3.36 1.61 1139 1558.6

SC3 60x40x120 7.3 - 0.35 2.65 3.51 1.32 1375 1187.6

SC4 60x40x120 7.3 - 0.35 2.71 3.29 1.21 1443 1014.5

(Valluzzi et al., 2004)

5I1 80x50x150 5.10 2.07 0.28 1.45 2.49 1.72 2210 2347

6I1 80x50x150 5.10 2.07 0.28 1.95 2.49 1.28 2210 2347

13I1 80x50x150 5.10 2.07 0.28 - - - 2210 2347

1I2 80x50x150 3.23 0.81 0.28 1.97 2.57 1.3 1506 2336

8I2 80x50x150 3.23 0.81 0.28 1.91 1.82 0.95 1506 2336

16I2 80x50x150 3.23 0.81 0.28 - - - 1506 2336

(Vintzileou and Miltiadou-Fezans, 2008)

1 100x45x120 4.50 2.79 0.27 1.82 3.00 1.65 1000 1200

2 100x45x120 8.16 3.24 0.27 1.74 3.75 2.16 1440 1550

3 100x45x120 4.50 2.79 0.27 2.26 3.73 1.65 1500 1300

[Mazzon 2010]1]

S - 12.8 2.12 2.33 - 7.72 - - 4379

R - - 6.87 - - 4001

Current experiment

B1 100x50x120 12.48 3.40 0.28 2.91 4.28[3]

1.47 2415 5203[3]

B2 100x50x120 0.28 2.47 1.73 2294

B3 100x50x120 0.28 2.10 2.29 2885

B4 100x50x120 0.28 2.49[2]

3.72 1.49 2531[2]

4725

B5 100x50x120 0.28 4.88 1.95 6781

B6 100x50x120 0.28 4.23 1.69 4103

D1 80x100x33 3.52 0.27 2.19 4.88[3]

2.23 1726 5125[3]

D2 80x100x33 0.27 2.80 1.74 2813

D3 80x100x33 0.27 2.23 2.19 2636

D4 80x100x33 0.27 2.41[2]

5.40 2.24 2392[2]

5030

D5 80x100x33 0.27 3.99 1.66 5708

D6 80x100x33 0.27 5.24 2.17 4637 [1]

This experiment is not used for the prediction of the fwc,s, only for the model calibration.

[2] Average values for scale 1:1 and 2:3, of non-injected panels tested in compression.

[3] Average values for scale 1:1 and 2:3, of injected panels tested in compression.



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[4] With transversal elements.

3.2.5 Calibration of the analytical model for the prediction of compressive strength of non-injected masonry walls

For the estimation of the compressive strength of the non-injected masonry panels in both scales, the derived formula by Vintzileou and Tassios (1995), Eq. 3.6, is used. Table 3.6 presents the experimental compressive strength (fwc,0) results obtained from the current experiments in panels of wall B (1:1 scale) and D (2:3 scale) tested in simple-compression, including the average compressive strength (fex,c) obtained from the four single-leaf panels (wall F).

The prediction of the resistance values with equation Eq. 3.6 gives 2.34 N/mm2 for the full scale panels and 2.76N/mm2 for the reduced scale panels. The comparison of the experimental values with the predicted ones using Eq. 3.6 proved to predict rather satisfactorily the compressive strength of the full scale panels with a slight average underestimation and yielding rather conservative values. On the other hand, predicting the compressive strength of the reduced scale panels, the formula allowed an overestimation with an error of maximum 26% for panel D1 and in average of 14.5%. A general overestimation of the reduced scale panels compressive strength was observed. For this reason, a correction factor of 0.79 was applied to the prediction formula only for the 2:3 scale panels, Eq. 3.11.

cext

w

exwc f

V

Vf ,3:20, ..79.0

Eq. 3.11

Table 3.6 - Experimental and predicted compressive strength results for the non-injected three-leaf masonry panels.

Panel Vext/Vw

[-] fext,c [N/mm

2] fwc,0 [N/mm

2] fwc,0 av

[N/mm2]

(Eq. 3.6) fwc,s pred

[N/mm2]

Error [%]

Error av [%]

Correction factor

B1 0.360 6.50 2.91 2.49 2.34 -19.6 -6.4 -

B2 2.47 -5.3

B3 2.10 11.4

D1 0.424 6.50[1]

2.19 2.41 2.76 26.0 14.5 0.79

D2 2.80 -1.4

D3 2.23 23.8 [1]

Assumed as equal to the results of the full scale panels, however experimental tests should be performed on single-leaf panels in scale 2:3.

3.2.6 Calibration of the analytical model for the prediction of compressive strength of injected masonry walls

In order to assess the reliability of the proposed models for the prediction of the compressive strength of the three-leaf masonry walls grouted with natural hydraulic lime and in different geometrical scales, the formulas developed by Vintzileou and Tassios (1995) - (Eq. 3.7), Valluzzi et al. (2004) - (Eq. 3.8; Eq. 3.9) and Vintzileou (2007) - (Eq. 3.9 and Eq. 3.10) are used. Table 3.7 and Figure 3.13 show a comparison of the obtained results, predicted with the analytical formulas and experimentally obtained from the compressive tests carried out on the full and reduced scale panels. For both scale panels, Eq. 3.8 and Eq. 3.9 developed by Valluzzi et al. (2004) lead to a better agreement (also underestimating the walls strength) with the experimental results, compared to Eq. 3.7 and (Eq. 3.10, Eq. 3.9) which gave lower values.

Table 3.7 - Comparison between experimental results and predicted, using the proposed equations.

Panels fwc,s fwc,s av (Eq. 3.7) (Eq. 3.8 and Eq. 3.9) (Eq. 3.9 and Eq. 3.10)



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[N/mm2] [N/mm

2] [Vintzileou and Tassios, 1995] [Valluzzi et al., 2004] [Vintzileou, 2007]

B4 3.72 4.28 3.73 4.20 3.32

B5 4.88

B6 4.23

D4 5.40 4.88 3.60 4.06 3.21

D5 3.99

D6 5.24

(a) (b)

Figure 3.13 - Comparison between experimental and predicted compressive strength of injected panels in full and re-duced scale. (a) For each panel; (b) Average results.

Furthermore, it was performed the re-calibration of the empirical formula proposed by Valluzzi et al. (2004) - Eq. 3.8, for the prediction of the compressive strength of the grouted infill material. This was done considering the available data from past experiments for the compressive resistance of the grout and that of the cylinders made of infill material (1:1 and 2:3) and injected in each case with the corresponding grout used to inject the wall specimens, Table 3.4, including the results of the current experimental campaign grouted with natural hydraulic lime, which added more data correspondent to low strength grouts.

The experiments of Vintzileou and Miltiadou-Fezans (2008), Mazzon (2010) and of the current experiment reduced scale samples were also included in the input data. From this calibration resulted three formulae for calculating the resistance of the wall’s core based on the compressive strength of the grout mixture, Figure 3.14. One formula considering all the available data, Eq. 3.12, another one considering all the walls in scale 1:1, Eq. 3.13, and another one considering only the walls in scale 2:3, Eq. 3.14.

B4 B5 B6 D4 D5 D6

(1:1) Reduced scale (2:3)

fwc,s pred. (Eq. 7.3) 3.73 3.73 3.73 3.60 3.60 3.60

fwc,s pred. (Eq. 7.4, Eq. 7.5) 4.20 4.20 4.20 4.06 4.06 4.06

fwc,s pred. (Eq. 7.5, Eq. 7.6) 3.32 3.32 3.32 3.21 3.21 3.21

fwc,s experimental 3.72 4.88 4.23 5.4 3.99 5.24

0.00

1.00

2.00

3.00

4.00

5.00

6.00

f wc,s

[N/m

m2]

(1:1) (2:3)

fwc,s pred. (Eq. 7.3) 3.73 3.60

fwc,s pred. (Eq. 7.4, Eq. 7.5) 4.20 4.06

fwc,s pred. (Eq. 7.5, Eq. 7.6) 3.32 3.21

fwc,s experimental 4.28 4.88

0.00

1.00

2.00

3.00

4.00

5.00

6.00

f wc,s

[N/m

m2]



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Figure 3.14 - Relation between the compressive resistance of the cylinders and the grout resistance.

