6.1 GENERAL

Chapter 6

VALIDATION STUDIES

In general, validation is the process of checking whether something

satisfies a certain criterion. Examples would include: checking if a statement is

true (validity), if an appliance works as intended, if a computer system is

secure, or if computer data are compliant with an open standard. Validation

implies that one is able to testify whether a model or process 1S correct or

compliant with a set of standards or rules.

In the present study, validation indicates checking the accuracy of the

prediction tool developed to simulate the behaviour of gabion faced reinforced

soil retaining walls. To be exact, it may be noted that, through the validation

studies, it should be ensured that the simulation of stresses, strains and

displacements should be representative in all respects.

For this, thorough and detailed validation studies were conducted at

each phase of the program development. To validate the performance of each

element, suitable independent examples are chosen and compared with the

available results.

6.2 FOUR NODED QUADRILATERAL ELEMENT

This validation study was conducted to check the appropriateness m

using the incorporated 20 four noded isoparametric quadrilateral element with

regards to linear elastic analysis. For this, a simple case of a cantilever beam

with rectangular cross section subjected to an end moment is considered.

Here the end moment was replaced by a couple of forces for the purpose of

analysis as in Krishnamoorthy (1987). The length of the beam is ta.k.en as

200cm, the width 20em and the depth 30em. The modulus of elasticity of the

109

material of the beam is 2 x 103 kN/cm~. The loading on the beam is shown in

Fig. 6.1 (a) while the discretisation used for the study is shown in Fig. 6.1 (b).

10 kN

10 l:N (a) Cantilever beam

3 6 12 15 18 .,- 30 33

11 1:: 13 1 ... 1:- 16 1- 18 19 20

1 .,

3 4 ::- 6 - 8 9 10 -1 10 13 16 19

.,., 31

(b) Discretisation

Fig. 6.1 Cantilever beam loaded with couple

Table 6.1 Comparison of deflection for cantilever beam

Distance Deflection value (cm) from Deflection value I (cm) from I from fIXed Node numbers

end (cm) Krishnamoorthy (1987) FECAGREW 40 7,8,9 0.002182 0.002182

80 13, 14, 15 0.008727 0.008727 ----_ ... _-

120 19,20,21 0.019636 0.019636

160 25,26,27 0.034909 0.034909 -----

200 31,32,33 0.054346 0.054346 .. _- ~----- ._--.. _- -----_ .... -

Linear plane strain elastic analysis was done using FE CA GREW and the

vertical deflections at the different nodes were noted dov.;n. The results

presented as Table 6.1 agree quite well with the results from the literature.

Hence it may be concluded that the developed code FECAGREW is working

110

---

---

properly and the incorporation of the quadrilateral element has been done

accurately.

6.3 TWO NODED TRUSS ELEMENT

Linear elastic analysis was conducted to check the accuracy in using the

incorporated 20 two noded truss element, in this validation study. For this, a

simple case of a two dimensional truss structure shown in Fig. 6.2 (a) was

considered. The geometry and loading are taken as symmetrical about the

centre line as in Krishnamoorthy (1987). The modulus of elasticity of the

material of the truss member is 2 x 104 kN/cm2 . The cross sectional area of the

truss member is 1 cm2 . The discretisation used for the study is shown in

Fig. 6.2 (b).

t 100 kN

1.00

~ 0.50

r866 ~I" O,86~ ~

100 kN ')

All dimensions are in n1etres

(a) (b)

Fig. 6.2 Plane truss structure

In this case also, linear plane strain elastic 3nalysis ,vas conducted using

FECAGREW and the deflections at the different nodes \vere noted dovv'll.

The results are presented in Table 6.2 and they agree quite well with the results

from the literature. Axial forces in the truss members \\'ere also determined.

From the FE analysis using FECAGREW, the axial force in element numbered

1 1 1

as 3 is obtained as 3.724625 kN and the corresponding value obtained from

literature (Krishnamoorthy, 1987) is 3.72 kN. Hence, here also, it may be

concluded that the incorporation of the truss element in FECAGREW has been

done accurately and the clastic analysis is working perfectly for any type of

structure.

Table 6.2 Comparison of deflection for a plane truss structure

Deflection value (cmt Deflection value (cm) Node number from Krishnamoorthy, 1987 from FECAGREW

1 ° ° 2 0.5558 0.555834

3 0.5372 0.537211

4 ° ° 6.4 MODELLING OF NON LINEAR BEHAVIOUR OF SOIL

In order to check the accuracy of formulation of non linear analysis,

simulation was done for the experiment results available from literature

(Duncan and Chang, 1970). The experiment was based on the behaviour of soil

loaded with a strip footing and the vertical displacements at point A (Fig. 6.3)

were taken for different loadings till failure.

