ShorWall Half Model Analysis 1.3 081012

7/29/2019 ShorWall Half Model Analysis 1.3 081012

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Draft 1.3 August 10, 2012

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raft 1.3

2012

Construction Company2259 Ward Avenue, Suite 200, Simi Valley, CA 93065

Alexandre Basso

[SHORWALL HALF MODELANALYSIS][Type the abstract of the document here. The abstract is typically a short summary of the contents of

the document. Type the abstract of the document here. The abstract is typically a short summary of the

contents of the document.]


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[TABLE OF CONTENTS]

1 Executive Summary ....................................................................................................................... 4

2 Introduction .................................................................................................................................. 4

3 ShorWall Model ............................................................................................................................ 5

3.1 Model Description ..................................................................................................................... 5

3.2 Model Setup .............................................................................................................................. 7

3.3 Material Properties ................................................................................................................... 8

3.4 Loading Conditions .................................................................................................................. 12

3.5 Symmetrical Boundary Conditions .......................................................................................... 12

4 Analysis Results ........................................................................................................................... 12

4.1 Half vs. Full Model ................................................................................................................... 12

4.2 Tendon Sensibility Analysis Results ........................................................................................ 13

4.3 Concrete Strength (fc) Sensitivity Analysis Results ................................................................. 14

5 Conclusion ................................................................................................................................... 16

6 References .................................................................................................................................. 17


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[TABLE OF FIGURES]

Figure 1. ShorWall Model Geometrical Imperfection ........................................................................... 6

Figure 2. ShorWall Half Model with Soil Springs ................................................................................... 7

Figure 3. ShorWall Model Elements ...................................................................................................... 8

Figure 4. Free Length for Reinforcements through the Joint Interface .............................................. 10

Figure 5. Interface Element Normal Function ..................................................................................... 11

Figure 6. Interface Element Shear Function ........................................................................................ 11

Figure 7. Symmetrical Boundary Conditions ....................................................................................... 12

Figure 8. Comparison of Full and Half Model Results ......................................................................... 13

Figure 9. Tendon Sensitivity Study Results .......................................................................................... 14

Figure 10. Concrete Strength Sensitivity Study Results ....................................................................... 15


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1 Executive SummaryThe unconventional shape and construction method of the ShorWall makes it difficult to determine

the structural behavior and material stresses using conventional calculations. Therefore a full finite

element model was created to analyze the wall but it was taking up to one hour to solve the model. As

a result, a study was conducted with a half model and it was determined that it was feasible to use this

model and still get the same results as the full model. The major benefit is that half model could be

solved in less than twenty minutes thus expediting the answers to different scenarios.

The following recommendations are based on sensitivity studies and should be taken into account

when designing the ShorWall.

Pre-stressed or post-tensioned tendons should not be used since they do not increase thebuckling load, cause large local stresses, and may make the wall joints stiffer than they are

in reality. Plus, the load-displacement curves were the same for the models with and

without the pre-stressed tendons.

The ShorWall should be designed as a rigid wall deflecting less than one inch under serviceloads in order to eliminate destabilization of adjacent foundations.

The wall thickness and/or the concrete strength should be increased to raise the load-deflection curve thereby raising the buckling failure load.

2 IntroductionCommon commercial building design and construction practice of relatively shallow underground

structures generally incorporates a two-step process: installation of temporary shoring to support earth

loads during excavation, followed by construction of the permanent structure. These structures are

typically rectilinear in shape. This approach is both time and cost intensive due primarily to thenecessity to provide temporary shoring and the time required to complete its construction.

The ShorWall utilizing a circular design which is capable of self shoring during construction

alleviates the inefficiencies found in the current practice. This structural system consists of a stacked

series of circular rings. Each ring is made up of curved precast concrete segments which are joined

together utilizing shear fittings and post tension structural elements. The process of constructing this

type of structure will usually begin with some form of perimeter soil improvement followed by

structural excavation of the soil up to 6 feet (1.8 m) deep and installation of damp-proofing material

against the soil face. Precast segments are then installed end-to-end forming a complete circle or ring.

Following ring completion, grout is applied under prescribed pressure to fill the space (annulus)between the ring and the damp-proofing/soil behind the ring, thereby engaging the ring in resisting

lateral soil pressure.