All specimens: 702.0

,inf, .757.0 cgrs ff

Eq. 3.12

Full scale specimens: 091.1

,inf, .345.0 cgrs ff

Eq. 3.13

Reduced scale specimens: 154.0

,inf, .10.2 cgrs ff

Eq. 3.14

The two last relations were then applied to equation Eq. 3.9 in order to determine the compressive strength of injected three-leaf masonry walls in scale 1:1 - Eq. 3.15 and 2:3 - Eq. 3.16.

Full scale specimens: 091.1

,inf

1:10,1:1, ..345.0 cgr

w

wcswc fV

Vff

Eq. 3.15

Reduced scale specimens: 154.0

,inf

3:20,3:2, ..10.2 cgr

w

wcswc fV

Vff

Eq. 3.16

The new calibrated equations were then applied to the experimental campaigns of Vintzileou and Tassios (1995), Valluzzi et al. (2004), Vintzileou and Miltiadou-Fezans (2008), Mazzon, (2010) and the current experiment. The obtained results were compared with the results obtained with the previously existent formulations of (Vintzileou and Tassios (1995) - (Eq. 3.7), Valluzzi et al. (2004) - (Eq. 3.8; Eq. 3.9) and Vintzileou (2007) - (Eq. 3.9 and Eq. 3.10), Table 3.8.

Table 3.8 - Comparison between experimental and predicted values of compressive strength.

Panel fgr,c / fgr,t [N/mm

2]

Vinf/Vw

[-] fwc,0

[N/mm2]

fwc,s [N/mm2] fwc,s pred

(Eq. 3.7)

[N/mm2]

fwc,s pred

(Eq. 3.8 and Eq. 3.9) [N/mm

2]

fwc,s pred

(Eq. 3.9 and Eq. 3.10) [N/mm

2]

fwc,s pred

(Eq. 3.15) [N/mm

2]

fwc,s pred

(Eq. 3.16) [N/mm

2]

(Vintzileou and Tassios, 1995)

1[1]

30/2.5 0.35 2.10 3.10 4.50 8.10 3.1 7.0 -

3[1]

30/2.5 2.40 4.30 4.80 8.40 3.4 7.3 -

5 30/2.5 1.70 4.20 4.10 7.70 2.7 6.6 -

y = 0.7571x0.7018

R² = 0.5934

y = 0.3451x1.0912

R² = 0.888

y = 2.0997x0.1537

R² = 0.2348

0

2

4

6

8

10

12

14

16

0 10 20 30 40 50

f cy

l,c

fgr,c

y = 0.7503x0.7099

R² = 0.6104

y = 0.3451x1.0912

R² = 0.888

y = 2.0438x0.1749

R² = 0.3448

0

2

4

6

8

10

12

14

16

0 20 40 60

f cy

l,c

fgr,c

[Miltiadou, 1990 and Vintzileou and Tassios, 1995]

[Valluzzi, 2000 and Valluzzi et al., 2004]

[Kalagri et al., 2010 and Vintzileou and Miltiadou-Fezans, 2008]

[Mazzon, 2010]

Current experiment

All data

(1:1)

(2:3)



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6 13/1.4 1.35 4.05 2.93 3.59 2.2 3.3 -

(Toumbakari, 2002)

BC2 9.0/1.1 0.35 2.41 3.15 3.72 3.86 3.2 3.74 -

BC3 19.5/4.5 2.09 2.91 4.02 5.70 3.4 5.18 -

BC4 7.3/1.7 2.18 3.00 3.36 3.31 3.0 3.24 -

BC5 7.3/1.7 2.28 3.86 3.46 3.41 3.1 3.34 -

SC1[4]

9.0/1.1 2.02 3.25 3.33 3.47 2.8 3.35 -

SC2 19.5/4.5 2.09 3.36 4.02 5.70 3.4 5.18 -

SC3 7.3/1.7 2.65 3.51 3.83 3.78 3.5 3.71 -

SC4 7.3/1.7 2.71 3.29 3.89 3.84 3.6 3.77 -

(Valluzzi et al., 2004)

5I1 5.10/0.35 0.28 1.45 2.49 2.24 2.04 1.9 2.0 -

6I1 5.10/0.35 1.95 2.49 2.74 2.54 2.4 2.5 -

1I2 3.23/0.35 1.97 2.57 2.59 2.31 2.5 2.3 -

8I2 3.23/0.35 1.91 1.82 2.54 2.25 2.4 2.3 -

(Vintzileou and Miltiadou-Fezans, 2008)

1 4.50/2.5 0.27 1.82 3.00 2.54 2.31 2.6 - 2.5

2 8.16/2.3 1.74 3.75 2.70 2.74 2.5 - 2.5

3 4.50/2.5 2.26 3.73 2.98 2.75 3.0 - 3.0

Current experiment

B4 12.5/2.75 0.28 2.49[2]

3.72 3.73 4.20 3.3 4.01 -

B5 4.88 3.73 4.20 3.3 -

B6 4.23 3.73 4.20 3.3 -

D4 0.27 2.41[2]

5.40 3.60 4.06 3.2 - 3.2

D5 3.99 3.60 4.06 3.2 -

D6 5.24 3.60 4.06 3.2 - [1]

With transversal elements.

[2] Average values for scale 1:1 and 2:3, of non-injected panels tested in compression.

(a)

1 3 5 6BC

2

BC

3

BC

4

BC

5

SC

1

SC

2

SC

3

SC

45I1 6I1 1I2 8I2 1 2 3 B4 B5 B6 D4 D5 D6

[Vintzileou and

Tassios, 1995][Toumbakari, 2002]

[Valluzzi et al.,

2004]

[Vintzileou

and

Miltiadou-

Fezans,

2008]

Current experiment

Eq. 7.3 45 12 -2 -28 18 38 12 -10 3 20 9 18 -10 10 1 40 -15 -28 -20 0 -24 -12 -33 -10 -31

Eq. 7.4 and Eq. 7.5 161 95 83 -11 23 96 10 -12 7 70 8 17 -18 2 -10 24 -23 -27 -26 13 -14 -1 -25 2 -23

Eq. 7.5 and Eq. 7.6 0 -21 -36 -47 0 18 1 -19 -15 2 0 8 -22 -2 -4 32 -14 -34 -19 -11 -32 -21 -40 -19 -39

Eq. 7.11 (1:1) 127 71 58 -18 19 78 8 -14 3 54 6 14 -19 1 -10 24 8 -18 -5

Eq. 7.12 (2:3) -16 -33 -20 -40 -19 -38

-100.0

-80.0

-60.0

-40.0

-20.0

0.0

20.0

40.0

60.0

80.0

100.0

Err

or

[%]



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(b) (c)

Figure 3.15 - Comparison between predicted and measured compressive strength of the injected walls. (a) Error (%). (b) Deviation for specimens in scale 1:1. (c) Deviation for specimens in scale 2:3.

The error analysis presented in Figure 3.15 allowed concluding that all the analytical formulations when applied to the results available on the current experimental campaign can predict the ultimate compressive load, making an error smaller than 32% for the 1:1 scale specimens and 40% for the 2:3 scale specimens. In what concerns the scale 1:1 specimens the equation Eq. 3.7 has the best prediction with an average over-estimation of 7%. For the scale 2:3 the analytical formulation of Valluzzi et al. (2004) - (Eq. 3.8; Eq. 3.9) presents the best prediction with an average underestimation of 20%. To better understand the capacity of each analytical formulation to predict the compressive resistance of walls injected with the different types of grouts it is presented next the comparison between predicted and measured compressive strength of the injected walls divided by types of grouts, (i) NHL grouts, Figure 3.16a, (ii) ternary grouts, Figure 3.16b and (iii) cement grouts, Figure 3.16c. For the NHL grouts the formulation of Valluzzi et al. (2004) - (Eq. 3.8; Eq. 3.9) is able to give the best prediction for both scale 1:1 (-3% underestimation) and scale 2:3 (-19% under-estimation), Figure 3.16a. For the ternary grouts the formula developed by Vintzileou and Tassios (1995) - (Eq. 3.7) presents the best prediction for both scale 1:1 (3% overestimation) and 2:3 (-27% underestimation), Figure 3.16b.