Analysis was conducted using the hyperbolic parameters and properties

of soil as given by Duncan and Chang (1970) in their model tests. The model

tests were conducted on a footing resting on a semi - infinite soil mass.

Strip footing was of 2A4 in (6.197 cm) \vide and 12.44 in (31.149 cm) long.

The hyperbolic parameters and the properties of soil used in their investigation

are listed in Table 6.3.

Table 6.3 Input data for soil medium (Duncan & Chang, 19701

Parameters ~ J~<P~)' --I K

_V_a_Iu_es_-----'-____ ---'---_O_ L~_QQ j ~kN jm~) p.-.J

,0 .. 55 : O·B3 ___ LI_1_7 __ A_9_--,---,-0---,.3:...c:5'---Ji

n

112

The same parameters were used for conducting the analysis using

FECAGREW. The finite element mesh fixed after mesh refinement studies and

boundary conditions employed for the analysis is given in Fig. 6.3 .

.. IB/2I, ........ .-

A ~ it> ~

it> ~ 6B

iD ~

(0

'~ ~ ~ ~ kiT

6B

Fig. 6.3 Discretisation of soil medium

The mesh consisted of 463 nodes, 400 soil elements and 20 linear

quadrilateral elements representing footing. The rigid footing was reprcsented

by two rows of quadrilateral elements with very high modulus and subjected to

linear analysis only. Since the system under analysis is symmetrical about the

centre line only one half portion (right hand side) \vas considered for the

analysis. The vertical displacements at point A (Fig. 6.3) were notcd for

113

different load increments until the system failed. Loads were applied as

equivalent concentrated loads at the topmost eleven nodes of the system in

increments of 2 .5 psi (17.5 kPa) upto 25 psi (175 kPa) to generate an accurate

comparison with the result of the model test. The FEM results of FECAGREW

were plotted along with the experimental results of Duncan and Chang (1970)

for validation purposes and both show very close behaviour (Fig. 6.4) . It can be

observed from the results that FECAGREW depicts the non linear behaviour of

soil with sufficient accuracy.

5 10 15 20 25 30

-.-Duncan aod Chang's ea:pedmental result

___ FECAGREW FE snalysls result

0.4

Fig. 6.4 ValidatJon of non linear analy.i. of .oil medium

6.5 MODELLING OF INTERFACE BEHAVIOUR

The four noded zero thickness line interface element proposed by

Goodman et al. (1968) was incorporated in FECAGREW to model the

soil - reinforcement interaction and the relative slip between each other.

The same element was used to model the interaction between soil and gabion

facing also. The problem of sliding blocks (Raghavendra. 1996) which

resembles the direct shear test was used to check the sliding behaviour

exhibited by these interface elements.

114

rx y

6 I~ 18 2 30 1 kN

8 0 0 G 5 Ll 17 e:J 1 kN

CD LO 16 1 kN Q,5x4=2M 9 15

CV 9 14

CV

I .. O,5x4=2M ..I (0.) Initio.l Mesh (10) DeforMed Mesh

Fig. 6.5 Sliding block problem

16 soil elements were used to model the soil blocks. To simulate sliding

between the top half and the bottom half, four interface elements were provided

in between (Fig. 6.5 (a)). The elements numbered inside circles represent soil

elements and those inside triangles represent interface elements. Another point

to be noted is that the nodal pairs 3-4, 9-10, 15-16, 21-22 and 27-28 were

given the same coordinates initially. Horizontal and vertical movements were

restricted for all the nodes at the left, right and bottom boundaries of the

bottom half of the system. The movements of all the other nodes were kept free.

Unit load was applied to the right nodes of the top half of the system to

simulate pulling effect in the horizontal direction. Soil elements and interface

elements were given the same parameters listed out in Table 6.4. The interface

properties ks and k" were given the values 1 x 10) kPa and 2 x 10K kPa

respecti vely.

After FE analysis, it was seen that nodes 4. 10, 16, 22 and 28 exhibited

positive non zero u values while the corresponding nodes 3, 9, 15,21 and 27 of

the nodal pairs listed abovc showed zero u values. This indicates that definitely

115

sliding occurred between the top and bottom half of the soil elements, which is

possible only due to the presence of the interface elements. This proves the

effectiveness of the action of the interface elements. From this, it may be

concluded that the zero thickness line interface element in FECAGREW is

functioning in a proper way.