During and following pressure grouting, the lateral soil pressure bearing on the ring applies

compressive forces that are carried by hoop stress throughout the ring. The friction between the

segments and the soil (resulting from the soil pressure), together with construction means and methods,

resists the gravitational weight of the segments, enabling the next phase of excavation below each


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completed ring (underpinning). Any number of additional rings can be constructed below a completed

ring by repeating these steps one ring at a time, until the design depth is achieved. This construction

sequencing is defined as a top down construction method.

Designing the ShorWall can prove to be a difficult task due to its structural behavior that is not

similar to conventional construction. Thus finite element models were created to analyze the behaviorof the structure and to determine the buckling load of the wall. This report will discuss the finite

element model simplification and the sensitivity studies that have been conducted to determine the

most efficient design for the ShorWall.

3 ShorWall ModelIn order to reduce the computational time of the ShorWall analysis, the full model was reduced in

half by identifying a symmetrical plane and removing the elements on one side of said plane. Next,

symmetrical boundary conditions were added to the wall on the symmetrical plane in order to represent

the influence of the removed half of the wall. To determine that the half wall was modeled properly, astudy was conducted to compare the deflection results of the half model to that of the full model, see

Analysis Results.

The ShorWall half model is based on the full model (PFM_2a3_v4_c45) created by Kasidit Chansawat

(KC). This model was in turn edited by TNO DIANA to mitigate the parallelism problems that KC ran into

as explained in the Nonlinear FE Modeling and Analysis of the Full and Detailed ShorWalldated

October 18, 2011.

3.1 Model DescriptionThe following are the geometrical properties that were used to model both the ShorWall full and

half models in DIANA 9.4.4.

Inside Radius (nominal) = 115 ft or 1,380 in (35 m or 3,505 cm)

Inside Diameter (nominal) = 230 ft or 2,760 in (70 m or 7,010 cm)

Total Height = 40 ft or 480 in (12 m or 1,219 cm)

Precast Segment Height = 5 ft or 60 in (1.5 m or 152 cm)

Precast Segment Thickness = 12 in (30.5 cm)

Precast Segment Length = 10 or about 20.16 ft (6.14 m)

Geometrical Imperfection = 0.5 in (12.7 mm)

Ellipse Major Radius = 1,380.5 in (3,506 cm)

Ellipse Minor Radius = 1,379.5 in (3,504 cm)

Mesh Width = 1 or about 24.3 in (61.7 cm)

Mesh Depth = 20 in (50.8 cm)

Mesh Thickness = 12 in (30.5 cm)


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Number of Rings = 8 rings per 40 ft depth

Number of Wall Segments = 36 segments per ring, 9 per quadrant

The loading onto the ShorWall is converted

into compressive hoop stresses which induce the

wall to behave similarly to a column undercompression. When a column is loaded under

compression, it will follow the primary path which

is the original load-displacement curve until the

critical load is reached and then it will track the

secondary path known as the post-buckling curve.

The point in which the two paths intersect is called

the bifurcation point. The primary path becomes

unstable after the bifurcation point even though it

is still mathematically possible to continue on that

path, nonetheless, a real structure will follow thesecondary path. In order to force the finite

element model to jump from the primary to the

secondary path, a geometrical imperfection needs

to be introduced to nudge the model into buckling.

Halcrow conducted a study on the ShorWall

buckling and determined that a geometrical imperfection of 0.5 inches was appropriate to induce

buckling without extensively de-stabilizing the structure. This results in a slightly elliptical shaped shaft

rather than a perfectly round shaft as illustrated in Figure 1.

Special consideration should be taken when designing the ShorWall since it is a thin-walled shellstructure that is sensitive to imperfections, meaning that the buckling load is affected by small changes

in geometry, distribution or orientation of loads, and manner of support.

Figure 1. ShorWall Model Geometrical Imperfection

Perfect Circle


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Figure 3. ShorWall Model Elements

The ShorWall model was created to be slightly elliptical in order for the wall to buckle, but this made

the model more complicated to create. For example, a single segment cannot be created in DIANA and

then copied radially about the center to create a ring of segments because it will either form a circular

shape or the nodes will not lineup properly. Also, after creating the first ring of segments, the ring

cannot be duplicated below the first ring and rotated to produce the running bond because the nodes

will not lineup in between rings due to the elliptical shape. Thus the first and second rings were created

separately with the running bond and than they were duplicated below to form the full height wall.