1:1 2:3 (a)

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

0.0 2.0 4.0 6.0 8.0

f wc,

s P

RE

D

fwc,s EXP

Eq. 7.3

Eq. 7.4 and Eq. 7.5

Eq. 7.5 and Eq. 7.6

Eq. 7.11

Linear (Eq. 7.3)

Linear (Eq. 7.4 and Eq. 7.5)


Linear (Eq. 7.11)

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

0.0 2.0 4.0 6.0 8.0

f wc,s

PR

ED

fwc,s EXP

Eq. 7.3

Eq. 7.4 and Eq. 7.5

Eq. 7.5 and Eq. 7.6

Eq. 7.12

Linear (Eq. 7.3)



Linear (Eq. 7.12)

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

0.0 2.0 4.0 6.0 8.0

f wc,s

PR

ED

fwc,s EXP

Eq. 7.3

Eq. 7.4 and Eq. 7.5

Eq. 7.5 and Eq. 7.6

Eq. 7.11

Linear (Eq. 7.3)



Linear (Eq. 7.11)

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

0.0 2.0 4.0 6.0 8.0

f wc,s

PR

ED

fwc,s EXP

Eq. 7.3

Eq. 7.4 and Eq. 7.5

Eq. 7.5 and Eq. 7.6

Eq. 7.12

Linear (Eq. 7.3)



Linear (Eq. 7.12)



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1:1 2:3 (b)

(c)

Figure 3.16 - Comparison between predicted and measured compressive strength of the injected walls. (a) NHL grout. (b) Ternary grout. (c) Scale 1:1 specimens injected with cement grout.

Finally, as can be seen in Figure 3.16c, in what concerns the cement grouts the analytical formulation of Vintzileou (2007) - (Eq. 3.9 and Eq. 3.10) is the one which best can predict the maximum compressive resistance in scale 1:1 specimens, with an under-estimation of -7%. There is no data available for scaled specimens.Valluzzi et al. (2004) related the error percentage to the strength of the grout and concluded that a simplified model based on the evaluation of simple geometrical and mechanical characteristics, can be appropriate for ratios fgr/fwc,0 not higher than approximately 4. Considering all the available data up to now, the present analysis showed that the simplified models use is limited to ratios between the strength of the grout and of the walls lower than 5 for both scales, Figure 3.17.

(a) (b)

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

0.0 2.0 4.0 6.0 8.0

f wc,s

PR

ED

fwc,s EXP

Eq. 7.3

Eq. 7.4 and Eq. 7.5

Eq. 7.5 and Eq. 7.6

Eq. 7.11

Linear (Eq. 7.3)



Linear (Eq. 7.11)

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

0.0 2.0 4.0 6.0 8.0

f wc,s

PR

ED

fwc,s EXP

Eq. 7.3

Eq. 7.4 and Eq. 7.5

Eq. 7.5 and Eq. 7.6

Eq. 7.12

Linear (Eq. 7.3)



Linear (Eq. 7.12)

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

0.0 2.0 4.0 6.0 8.0

f wc,s

PR

ED

fwc,s EXP

Eq. 7.3

Eq. 7.4 and Eq. 7.5

Eq. 7.5 and Eq. 7.6

Eq. 7.11

Linear (Eq. 7.3)



Linear (Eq. 7.11)

-100.0

-50.0

0.0

50.0

100.0

150.0

200.0

0.0 5.0 10.0 15.0 20.0

Erro

r [%

]

fgr/fwc,0

Eq. 7.3

Eq. 7.4 and Eq. 7.5

Eq. 7.5 and Eq. 7.6

Eq. 7.11

-100.0

-50.0

0.0

50.0

100.0

150.0

200.0

0.0 5.0 10.0 15.0 20.0

Erro

r [%

]

fgr/fwc,0

Eq. 7.3

Eq. 7.4 and Eq. 7.5

Eq. 7.5 and Eq. 7.6

Eq. 7.12



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Figure 3.17 - Error vs. fgr,c/fwc,0. (a) 1:1. (b) 2:3.

From previous analysis the influence of the strength of the grout on the grouted infill and the whole wall strengths showed that the use of high-strength grouts has a very low influence on the increase of the ultimate load capacity of the wall, whereas, the compressive strength of the cylinders increases more significantly, (Valluzzi et al., 2004). Continuing the analysis with all the available results, the trend of the cylinders strength and of the increment of the wall’s strength vs. the strength of the grout is shown in Figure 3.18, where it can be seen that both increase, when high strength grouts are used, but the increase is much lower for the walls when compared to the cylinders. When the fgr/fwc,0 ratio exceeds a value of about 5, the strength of the cylinder is not passed into the wall.

Figure 3.18 - Normalized cylinders strength and walls strength increase vs. normalized compressive grout strength.

The percentage of infill strength (f*inf,s) that actually contributes to the panels strength up to failure

can be estimated through an analysis based on the strength values (fwc,0 and fwc,s) obtained from the tested panels, Eq. 3.17, as suggested by (Valluzzi et al., 2004).

V

V

fff

wcswc

s

inf

0,,*

inf,

Eq. 3.17

According to (Valluzzi et al., 2004) the injection effectiveness can be estimated considering the

ratio between the strength effectively implemented by the wall and the whole infill strength (η =

f*inf/fcyl). The correlation between the real effectiveness of the infill strengthening (average values)

and the grout strength is shown in the graph of Figure 3.19, that is an enriched version of the one

presented in (Valluzzi et al., 2004). From the graph it is possible to observe the decreasing trend of

η with increase of the grout the strength in relation to the initial capacity of the walls. Taking into

account the latest available results, it is clear that for fgr/fwc,0 higher than 5 the utilization of the η is

reduced (η<1). Therefore, the ratio η is not generally definable as 0.5 (as in Eq. 3.7), but such

value is reached only for fgr/fwc,0 ratios higher then 12.5, corresponding to high-strength grouts in

particular to the cement grouts. As the panels cannot implement a percentage of the infill strength

exceeding the infill strength itself, the presence of values of η>l in Figure 3.19 can be due to the

interaction between the external and the internal layers.

-2.0

0.0

2.0

4.0

6.0

8.0

10.0

0.0 5.0 10.0 15.0 20.0

fgr/fwc,0

(fwc,s-fwc,0)/fwc,0

fcyl/fwc,0

fwall

fcyl



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Figure 3.19 - Estimation of the efficiency of the infill strengthening for different grout strengths.

As shown in Table 3.9, the cylinders injected by admixtures more compatible with the existing

materials (NHL based) have mechanical characteristics lower than the original walls, in comparison

with the cement based ones. It is possible to conclude that when low-strength grouts are used, a

more uniform distribution of the vertical stresses on the loaded sections is achieved, with a

consequent general improvement of the behaviour of the wall. This because when the inner layer

as approximately the same resistance and stiffness as the external leaves (as in the case of being

strengthened by NHL grouts) together with the transverse connection improvement caused by the

injection itself, a triaxial state of stresses acts in the inner layer, so the ultimate load capacity of the

wall is increased. On the other hand, when high-strength grouts are used, the stiffer internal core

carries a higher portion of the normal stresses than the external layers, and a uniform distribution

of loads is not achieved. In such case, a brittle collapse of the system has to be expected, due to

the crushing of the infill and the consequent thrust to the external layers.

Table 3.9 - Average values of the mechanical characteristics of grouts and cylinders on the original walls ones.

Type of grout fgr/fwc,0

[-] fcyl/fwc,0

[-] Ecyl/Ewc,0

[-]

Cement grouts 14.8 6.6 3.5

NHL grouts 3.3 1.0 1.2

Ternary grouts 9.6 7.0 -

3.2.7 Conclusive Remarks

In this Chapter it is provided a data enriched analytical formulae based on the previous proposals

by Egermann (1993), Vintzileou and Tassios (1995), Valluzzi et al. (2004) and Vintzileou (2007) for

the prediction of the compressive strength of three-leaf masonry panels (full and reduced scale)

both before and after the consolidation. The calibration of the analytical model was done based on

the existing experimental results enriched with the experimental results of the previous chapter.

Results were obtained concerning (i) the prediction of the compressive strength with the use of

hydraulic lime-based grouts, (ii) the effectiveness of the infill strengthening and (iii) the influence of

the geometrical scaled specimens.