6.6 MODELLING OF REINFORCED SOIL BEHAVIOUR

Next step in the validation studies is checking the effectiveness of

soil - reinforcement interface friction. For this, the model study conducted on

footing resting on reinforced soil by Singh (1988) was used. The hyperbolic

parameters needed for modelling the soil as well as the interface in this study

were taken from Raghavendra (1996) who numerically simulated the above

model tests.

Singh (1988) conducted model tests on a sand bed of dimensions 390 cm

x 390 cm x 210 cm, using three horizontal layers of aluminium strips as

reinforcement. The footing dimensions were 15.24 cm x 91.4 cm. The input

parameters needed for the analysis are listed in Table 6.4.

Table 6.4 Input data for reinforced soil foundation (Raghavendra, 1996)

~ C y Soil Parameters

(degrees) (kPa) K n I Rr Kmu m

(gjcc) Values 42 0 540 0.35 0.67 489 0.1 1.73

Aluminium Parameters E A (kgjcm2) (cm2)

strips Values 1.5 x 106 0.054

i Parameters 0 Kt nl RI

Interface (degrees) I

Values 38 124 0.54 0.56

The finite element mesh fixed after mesh refinement studies and

boundary conditions employed for the analysis is given in Fig. 6.6. Vertical

spacing of reinforcements;; 3.81 cm, number of layers of reinforcement ~ 3 and

the length of reinforcements;; 45.72cm.

116

~, , .a

\, "U

~ ~~

~ ,.~ ['Q

~ l'B '13

tP' t;:;. t.;;,. /~

130

(a) Discretisation or soil inside tank

2LD

Lv ~ ,

ejL

pJl dimensions in 'centimetres

~-- 22,86 ----tl0-1

7 ~~, , ,be.

(b) Enlarged view of the reinforced (circled) portion

Fig. 6.6 Discretisation of reinforced soil medium

The mesh consisted of 899 nodes, 840 soil elements, 4 linear

quadrilateral elements representing footing, 36 truss elements and 72 interface

elements, The rigid footing is represented by one row of quadrilateral elements

with very high modulus and subjected to linear analysis only. Since the system

under analysis is symmetrical about the centre line, only one half portion (right

hand side) is considered for the analysis. The vertical displacemcnts below the

centre of the footing were noted for different load increments until the system

failed. Load was applied as a singlc concentrated load at the top left node of the

system in increments of 600 kg (6 kN) till failure. The FEM results of

FECAGREW wcrc plotted along with the experimental results of Singh (1988) for

validation purposes and both show very close behaviour (Fig. 6.7). This means

that modelling of the behaviour of reinforcement as well as the

117

soil - reinforcement interaction using FECAGREW has been made quite

precisely.

0

0

0.5

i .!!. ~ • • 1.5 a :! ~ • 2 ..

2.5

3 ·

2000 4000

Load (kll

6000 8000 10000

-*,- Singb (198 81 experime n tal result

___ FECAGREW FE a.nalysls result

Fig. 6 .7 Validation of reinforced eoil behaviour

6.7 MODELLING OF REINFORCED SOIL WALL

12000

The effectiveness of FECAGREW in simulating the non linear behaviour

of reinforced soil has been proved in the previous sections. The next step is to

check its applicability in the prediction of behaviour of retaining walls which is

the major aim of the present work. For this, the modelling of the construction

phases described in Section 4.6, should be accurate. To val idate this aspect,

the FEM results from Helwany et al. (1999) was chosen.

Helwany et al. (1999) used a modified version of DACSAR (Defonnation

Analysis Considering Stress Anisotropy and Reorientation) to predict the

behaviour of geosynthetic reinforced soil retaining walls. The accuracy of this

finite element program was verified by comparing the analytical results with the

measured results of a 3m high and 1.2m wide test wall. The same resu lts are

used here for the validation of the behaviour of reinforced soil walls.

The discretisation used for the study is shown in Fig. 6.B .

118

~ ~

$

3.00 $

~ '81

(0,0)

~ ~~ ~ .J, ~ ~ 1.68

1.98

--

--...