3.3 Material PropertiesConcrete

Various concrete properties were used to model the pre-cast concrete segments in order to

determine which variables affected the buckling capacity of the ShorWall. Due to the limitationsin Diana, the model had to be converted to SI units before the concrete properties for the ACI

209R-92 model could be entered. The properties are listed below for the different half model

versions that it applies to.

Half Model v1 to v4

Compressive Strength (f'c) = 8,000 psi (55 MPa)

Youngs Modulus (E) = 57,000 x sqrt(8,000 psi) = 5.0E+09 psi (3.45E+07 MPa)

Poison Ratio () = 0.2

Half Model v5 & v8

The ACI 209R-92 model code regulation was used to derive the non-linear material

properties for concrete. Below are the input parameters for DIANA 9.4.4.

Compressive Strength = 55 MPa (8,000 psi)

at 28 days (FCM28)

Poisson Ratio () = 0.2

Vertical and

Horizontal Interface

Elements (CQ48I)

Soil Springs

(SP2TR)

Vertical

Tendons

Horizontal

Tendons

Alignment

Pins (CQ48I)


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Density () = 2.4 kN/g

Cement Type = III

Curing Method = Steam

Cracking Function (CRACKN)

Analysis Type = Plasticity Function (PLASTN)

Concrete Tensile Strength Limit (FTMODN)

Half Model v6 & v9

The compressive strength at 28 days was changed to 27.5 MPa (4.0 ksi).

Half Model v7 & v10

The compressive strength at 28 days was changed to 82.5 MPa (12.0 ksi).

Tendon (Steel)

In DIANA, the tendons do not interact with the mother elements (in this case the pre-cast

segments) unless they are bonded to them. In the post-tension element model, the tendons

have to be manually bonded to the mother element after they are tensioned. Therefore, the

tendons were modeled as pre-stressed elements since they are automatically bonded. Also, the

tendons do not need any boundary conditions at the symmetric plane because they are

embedded into the mother element before the pre-stressing load is applied.

The Youngs Modulus used for the steel tendons is lower than an actual post-tension cable in

order to stay consistent with KCs work. However, it still gives a good determination of the

systems behavior.

Diameter = 0.5 in (12.7 mm)

Area = 0.1963 in (127 mm)

Youngs Modulus (E) = 29.0E+09 psi (2.0E+08 MPa)

Poison Ratio () = 0.3

Yield Strength (fy) = 1.0E+05 psi (690 MPa)

Free Length = 1.0

The reinforcement free length is used to determine the stiffness in the normal and shear

direction of the tendon in the interface element. The value for the free length can only be

entered in the DIANA Mesh Editor and the stiffness per unit area in the normal direction (kn) and

in the shear directions (ks & kt) are determined as follows

The stiffness in the shear direction is caused by the dowel effect of the reinforcement bars

through the interface and is assumed to be half the stiffness of the normal direction, see Figure


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4. The dowel effect means that the reinforcement has the ability to be a major contributor to

shear resistance at the joint much like a dowel or alignment pin.

Figure 4. Free Length for Reinforcements through the Joint Interface

If the free length is not specified, DIANA uses the thickness of the interface element. But if the

thickness is zero, then DIANA uses a virtual thickness of 10-5

times the distance from the first to

the second node of the interface element. This could potentially make the steel reinforcement

in the joint very stiff therefore the free length was manually specified to be one. For more

information see section 14.5.1 in the Element Library manual.

Soil Spring

Soil springs were used to represent the interaction between the ShorWall and the surrounding

soil. The springs have been modeled to resist a maximum compressive load of 562,302 pounds

per inch and to not resist any tensile loads. Below are the parameters used to determine the

spring stiffness.