For the prediction of the compressive strength of non-injected masonry, Vintzileou and Tassios

(1995) formula Eq. 3.6 proved to predict rather satisfactorily the resistance of the full scale (1:1)

panels of the current experimental campaign, under-estimating the maximum resistance of the

0.0

1.0

2.0

3.0

4.0

5.0

0.0 5.0 10.0 15.0 20.0

η

fgr/fwc,0



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unstrengthened panels. However, a general overestimation of the reduced scale (2:3) panels

was observed. For this reason, a correction factor of 0.79 was applied to the prediction formula,

producing a more conservative model for the 2:3 scale walls.

For the prediction of the compressive strength of the injected walls in both scales, the three

formulas developed by Vintzileou & Tassios (1995) (Eq. 3.7), Valluzzi et al. (2004) (Eq. 3.8 and

Eq. 3.9) and Vintzileou (2011) (Eq. 3.9 and Eq. 3.10) were used for the comparison with the

current experimental results. The best agreement (also underestimating the walls strength) with

the experimental results was found by using Valluzzi et al. (2004) equation. Based on these re-

sults, an attempt was made to re-calibrate the empirical formula proposed by Valluzzi et al., Eq.

3.8, for the prediction of the compressive strength of the grouted infill material, based on the

results obtained from testing cylinders made of filling material and adding more data corre-

spondent to low-strength grouts and reduced scale specimens from previous experiments,

(Vintzileou and Miltiadou-Fezans 2008 and Mazzon 2010).

For the NHL grouts the formulation of Valluzzi et al. (2004) - (Eq. 3.8; Eq. 3.9) is able to give

the best prediction for both scale 1:1 and 2:3. For the ternary grouts the formula developed by

Vintzileou and Tassios (1995) - (Eq. 3.7) presents the best prediction for both scales 1:1 and

2:3. Finally, the formulation of Vintzileou (2007) showed the best agreement (also underesti-

mating the wall strength) when applied to walls injected with high-strength grouts.

The new formulations presented a good capacity to predict the resistance of specimens in

scale 1:1 injected with NHL and ternary grouts. In terms of specimens strengthened with ce-

ment grouts it gives better results than the formulation of Valluzzi et al. (2004).

In all formulations the reduced scale specimens exhibited the highest error percentage due to

the influence of the geometrical characteristics of the layers on the behaviour of the whole wall.

Considering all the available data up to now, the present work showed that the use of the sim-

plified formulations with a low error is limited to ratios between the strength of the grout and of

the walls (fgr/fwc,0) lower than 5 for both panel scales (1:1 and 2:3). In comparison to the previ-

ous work of (Valluzzi, 2004) the exploitation range of the update formula increased from a

fgr/fwc,0 of 4 to 5.

In grouts with a fgr/fwc,0 ratio higher than 5, the strength of the grout is not passed into the wall,

as so the use of high-strength grouts, such as the cement ones, has a very low influence on

the increase of the ultimate load capacity of the walls.

This study also showed that the hydraulic lime based grouts can sum the advantages of being

the most compatible (mechanical, physical) with the complete exploitation of its mechanical

strength on the walls.



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4 WORK PROGRAM AND RESULTS OF UMINHO

4.1 HALF-TIMBERED WALLS PARAMETRIC ASSESSMENT

4.1.1 Introduction

A parametric study has been planned and is currently being carried out considering the preliminary calibrated material properties defined in D4.4. The parameters that are being studied are the vertical pre-compression level, the bolts diameter and the thickness of the steel plates adopted in the strengthening techniques (this task is currently being developed) and different boundary conditions for the constraining of the top of the wall (this task still has to be approached) in order to study their influence on the global behaviour of half-timbered walls in terms of ultimate capacity and ductility, as well as failure modes of the walls.

4.1.2 Parametric assessment

The numerical model used is the same one adopted in the calibration of the model described in D4.4. The model of the wall was created using DIANA (Diana 2009). The model was created using 20-nodes brick elements (CHX60) to simulate timber and masonry and plane quadrilateral, 8+8-nodes interface elements (CQ48I) to simulate the timber-timber contact and the timber-masonry contact (see Figure 4.1). Different vertical pre-compression load level were applied to the three posts of the wall, namely 25kN on each post and 50kN on each post, as done during the experimental campaign. Different strengthening techniques were used to retrofit the walls, among which bolts were used in the overlapped connections. In order to simulate the bolts, a first approach was done altering the normal stiffness of the interface elements interested by the presence of the bolts, but results showed that for higher values of normal stiffness, the results did not change, so it was decided to model the bolts using curved 3-nodes beam elements (CL18B) in order to connect the vertical post to the beam.

(a) (b)

Figure 4.1 - Model geometry: a) general view of the mesh: in blue the timber elements, in red the infill b) example of the bolt modelling that will be adopted in the following models.



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For the strengthening with the steel plates, additional membrane elements will be inserted simulating the plates, in order to connect the bolts in the connections.

The materials used are those described in D4.4, i.e. the Hill anisotropic constitutive law for timber and the Mohr-Coulomb friction model for the interface elements. The infill was assumed linear elastic.

A constant vertical pre-compression load was applied on each post and a horizontal displacement was applied to the top beam of the wall, to simulate a monotonic test.

The parameters that will be analysed, as mentioned before, will be the vertical pre-compression level, the diameter and thickness of the reinforcement as well as the boundary conditions. So far, only the first issue has been carried out, considering that additional pre-compression levels will be considered. For now, only the vertical load level considered in the experimental campaign were analysed, i.e. 25kN/post and 50kN/post.

4.1.3 Results

Considering the results obtained so far, it can be pointed out how an increase in the vertical pre-compression levels lead to a higher load capacity for the wall, with an increase in the maximum load of 13% (Figure 4.2a), whilst in the experimental campaign the load gain was of 40%, so this issue should be studied better.

The overall behaviour of the wall is similar to what observed experimentally, with a predominant flexural behaviour of the wall, as evident from the uplift of the posts (Figure 4.2b). The model subjected to a higher vertical load level has a lower vertical uplift (30%less).

Comparing the stresses distribution for the two vertical load levels (Figure 4.3), the distributions are similar. The model with the higher vertical load is interested by higher stresses, but the concentration of stresses in the central node is not present as strongly as what experienced in the experimental campaign.

(a) (b)

Figure 4.2 - Results: a) monotonic curves for different vertical load levels; b) vertical uplift of lateral post for different ver-tical load levels.



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(a) (b)

Figure 4.3 - Stresses distribution: a) lower vertical load; b) higher vertical load.

4.1.4 Conclusions

FE analyses were performed on half-timbered walls to study the influence of different parameters on their overall behaviour. Even though the analyses are not complete, it is possible to conclude that the vertical pre-compression load level influences the response of the wall, increasing its load capacity and slightly its initial stiffness, as well as changing the failure mode of the wall, which, at a higher vertical load level, is more subjected to shear failures. Further studies are ongoing to study the parameters influencing the strengthening techniques adopted.

4.2 RAMMED EARTH PARAMETRIC ASSESSMENT

4.2.1 Introduction

A parametric analysis followed the calibration of the FEM models simulating the tests on rammed earth wallets carried by BAM-ZRS. The wallets built with unstabilized earth were tested under compression and under diagonal compression with load applied monotonically. In average, the compressive strength (fc) obtained is of about 3.74 N/mm2 and the shear strength (fs) of about 0.7 N/mm2.

Two approaches were followed regarding the simulation of the tests as described in derivable D4.4: macro- and micro-modelling. The micro-modelling approach consisted of a multi-layered model with Mohr-Coulomb failure criteria at the interfaces between compaction layers, which aimed to simulate possible failure through them. The models calibrated according to both approaches were included in the parametric analysis.

The constitutive law adopted in both calibrated models is the Total Strain Crack Model with fixed crack orientation, detailed in DIANA (2009), whereas the stress-strain relations were assumed to be multi-linear in compression, exponential in tension and linear in shear. The calibrated parameters and strain-stress relation in compression are given in Table 4.1 and Figure 4.4, respectively. Both compression and diagonal-compression models have acceptable agreement with the envelopes of the experimental results, see Figure 4.5.

Table 4.4.1 - Calibrated parameters.