~ ~

Facing

Soil

Geotextile

All dimensions in metres

Fig. 6.8 Discretisation used for validation of reinforced soil wall

The timber facing was represented by beam elements (incorporated in

FECAGREW for the sole purpose of modelling this reinforced soil wall for

validation), geotextile reinforcement by truss elements and the soil by plane

strain four noded isoparametric quadrilateral elements. The discretised mesh

consisted of 775 nodes, 720 soil elements, 210 truss elements and 30 beam

elements as given by HehvclnY et a1. (1999). Interface elements were not used as

they were not used for modelling in the literature and the purpose of the

present study is to reproduce the results obtained by Helwany et al. (1999)

using FECAGREW. The construction sequence was simulated by ten

construction lifts. The boundary conditions adopted were: all the bottom nodes

were completely fixed, top right node \vas fixed (in order to simulate the field

test where fixity was provided at the top) and horizontal motion of all the left

119

extreme nodes was restricted. The parameters used for modelling the

reinforced soil wall are listed out in Table 6.5.

Table 6.5 Input data for reinforced soil wall

Soil ! Parameters I ~ (degrees) C (kPa) K 1 n I Rr I Kmu I ! Values ! 38.4 0 1116 I 0.66 1,2.87 1 907 1

G t tU ! Parameters i E(kPa) A (~2) eo ex e Values 1 5.4 x 103 0.0025 Timber Parameters ! E (kPa) A (m2) I (m4) 1

facing Values I 1.4 x 105 0.0025 4 x 10-7 1

Surcharge was given as equivalent concentrated loads at the top nodes

after simulating all the ten construction phases. The responses of the wall at

105 kPa were considered for comparison purposes. Fig. 6.9 shows the facing

deformation of the reinforced soil wall while Fig. 6.10 shows the strains

developed in the geotextile at different elevations.

The results obtained from FECAGREW show close agreement with the

results of Helwany et al. (1999). From this, it can be stated that FECAGREW is

fairly effective in simulating the behaviour of reinforced soil walls and the

modelling of the construction phases is accurate.

6.8 MODELLING OF GABION FACED REINFORCED SOIL WALL

After successful verification of each component of FECAGREW, it is

attempted in this section to compare the load displacement behaviour of a

gabion faced retaining wall with the results from actual laboratory experiments.

The final step in the development of the FE code was the incorporation of a

composite model to represent the behaviour of gabion facing which is detailed

in Section 4.5.

Experimental results on such type of '.valls are very much limited in

number in literature as e\'ident from Chapter 2. Hence for validation purposes,

test results obtained from the experimental programmes detailed III

Section 5.2.2 were used. For modelling purposes, laboratory determination of

the hyperbolic constants of soil (as described in Section 4.3.2.1) and interface

120

m I 0 1

(as given in Section 4.4.3. 1) as well as the elastic properties of the fill materials

were carried out as follows:

4 UU

350

, II Hehuny et .1. (1999) FEM

.. eeutt __ 'Jt.CAGREW BEM n :eutt

024 6 Horizonta l de forma tion (cm)

Fig. 6 .9 Validation of re inforced s oil wall - Facing deformation

. _------------3 Geot extlle a t 0 .9 H

l . ~,----------~-~~~ :! GeoteJI:tlle a t O.SH

=:" 3 , 0 _ - a a 0 _ _ ""--- _ -e 2 0- -O A :. .o~~-e

.! I ., tJ. Hel"'any et al . (1999) FEM ",eutt :-o.......u.....,

a 0 1 - _ FECAGREW FE ...... ut t

.~ _ 0 Hel",.ny et aJ . (1999) e:zperiment reeu.1t

. ~,--

3 Geot e lltlle at O .~H

o 0 o 0 tl' Q -A 0.-0

0 __

o 30 60 90 120 150 180

Diet.nee from wall f.dlll (cm)

Fig. 6.10 Valldation of reinforced .oll wall - Strain in geoteztile

121

(

Several methods exist for the evaluation of Kondner's constants a) and b l

in the hyperbolic formulation of non linear behaviour of soils. Transformed

stress - strain curve method (Section 4.3.2.1) is one of them and another

method called two point method is used in the present study, due to its

simplicity. A hyperbola is completely defined by its constants a l and b l , if it is

constrained to pass through any two points on the actual stress - strain curve.