Subgrade Reaction Modulus = 1,157 psi/in (314,000 kPa/m)

Mesh Size = 24.3 in x 20 in (61.7 cm x 50.8 cm)

Spring Stiffness = 1,157 x 24.3 x 20 = 562,302 lb/in (98,474 kN/m)

Interface Elements

The vertical and horizontal interface elements have the same properties as the alignment pin,

see Figure 5 and 6. TNO DIANA made this change because KC modeled the vertical and

horizontal interface elements as Coulomb friction which made the model unstable. The

instability originated from the fact that the shear resisting force at the joints is calculated using

the normal force which is derived from the hoop stress in the horizontal direction and the self

weight of the segments in the vertical direction. As a result the normal force in the vertical

direction was not large enough to generate the appropriate shear resisting force to keep the

panels in place.


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Figure 5. Interface Element Normal Function

Figure 6. Interface Element Shear Function

Normal Function

Displacement (in) Traction (psi)

-1.0E+09 -7,600

-0.00113 -7,500

0 0

0.08 23

0.20 31

1.0E+09 41

Shear Function

Displacement (in) Traction (psi)

-1.0E+09 -87

-0.43 -77

0 0

0.43 77

1.0E+09 87


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3.4 Loading ConditionsThe loads were applied in construction phases with the first phase adding the weight of the

structure to the model in one load step. In the second construction phase, the steel tendons were pre-

stressed to 80 ksi (80% of the yield strength of the steel) in one load step. Next, a uniformly distributed

lateral pressure of 60 psi was gradually applied to the exterior face of the ShorWall to represent the soil

loading. The load was applied in small incremental load steps in order to capture the behavior of the

wall as the load increased.

3.5 Symmetrical Boundary ConditionsOnce the model was cut in half, symmetric boundary

conditions had to be applied to mimic the interaction between

the two halves. In order to keep the model symmetrical, the

precast segments on the odd rings (1, 3, 5, and 7) were left at

full size with the vertical interface element on the outside.

Boundary conditions in the direction normal to the segment

face were applied to the joint interface to model the panel, on

the other side, resisting the hoop stresses. The even ring (2, 4,

6, and 8) precast segments had to be cut in half and both

normal and moment reactions were attributed to the nodes to

model the internal forces.

Dummy shear boundary conditions, radially perpendicular

to the joint face, were not needed to make the model stable

since the soil springs stabilized the model. The dummy shear reaction would be used on one of the

symmetrical planes in order to anchor the model and keep it from freely moving in the 3D environment

during the finite element analysis of the structure.

4 Analysis Results4.1 Half vs. Full Model

In order to determine that the ShorWall half model was working properly, the results of the half

model were compared to that of the full model analyses. Figure 8 is a comparison between three

models. The first model, PFM_2a_Base1, is a full model of the ShorWall without any joints or post-

tension cables; please refer to KCs work for additional information on the model. The

PFM_2a3_v4_c45 is the analysis result for KCs fullmodel which was edited by TNO DIANA. HalfModel v1 (w/PT) is the half model results after all the appropriate changes were made from the full

ShorWall model. The results of the half model are the same as the full model which proves that it was

modeled correctly and that it can be used to analyze the structural behavior of the ShorWall.

Figure 7. Symmetrical Boundary Conditions

Reaction Normal to the

Segment Face (Red)

Internal Moment

Reaction (Blue)


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Figure 8. Comparison of Full and Half Model Results

4.2 Tendon Sensibility Analysis ResultsThe ShorWall half model was analyzed to determine the systems sensibility to the pre-stressed

cables in an attempt to determine how much the walls buckling resistance is influenced by the tendons.As it can be seen from Figure 9, the results from models v1 through v4 yielded the same curve for

inward deflections of up to three inches. When looking at the data past the three inch deflection, it can

be noticed that the third model with only vertical pre-stressed tendons and fifth model without pre-

stressed cables had similar responses and failed sooner than the fourth model with only horizontal pre-

stressed tendons. Thus the inclusion of only horizontal tendons is more beneficial in delaying failure of

the wall rather than stiffening it. Therefore, inclusion of the tendons does not help to increase the

buckling failure load or, in other words, raise the load-deflection curve. This means that for the same

deflection, the stiffer model would be able to carry a higher load than the less stiff model.