Parameter Calibrated value Note

E0 (N/mm2) 4140 -



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0.27 -

ft (N/mm2) 0.374 fc /10

Gf1 (N/mm) 0.1081 0.29xft

0.01 -

D11 (N/mm3) 414 E0 /10

D22 (N/mm3) 163 (E0/(2x(1+ ))/10

c (N/mm2) 0.561 1.5x ft

tan( ) 0.754 º

tan( ) 0 º

Gapval (N/mm2) 0.249 Min(2/3xft; c/tan( ))

Figure 4.4 - Multi-linear relation used for the behaviour under compression.

(a) (b)

Figure 4.5 - Calibrated models: (a) compression and (b) diagonal compression.

Regarding the dimensions of the models, it was adopted the average dimension of the specimens, i.e., (0.499 x 0.505 x 0.117) m for width, height and thickness, respectively. The thickness adopted for the layers was of about 0.084 m. Plane stress state was assumed in the models, and it was used quadrilateral elements of 8 nodes and zero thickness interface elements of 6 nodes in the



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case o the micro-model. Only, the vertical displacements at the top and bottom of the models simulating the compression tests were constrained, resulting in a zero confinement condition. The load was applied by means of imposed vertical displacement applied to the constrained nodes at the top of the model. The modelling of the diagonal compression tests was carried out in a similar way, whereas the width of the supports was considered to be of about 0.125 m. The self-weight of the material was not considered. The displacements of the nodes corresponding to the measurement points of the LVDT’s instrumentating the specimens were controlled and used to compute average strains. The parametric analysis was carried out for both model approaches and deals only with the shear behaviour of the wallets. There were assessed geometrical and parameters of constitutive laws adopted for the material, which included: layer thickness, compression behaviour scaling, tensile strength, fracture energy and the properties of the interfaces. The analysis was carried out by fixing all parameters and changing only that at study. The aim was at investigating the effect of the variability of these important features on the shear behaviour of rammed earth.

4.2.2 Layer thickness

The layer thickness found in rammed earth constructions is in general variable and ranges from 0.03 m to 0.10 m. The impact of this geometrical property on the shear behaviour of rammed earth was assessed using the micro-model. Several layer thicknesses ranging from 0.025 m to 0.125 m were considered and the results in terms of fs variation are shown in Figure 4.6. As can be seen fs varies slightly with the layer thickness, showing that, in this particular case, this is a parameter with few importance.

Figure 4.6 - Influence of the layers thickness on the shear strength.

4.2.3 Compressive strength

The variability of earthen materials regarding to their mechanical properties is a well known issue. Moreover, the water content of these materials has a great impact in their strength, which, for example, can be halved by the presence of high moisture. Thus the influence of the compressive strength on the shear strength was assessed by applying a scaling factor to the adopted multi-linear compressive stress-strain relation, in order to change fc, while maintaining the original strains. Several factors were tested in both micro- and macro-model and included: 0.6, 0.8, 0.9, 1.1, 1.2 and 1.4. The normalized shear strength is presented as function of the scaling factor in Figure 4.7, whereas the shear strength decreases substantially with decreasing compressive strength (represented by the scaling factor) and vice-versa.



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Figure 4.7 - Influence of the compressive strength on the shear strength.

4.2.4 Tensile strength

The tensile strength of earthen materials is usually unknown and its experimental assessment is very difficult due to particular features of these materials (such as very low strength and disaggregation of unstabilized materials). Several scaling factors (0.5, 0.75, 1.25 and 1.5) were applied to the tensile strength obtained from the calibration and then both micro- and macro-model were computed. The results are presented in Figure 4.8, where as the tensile strength decreases there is a decrease of fs. However when the tensile strength increases (relatively to the calibration value) fs keeps almost constant. This is probably related with the relation between ft and Gf1 (fracture energy in tension), which becomes short and introduces convergence problems that stop the analysis without achieving post-peak behaviour. Eventually the factor in the relation given in Table 4.4.1 should be increased.

Figure 4.8 - Influence of the tensile strength on the shear strength.

4.2.5 Fracture energy in tension

The fracture energy in tension of earthen materials is another parameter of difficult experimental determination by similar reasons to those of the tensile strength. This parameter was tested in both macro- and micro-models by applying the following scaling factors: 0.2, 0.5, 2 and 5. The results are presented in Figure 4.9, where it can be seen that fs increases with the fracture energy. This is consequence of a larger distribution of the damage in the model as the material has larger capacity to retain higher stresses levels in the post-peak behaviour. Changing the fracture energy resulted in the adjustment of the relation between fracture energy and ft, which is again shown to have important role in the shear behaviour, and thus, this is a relation that should be evaluated in further experimental investigation.



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Figure 4.9 - Influence of the fracture energy in tension on the shear strength.

4.2.6 Interface parameters

The influence of the parameters that mainly control the behaviour of the interfaces between layers was also tested, namely the cohesion and the friction angle. The cohesion was tested by applying the following scaling factors: 0.5, 0.75, 1.5 and 2. On the other the analysis of the friction angle was carried out by testing several values, namely: 20º, 30º, 40º and 50º.

The results are presented in Figure 4.10, where it can be seen that for values of the parameters larger than those obtained from the calibration, there is almost no variation of the shear strength. The shear strength decreases, however for lower values. The cohesion seems to have the most important role within the tested ranges of values.

(a) (b)

Figure 4.10 - Influence of the (a) cohesion and (b) friction angle of the interfaces on the shear strength.

4.2.7 Conclusions

A simple parametric analysis was carried out in order to test several parameters from the adopted models, which can be further used in simulations of higher complexity. The thickness of the compaction layers was one of the tested parameters, but the analysis revealed that it has little importance for this case. However, the decrease of the parameters that control the interfaces resulted in an important reduction of the shear strength.

The compressive strength of the rammed was shown to have very important effect on the shear behaviour, which reveals that other important parameters affecting the compressive strength (such as moisture content) are also important for the shear strength. The tensile strength and respective fracture energy are other parameters that were shown to clearly affect the shear behaviour.

Thus, the correct and precise evaluation of the tested parameters should be focus of further experimental investigation.



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5 WORK PROGRAM AND RESULTS OF UPC

5.1 INTRODUCTION

5.1.1 Overview

In the context of the NIKER Project Workpackage 4.3, a number of experiments on masonry walls have been performed in ITAM in Prague. Three distinct wall groups were tested: adobe units with clay mortar, dry brick units with cement mortar and solid brick units with cement mortar. These walls were subjected to a vertical pre-stress, followed by cyclic in-plane loads of increasing magnitude until failure was observed. Both plain and reinforced walls, strengthened using two different methods, were tested.

A numerical simulation of the results obtained by these experiments has been carried out at UPC in Barcelona. The model utilized was calibrated by comparison with the experimental results as described in deliverable D4.4. The model has been then utilized for a detailed parametric study. The experimental campaign is still underway, and, as more experimental results are made available, it will be possible for the analytical efforts to similarly expand in order to incorporate the newer data.


In the micro modelling approach adopted in the present analyses, the constituent materials comprising the masonry composite (units and mortar) are modeled separately and their individual properties are incorporated into the model, thus reducing the necessary degree of homogenization in an effort to more accurately model the composite behaviour of masonry derived by the individual properties of the constituent materials.

In the present analyses, the simplified micro modelling approach was adopted, in which “unit” elements are expanded to include half the actual width of the joints and the joints themselves are modeled using zero-thickness interface elements.

For the elements comprising the units, a multi-directional fixed crack material model was employed (smeared cracking), with linear stress cut-off, brittle cracking and constant shear retention. This material model can capture the effect of cracking of the units in a biaxial stress state. Crushing is also possible to be modeled in the units, but, since the joints have a lower compressive strength, it is a failure mode that is mostly concentrated at the interface elements and not the units. However, by limiting the compressive strength of the units, it is possible to also limit the tensile strength due to biaxial stress state phenomena.

For the interface elements, a combined cracking-shearing-crushing material model was employed. It can model all of the above modes of failure in interfaces under normal and shear stress. Shearing failure is simulated using a Mohr-Coulomb criterion, cracking failure by a stress cut-off criterion and crushing by a cap criterion, all of which are combined into a composite failure criterion in two dimensions.

Figure 5.1 - Layout of elements in the micro model.



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The micro modelling method employed prioritizes failure at the interfaces; therefore the parameters involved in the description of the interface material model are the most crucial.

Each complete unit was modeled using 4x2 quadrilaterals, amounting to a mesh of 17x32 elements across the entire surface of the wall, not including the interface elements.

In addition to the stiff upper beam used for the macro models, the lowest unit course was connected to a similar stiff beam, serving as the foundation of the model, through interface elements.

5.1.3 Modelling of strengthening techniques

The steel wires were simulated with simple 2 node truss elements with zero stiffness in compression and an elastic/perfectly plastic behaviour in tension. No bond was considered between the masonry and the wires and the anchoring on the wall was considered rigid.

The geo-nets were taken into account as an embedded reinforcement grid, which increases the stiffness of the units. The properties of this grid were derived from the relevant data made available in the experimental report.

Figure 5.2 - Macro model mesh, micro model mesh and micro model mesh with wire strengthening.

5.1.4 Initial material properties

The determination of the material properties to be used for the analyses was achieved by calibration of several parameters, mostly based on the results for the adobe brick masonry. In the following table, the material properties used in the micro models to simulate the experiments are summarized.

Table 5.1 - Micro model material properties.

Eu

[N/mm2]

fcu [N/mm

2]

ftu

[N/mm2]

ν [-]

fcj

[N/mm2]

ftj

[N/mm2]

C0 [N/mm

2]

Gfc

[N/mm] Gft

[N/mm] kn [N/mm

3]

ks [N/mm

3]

ABW 1375 5.5 0.275 0.35 5.5 0.1 0.14 8.8 0.01 48 18

DBW 2500 10 0.1 0.25 4 0.1 0.14 6.4 0.01 235 112

SBW 6750 27 2.7 0.30 10 0.1 0.14 16 0.01 145 65

Eu = Brick Young’s modulus



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fcu = Brick compressive strength

ftu = Brick tensile strength

ν = Brick Poisson’s coefficient

fcj = Interface compressive strength

ftj= Interface tensile strength

C0 = Cohesion at brick mortar interface

Gfc = Fracture energy in compression at brick mortar interface

Gft = Fracture energy in tension at brick mortar interface

kn = Normal elastic stiffness constant at interface

ks = Tangent elastic stiffness constant at interface

5.2 MODEL CALIBRATION AND INITIAL RESULTS

The results for the micro models in terms of horizontal load capacity, already presented in deliverable D4.4, are as shown in Tab. 5.2. The agreement between experimental and numerical results is considered acceptable and therefore the model is used to carry out the parametric study.

Table 5.2 - Micro model results.

Experimental [kN] Numerical [kN] Difference [%]

ABW 67 71.4 +6.5

ABW/GEONET 80 89.6 +12.0

ABW/WIRES 110 106 -3.6

DBW 80 78.6 -1.75

DBW/GEONET 87.8

DBW/WIRES 99.4

SBW 200 209 +4.5

SBW/GEONET 211

SBW/WIRES 226

5.3 PARAMETRIC INVESTIGATION

5.3.1 Overview. Object of parametrization and variables considered.

In order to obtain a wider perspective on the response of un-strengthened and strengthened masonry walls under in plane loading a parametric investigation was conducted on several parameters. The study was intended to provide additional insight into how the parameters used in the analysis influenced on the capacity. In addition, the applicability of the numerical tool and criteria adopted in the analysis, as particularly the methods used for modelling the strengthening, were also investigated. The following sections present the results of the parametric study. As a general criterion, a specific parameter is altered while the rest maintain their initial values as described in Tab. 5.1. The parameters considered for variation are the boundary conditions, the masonry compressive strength, the vertical pre-compression and the amount of reinforcement.

Most of the parametric studies have been done on a model representing the dry brick masonry walls tested in the laboratory. However, the studies concerning the amount of reinforcement have been carried out on a model representing the adobe walls, which are the only ones with experimental results on strengthened specimens at the time of writing.

5.3.2 Boundary conditions - amount of vertical restraint



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Firstly, the response of the walls is analyzed for different boundary conditions at the top border, ranging from free rotation to perfectly fixed rotation. Intermediate cases are modeled by means of a set of springs with varying elastic constants.

Considering a cantilever configuration, in which the top beam is free to move vertically, the ultimate capacity is mainly governed by the applied vertical load rather than the elastic and strength properties of the materials. The results from this set of analyses closely approximate those of simple hand calculations, where the ultimate horizontal load is determined by moment equilibrium around the compressed foot assuming full plastic rotation. Clearly, in this configuration, where failure is not due to excessive diagonal cracking, the strengthening techniques are of very limited effectiveness.

Applying elastic springs to an otherwise unrestrained top beam in the vertical direction causes an increase in the maximum vertical displacement and the capacity of the walls compared to a cantilever wall. Generally, an increase in stiffness will result in an increase in capacity and enhance post peak response. Additionally, it will affect the stiffness of the response by limiting the propagation of cracking.

It is possible to increase the capacity and post peak response of a wall by prescribing an elastic/perfectly plastic behaviour to the springs. By limiting the maximum load they are capable of resisting, it is possible to suppress the formation of large horizontal cracks in the uppermost joints and/or units.

An interesting observation was made during the investigation of the effect of spring stiffness to the capacity. For very low spring stiffness the effect of the reinforcement is practically zero, since the failure is governed by crushing in the joints. Gradually increasing the spring stiffness makes the effect of the reinforcement more pronounced with the net reinforcement being more effective in the mid range of the spring stiffness values applied. However, the wire reinforcement becomes more effective for the higher values of spring stiffness, which is consistent with the experimental and numerical results obtained for the configuration assuming a vertically fixed beam.

As a final note, it should be mentioned that the assumption of an elastic or elastoplastic restraint at the top beam is clearly intuitive, and can only be the subject of parametric investigation, since it is not practically possible to measure the necessary parameters to accurately simulate such configurations in experimental setups or actual structures. But, given the above observation for the effectiveness of the reinforcement techniques for different degrees of vertical restraint, it is clear that boundary conditions are important in determining the optimal strengthening solution between the two types discussed.

In the following figure the results for various degrees of vertical constraint are presented for the case of the dry brick masonry. The value of zero spring stiffness corresponds to the cantilever configuration. The values of the horizontal axis correspond to the equivalent distributed stiffness of the discrete springs along the length of the loading beam per unit length. The attainment of a horizontal branch in several of the curves included in the figure occurs when the failure is governed by the masonry compression strength.



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Figure 5.3 - Influence of top boundary conditions, represented by a set of springs with a given stiffness, on the capacity of walls.

5.3.3 Masonry compressive strength

As expected, an increase in the compressive strength of the interfaces results in an increase of the capacity of the wall. Additionally, such an increase also increases the effectiveness of the strengthening measures simulated in the analyses, as cracking of the units and the joints becomes the predominant failure mechanism.

It is interesting to note that bellow a certain value for the compressive strength for the interfaces, the strengthening measures become practically ineffective. Additionally, for higher values of compressive strength the rate of increase of capacity of the unreinforced wall becomes lower whereas the rates for the reinforced cases are affected to a smaller degree.

The following graph illustrates results obtained by altering the compressive strength of the joints for the case of the dry brick wall. The values used range from 50% the value initially used up to the compressive strength of the units themselves.

Figure 5.4 - Influence of the masonry compressive strength on the capacity of walls.

20

30

40

50

60

70

80

90

100

110

0 50 100 150 200 250 300 350 400

Cap

acit

y [K

N]

Stiffness [N/mm/mm]

Plain Wall

Net Reinforcement

Wire Reinforcement

0

20

40

60

80

100

120

140

160

180

200

0 2 4 6 8 10 12

Cap

acit

y [K

N]

fcj [MPa]

Plain Wall

Net Reinforcement

Wire Reinforcement



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5.3.4 Vertical pre-stress

The effect of a variation in the applied vertical pre-stress has been investigated in terms of capacity and post-peak response. The self weight was not altered.

An increase in the initial vertical load leads to an increase in the capacity and a reduction in the post peak deformation of the wall. The latter is especially true in cases with low interface compressive strength. Maximum horizontal capacity is achieved for a vertical load corresponding to roughly 30% of the compressive strength of the joints. As the vertical pre-stress surpasses that value the horizontal capacity begins to decrease as crushing at the joints occurs for lower values of horizontal displacement. This renders the net reinforcement practically ineffective for greater pre-stress levels. However, the wire reinforcement appears to remain effective for a wider range of vertical loads, including values past which the net reinforcement practically loses all effectiveness.