0

5

10

15

20

25

30

-12-11-10-9-8-7-6-5-4-3-2-10

Load

(psi)

Displacement (in)

PFM_2a_Base1

PFM_2a3_v4_c45

Half Model v1 (w/PT)


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Figure 9. Tendon Sensitivity Study Results

In the half model without the tendons, the pre-cast panels began to shift out of their original

configuration under high inward deflection due to the lack of tendons. This could mean that the joint

stiffness is higher when the pre-stressed tendons are used. The bonded tendon feature in DIANA which

only allows the part of the cable in the joint interface to deform might be contributing to the higher joint

stiffness. It should be noted that this is not a realistic representation since the post-tension cables will

not be grouted to the panels thus allowing the whole cable to elongate and not just the section going

through the joint. Thus it is recommended that the ShorWall be modeled without the pre-stressed

cables in order to make the design more conservative.

It is also recommended that the ShorWall design limits the deflection of the wall to less than one

inch when under service load conditions to mitigate the mobilization of the surrounding soil which can

cause adjacent foundations to fail. Consequently, the ShorWall needs to be designed as a rigid structure

rather than flexible one.

4.3 Concrete Strength (fc) Sensitivity Analysis ResultsThe concrete strength sensitivity study was conducted to determine how much the strength of the

concrete (fc) affects the buckling resistance strength of the ShorWall. The half model was tested with

three different concrete strengths (4.0, 8.0, and 12.0 ksi) and with and without pre-stressed cables.

These models used non-linear concrete properties with cracking. At the lower fc, the model

0

5

10

15

20

25

30

-12-11-10-9-8-7-6-5-4-3-2-10

Load

(psi)

Displacement (in)

PFM_2a_Base1

Half Model v1 (w/PT)

Half Model v2 (vert PT only)

Half Model v3 (horiz PT only)

Half Model v4 (no PT)


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experienced failure in buckling but as fc increased, the model was more prone to suddenly failing due to

crack formation when steel tendons were included in the model.

From Figure 10 it can be seen that increasing or decreasing the concrete strength by 4.0 ksi causes

the load-displacement curve to significantly move up or down, respectively. At one and two inch

deflections, model v6 with a concrete strength of 4.0 ksi had a 29% lower load capacity than model v5(f

c = 8.0 ksi) while model v7 (12.0 ksi) had a 23% higher load capacity. Thus, it can be safely stated that

the buckling resistance of the ShorWall is highly dependent on the strength of the concrete.

Figure 10. Concrete Strength Sensitivity Study Results

The models with and without the tendons generated the same load-deflection curve. However,

interestingly enough, the models with the pre-stressed cables failed sooner than the models without the

tendons when non-linear concrete properties were used. This phenomenon should be further

investigated if the steel tendons are to be used in the design of the ShorWall. Also, models v5 and v8

had a load deflection curve slightly higher than the base model (PFM_2a_Base1) which can be attributedto rounding down the Youngs modulus from 5.098235E+09 psi to 5.0E+09 psi in the concrete properties

of the base model.

0

5

10

15

20

25

30

-12-11-10-9-8-7-6-5-4-3-2-10

Load

(psi)

Displacement (in)

PFM_2a_Base1

Half Model v5 (f'c = 8.0ksi)



Half Model v8 (no PT, f'c = 8.0 ksi)



Wall Failed After

Crack Formation


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5 ConclusionThe DIANA half model provides the same solution as the full model and is adequate to be used in

the design of the ShorWall. This will reduce the analysis time, providing quick answers to different

scenarios. The following recommendations are based on the studies outlined above and should be

taken into account when designing the ShorWall.

Pre-stressed or post-tensioned tendons should not be used since they do not increase thebuckling load, introduce high local stresses at the joints, and may make the wall joints

stiffer. Plus, the load-displacement curves were the same for the models with and without

the pre-stressed tendons.

The ShorWall should be designed as a rigid wall deflecting less than one inch under serviceloads in order to eliminate destabilization of adjacent foundations.

The wall thickness and/or the concrete strength should be increased to raise the load-deflection curve thereby raising the buckling failure load.


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6 ReferencesCook, R. D., Malkus, D. S., Plesha, M. E., & Witt, R. J. (2007). Concepts and Applications of Finite

Element Analysis (4th ed.). Singapore: John Wiley & Sons.

ShorWall Half Model Analysis 1.3 081012

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