The following figure illustrates the effect of vertical pre-stress on the horizontal load capacity of a dry brick wall.

Figure 5.5 - Influence of vertical precompression on the capacity of walls.

In addition to the above investigation, similar sets of analyses were carried out on models with increased joint compressive strength for the case with the steel wire reinforcement. The numerical results from this and the above sets were normalized by dividing them with the product of the plan cross sectional area of the wall and the compressive strength of the interfaces and subsequently combined in the same graph. The normalized curves exhibit substantial coincidence.

50

60

70

80

90

100

110

120

130

0 200 400 600 800

Cap

acit

y [K

N]

Vertical Load [KN]

Plain Wall

Net Reinforcement

Wire Reinforcement



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Figure 5.6 - Influence of vertical precompression (normalized) on the capacity of wall, with fcj = compressive strength, Aw = wall section, H = horizontal force.

5.3.5 Amount of reinforcement steel

The effect of the amount of reinforcement steel has been investigated on a wall model representing the experimental adobe ones. The positioning or the number of the steel wires is not altered. Variations in the reinforcement area were taken into account by changing the diameter of the reinforcement wires in the numerical model.

As shown in the graph below, increasing the amount of reinforcement past a certain small value does not significantly increase the capacity. This is especially noticeable for lower values of compressive strength of the joints. There is, however, a noted increase in the post-peak behaviour of the walls for higher reinforcement amounts.

The results obtained for different compressive strengths have been combined into normalized graphs with the aim of providing design charts for confined walls.

Figure 5.7 - Influence of reinforcement amount on the capacity of walls.

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

H/(

fcj*

Aw

)

V/(fcj *Aw)

fcj = 4MPa

fcj = 5MPa

fcj = 6MPa

70

80

90

100

110

120

130

140

150

160

170

0 20 40 60 80 100

Cap

acit

y [K

N]

Reinforcement Area [mm2]

fcj = 4MPa

fcj = 5MPa

fcj = 6MPa

fcj = 7MPa



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The reinforcement area has been normalized into a reinforcement ratio by dividing it by the plan cross sectional area of the wall. The capacity has been normalized by dividing it with the product of the joint compressive strength and the plan cross sectional area of the wall. The resulting curves are shown in the following figures.

Figure 5.8 - Influence of reinforcement amount on the capacity of walls (normalized), with As = reinforcement section, Aw = wall section, H = horizontal force and fc = compressive strength of masonry.

5.3.6 Young’s modulus of units

An investigation of the ratio between the Young’s modulus and the compressive strength of the units was conducted on the dry brick wall assembly by considering a constant value for the compressive strength and modifying the Young’s modulus. The range of values considered covers the ratios assumed in a number of masonry design codes as well as the ratios normally encountered in practice.

The horizontal load capacity clearly demonstrates a tendency to increase for an increase in the Young’s modulus for the range of values considered.

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0.11

0 0.1 0.2 0.3 0.4 0.5

H/(fcj*Aw)

fys*As/(fcj*Aw)

fcj = 4MPa

fcj = 5MPa

fcj = 6MPa

fcj = 7MPa

0.05

0.06

0.07

0.08

0.09

0.1

0.11

0 0.02 0.04 0.06 0.08 0.1

H/(fcj*Aw)

fys*As/(fcj*Aw)

fcj = 4MPa

fcj = 5MPa

fcj = 6MPa

fcj = 7MPa



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Figure 5.9 - Influence of reinforcement amount on the capacity of walls for varying Eu.

5.4 CONCLUSIONS

A parametric investigation has been carried out with the purpose of deriving generalized design criteria for masonry structures in terms of reinforcement application of the types investigated in the experimental campaign. Given the remarkably wide range of possible combinations of materials, unit stacking/bond methods for masonry and the amount of computational time required for non linear analysis of a masonry micro model, this is not an easy task. Even for the specific structural type of masonry examined in the present study (Flemish bond), the parametric investigation by means of a micro model would be unwieldy if it was attempted to couple more than a few parameters instead of investigating each one individually. Therefore, it was necessary to limit the combination of parameters to be investigated to those most significantly influencing the capacity of the plain and reinforced masonry walls.

As a general trend, in plane capacity is increased for an increase in the amount of vertical restraint and the compressive strength of the joints. In order for the reinforcement techniques employed to be effective, it is necessary for an amount of vertical confinement to be provided. Additionally, capacity increases with an increase of the vertical pre-stress from 0% to 30% of the vertical capacity load (governed by the compressive strength of the joints), above which capacity declines for further load increase. Furthermore, compressive pre-stress influences the effectiveness of the reinforcement techniques, especially in the case of net reinforcement, while the effect is less pronounced in the case of the steel wire intervention. The amount of steel reinforcement in the form of wires and its effect on capacity has been found to have a distinctive effect on the response. While the capacity is not strongly influenced for reinforcement amounts higher than a relatively low value, higher geometrical reinforcement ratios appear to benefit the structure in its post peak response. Material properties are not the sole parameter to be considered in the design of structural intervention on masonry walls. The determination of the appropriate course of action requires an estimation of the boundary conditions in the actual structure, something which can pose a significant challenge in the effort to quantify these conditions.

As a general guideline, it could be derived that for masonry walls with a larger amount of vertical constraint and vertical load, which generally tend to coincide, wire reinforcement appears to be the most effective strengthening technique, whereas net reinforcement functions better for lower amounts of vertical pre-stress and less rigid boundary conditions restraining the movement of the top of the wall. As an example, walls situated in the lower storeys of a masonry building would fall into the former category, while those situated in the upper storeys to the latter.

60

70

80

90

100

110

120

130

200 400 600 800 1000

Cap

acit

y [K

N]

Eu/fcu

Plain Wall

Net Reinforcement

Wire Reinforcement



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6 WORK PROGRAM AND RESULTS OF ENA

6.1 INTRODUCTION

Optimization of the earthen wall dimensions:

To determine the optimal dimensions of a mud wall two approaches are adopted: The first based on the calculation of the applied forces is a quasi-static analysis of the mud wall behaviour. The second based on the calculation of displacement of the wall under the effect of the seismic action, is a non-linear dynamic analysis performed using ANSYS computer software.

6.2 PARAMETRIC ASSESSMENT


6.2.1.1 Dimensions optimization by the quasi-static analysis

In this section we begin by calculating the ratio of the wall dimensions deduced from the equilibrium equations of the applied forces. Then, we compare the obtained results with the Code recommendations of different countries.

According to the Moroccan project of the seismic regulations for earthen constructions:

- The ultimate applied effort N should check the following condition of resistance:

AK6.0<N c Eq. 6.1

where A is the wall section, σc is the compressive strength of the earthen wall and K is the coefficient depending on the slenderness and eccentricity:

Then: 0,6n ck

Eq. 6.2

Where σn is the normal applied compressive strength.

- The applied bending moment M should verify the following condition:

0,08 u cM Z

Eq. 6.3

Zu is the lateral module of the wall brut section

Hence0,08 u c

t

Z y

I

Eq. 6.4

where σt is the applied shear stress, y is the position of the neutral axis and I is the moment of inertia with wall length L and wall thickness t:

12

LtI

3

Eq. 6.5

It is known that in a granular material:



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t n tg c Eq. 6.6

φ is the friction angle of the earth and c is its cohesion. - The eccentricity at the head and the base of the wall must verify the following:

0,05450

t

n

I ht

t L y Eq. 6.7

A system of four equations is then obtained and the unknowns are the three dimensions of the wall:

0,6

0,08

0,05450

n c

u ct

t n

t

n

k

Z y

I

tg c

I ht

t L y

Eq. 6.8

6.2.1.2 Optimization by the non-linear dynamic analysis

The non-linear dynamic computation is made using ANSYS software applied to a mud wall model. To validate the correlation between the computer model and the real wall, a comparison between the obtained experimental results and numerical calculation is performed.

Uniaxial compression test and spectral displacement of an unstabilized rammed earth wall

The purpose of these tests is to study the mechanical behaviour of the mud wall by laboratory tests. Three different scales approaches are adopted as shown in Figure 6.1.



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Figure 6.1 - The 3 different scales of the model.

The first scale approach is related to the wall on site. Dynamic measurements were performed on site to determine the displacement response of the wall as a result of the acceleration. The selected “L” wall has the following geometric properties:

Figure 6.2 - The geometric properties of the selected “L” wall.

To determine the natural frequencies of the wall, several shocks were applied in different directions on the wall and the response was recorded using accelerometers and a data acquisition system. The position of the sensors on the wall and the location of the shocks are illustrated in Figure 6.3.

Figure 6.3 - Three shocks on the wall.

The second approach is the scale of a Representative Elementary Volume (REV), samples were manufactured on site. The uniaxial compression test perpendicular to the bed which was conducted shows the results in Figure 6.4.



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Figure 6.4 - The uniaxial compression test results.

Finally, regarding the latter approach, on the microscopic level, tests are performed on compressed earth blocks (BTC) equivalent, which can replace the clay samples to facilitate the process of laboratory testing. A homogenization procedure is implemented to find the relationship between compressive strength and modulus of elasticity of the CEB and VER.

Wall modelling and validation

From the results obtained previously relating to physical properties of the mud, a “L” wall is modeled using ANSYS software with the same dimensions as the prototype test.

Figure 6.5 - Wall mesh modelling.

6.2.2 Parameters

The analysis parameters are the three dimensions of the wall: the height, the thickness and the length of the wall

6.3 RESULTS

6.3.1.1 Dimensions optimization by the quasi-static analysis

The following result is then obtained after solving the system Eq. 6.8 given by the quasi-static analysis

14t

h4

Eq. 6.9

L

t02.0

Eq. 6.10

6.3.1.2 Optimization by the non-linear dynamic analysis



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The experimental vertical deformation depending on the applied stress is compared to the calculated maximum plastic vertical deformation obtained by the software ANSYS.

Figure 6.6 - Experimental and numerical results.

According to the response spectrum of the displacement of the wall given by ANSYS, the maximum displacement is 5.7.10-5, which is very close to the value 4.7.10-5 given by the experimental curve. We can say that the adopted model is quite appropriate to represent the actual behaviour of an adobe wall.

Figure 6.7 - The response spectrum of the displacement of the wall.

Now we would like to study the stability of the wall by the non-linear dynamic analysis. The behaviour equation governing the swing is similar to that of a localized single mass.

But the wall is of mud and we can not consider it as an infinitely rigid system. To overcome this difficulty, the wall will be modeled as two springs placed in series, whose stiffness k are identical.



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Figure 6.8 - Wall modeled as two springs placed in series.

Thus, two proper modes of vibration are obtained; the pulsations of these two modes are given by solving analytical equations and then the period, the frequency and the eigenvectors of each mode are deduced. The relative displacements for a given mode are measured by dividing the acceleration by the square of the pulsation.

Mode Horizontal displacement [mm]

1 2

U1 15.0 0.89

U2 1.25 1.49

For the first mode, the analytical results show that the movements are excessive and the potential energy related to this first mode is very important. The mode 1 is dominant in practice.

The results are then compared with those related to the modes provided by the software ANSYS.

Figure 6.9 - Wall movements for modes 1 and 2.

The dynamic analysis method reveals that the displacement of the wall is excessive and it increases with decreasing the square of its pulsation. A condition on the height wall h is then deduced from equation 6.1:

For the period values

s65.0Ts25.0 Eq. 6.11

0.1 g (1.25 mm)

0.175 g (15 mm) -0.03 g (0.89 mm)

0.05 g (1.49 mm)



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and for the pulsation values

293 631 Eq. 6.12

h must verify the following:

m5.5hm05.2 Eq. 6.13

The following table gives the comparison with some country codes in terms of the height, the thickness and the length of the wall.

Code Length L [m] Thickness t [m] h/t Heigth h [m]

Peru < 12 0.30 - 0.50 < 9 2.4 - 4.5

India < 10 0.30 - 0.40 - < 3.2

New Zeland - ~ 0.25 < 10 -

Zimbabwe - > 0.30 8 - 16 -

USA - 0.25 - 0.60 < 10 -

Spain - 0.30 - 0.50 - -

Present study < 50 0.40 - 0.55 4 - 14 2.05 - 5.5

6.4 CONCLUSIONS

Regarding the optimization of the geometry of the wall, this contribution presents a dynamic approach in parallel with a "classical" static approach to determine the ratios of these dimensions. The dynamic analysis is performed using the software ANSYS nonlinear calculation and the wall model is validated by comparing results with experimental tests.



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7 REFERENCES

Benedetti D., Tomaževič M. (1984). Sulla verifica sismica di costruzioni in muratura. Ingegneria Sismica, Vol. I, No. 0, pp. 9-16, (in Italian).

Bernardini A., Modena C., Turnšek V., Vescovi, U. (1982). A comparison of laboratory test meth-ods used to determine the shear resistance of masonry. VII World Conference on Earth-quake Engineering, Istanbul, Turchia, vol. 7, pp. 181-184.

CEA (1990). Visual Cast3M - Guide d' utilisation. France.

CIMNE (2011). http://gid.cimne.upc.es/index.html, GiD.

DIANA (2009). Diana Finite Element Code, Version 9.4. TNO Building and Construction Research, Netherlands.

Faria R. (1994). Avaliação do comportamento sísmico de barragens de betão através de um modelo de dano contínuo. PhD Thesis, Faculdade de Engenharia da Universidade do Porto, Porto, Portugal (in Portuguese).

Faria R., Oliver J., Cervera M. (1998). A strain-based viscous-plastic-damage model for massive concrete structures. International journal of solids and structures, Vol.35, No. 14, pp.1533-1558.

Kalagri A., Miltiadou-Fezans A., Vintzileou E. (2010). Design and evaluation of hydraulic lime grouts for the strengthening of stone masonry historic structures. RILEM Materials and Structures (published on line, 14.01.10).

Mazzon N. (2010). Influence of Grout Injection on the Dynamic Behaviour of Stone Masonry Build-ings. Ph.D. thesis, Università degli Studi di Padova, Padua, Italy.

Miltiadou A. (1990). Etude des coulis hydrauliques pour la réparation et le renforcement des struc-tures et des monuments historiques en maçonerie. PHD Thesis, ENPC Pub. in 1991 by LCPC ISSN 1161-028X, Paris, France.

PCM, Presidenza del Consiglio dei Ministri (2003). Primi elementi in materia di criteri generali per la classificazione sismica del territorio nazionale e di normative tecniche per le costruzioni in zona sismica. OPCM n. 3274, 20 March. Official Bulletin No. 105, 8 May 2003. In Ital-ian.

Toumbakari E. E. (2002). Lime-pozzolan-cement grouts and their structural effects on composite masonry walls. PhD Thesis, Katholieke Universiteit Leuven.

Turnšek V., Cacovic F. (1971). Some experimental results on the strength of brick masonry walls. II International Brick Masonry Conference, pp. 149-156. Stoke-on-Trent.

Turnšek V., Sheppard P. (1980). The shear and flexural resistance of masonry walls. Research Conference on Earthquake Engineering, Skopje, pp. 517-573.

Valluzzi M. R. (2000). Mechanical behaviour of historic masonry walls consolidated with lime-based materials and techniques. Ph.D. Thesis, University of Trieste, Trieste, Italy (in Ital-ian).

Valluzzi M. R. (2004). Consolidamento di murature in pietra. Iniezioni di calce idraulica natural. Collana Scientifica REFICERE, Gruppo Editoriale Faenza Editrice S.p.a., p. 128.

Vintzileou E., Tassios T. P. (1995). Three-leaf stone masonry strengthened by injecting cement grouts. Journal of Structural Engineering, Vol.121, No. 5, May 1995, pp. 848-856.



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Vintzileou E. (2007). Grouting of three-leaf masonry: experimental results and prediction of mechanical properties. Evoluzione nella sperimentazione per le costruzioni, Cipro, CD-ROM.

Vintzileou E., Miltiadou-Fezans A. (2008). Mechanical properties of three-leaf stone masonry grouted with ternary or hydraulic lime-based grouts. Engineering Structures, Seismic reli-ability, analysis, and protection of historic buildings and heritage sites, Vol. 30, No. 8, pp. 2265-2276.

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