DUncan and Chang (1970) suggested fitting the hyperbola through two points

on the stress - strain curve where deviator stresses are equal to 70% and 95%

of peak deviator stress, representing the failure. Same procedure is adopted

here as it has been found to work well for a variety of soils as cited by Duncan

and Chang (1970). When the hyperbola is fitted through 70% and 95% of

stress level, the coefficients a 1 and b l may be obtained as follows:

...................... (6.1)

...................... (6.2)

( ) £ °0

(J -u, == I .. co I /. I

(/ +) C 70 ...................... (6.3)

I £ ')5 a == -r-;-:---; )--

\CT 1 - ")5

- hi C' 95 ...................... (6.4)

]1 \

[; co 1 .- 'u----=-;:~-r- ~--~-;~ I

\0 I CJ, '711 ,,95 .. " /

...................... (6.5)

in which, subscripts 70 and 95 indicate the percent of stress level used

in the curve fitting. On similar lines, the interface constants ui and bi can also

be obtained as:

...................... (6.6)

......... _ ............ (6.7)

122

6.8.1 Hyperbolic constants for soil

Consolidated drained triaxial tests were conducted on sand s pecimens

prepared at the same density as tha t of the model tests and the stress - s t rain

curves are shown in Fig. 6. 11 (a). Kondner's constants a l and b l were

calculated using Eqns. 6.4 and 6.5 respectively. The initial modulus, E, ;; l /a

and the failure ratio, Rf. were also calculated for each c urve in Fig. 6 . 11 (a) .

Then, [~) vs. [G , ) was plotted to log - log scales a nd K and n we re P",,,. P",,,,

determined as shown in Fig. 6 .11 (b) . The value of Rf is taken as the average

value obtained from the three curves.

Cd 800 .. :!. 2000 • 600 • • l t ~ • 1000 • 400 • • .;: ~ • - - 600 • .. • 200

t:C Q

-A- 03 '"" 1 OOkPa 400 1

0 2 3

CJ3 I P.I. (toe) 0 10 20

Strain (%)

la) Deviator stress vs. strain curve (b) Hyperbolic constants 3_ lOCO C--------------,

lu I , 600 ,-__________ -,

; ...

o -0.5 -

,I",r - .. o· IOOU.

10 20

j 200 • •

c - OkP.

. . 38 .9-

0 '---____ --'

o 200 400 600 p • 101 .. 0,,) / :I IIIP_)

(c) Volumetric atrain v.. (d) Modified hyperbollc (e) Shear strength axial .train curve constanu parameten

Fig. 6 .11 Determination of Don Unear eta.tic properties for •• nd

123

In a similar manner, the modified hyperbolic constants Kmu and m, for

the determination of Poisson's ratio, p may be obtained. For this, the

volumetric strain vs. axial strain curves for the same triaxial tests are plotted as

shown in Fig. 6.11 (c). The deviator stress (cri - 0"3)70 and volumetric strain (Ev70)

at 70% stress level were calculated for each curve in Fig. 6.11 (c).

[

(0"1-0"1)70 l Then, E: . ., Palm vs. (;' I was plotted to log - log scales and Kmu and m

I .() at", )

3

were determined as shown in Fig. 6.11 (d). The triaxial tests results were then

plotted as p vs. q curve (Fig. 6.11 (e)) to calculate the shear strength parameters

c and~. The values obtained are listed in Table 6.6.

Table 6.6 Non linear elastic properties of sand

Parameters Values

Hyperbolic constant, K 479

Degree of curve, n 0.61

Failure ratio, RI 0.84

Hyperbolic constant, Kmu 360

Degree of curve, m 0.32

I Cohesion, c (kPa) 0

Angle of internal friction, <j> 39 (degrees) ----_.

6.8.2 Elastic constants for gabion fill materials

The coarse aggregate and quarry dust were used as a gabion fill material

in the model studies. In FE modelling, the gabion fill material is treated as a

linear elastic material. Hence, the elastic modulus', E and the Poisson's ratio, ~l

are the parameters to be determined. For this, three consolidated drained

triaxial tests were conducted on coarse aggregate and quarry dust specimens

prepared at the same density as that of the model tests. In the case of coarse

aggregate, the tests were conducted on large sized (20 cm dia.) specimens as

the avel'age size of the coarse aggregates was 20mm while for the quarry dust

the same dimension (7.5 cm dia.) used for testing sand was used. The

124

stress - strain curves for the coarse aggregate are shown in Fig. 6. 12 (a) and

that for quarry dus t in Fig. 6.13 (a ). Kondner 's constant at was calculated fo r

each cu rve using Eqn. 6.4 and the initial elastic modulus was taken as

Ei = l / a 1 . The value of E is taken a s the average value of Ei obtained fro m the

three curves. Pois son's ratio was determined from Eqns. 4 .17 and 4 .18 after

obtaining the t> value from the p vs . q curve (Figs. 6.12 (b) and 6.13 (b) ) drawn

using the triaxial test res ults . The properties of coarse aggregate and quarry

dust used for validation are tabulated in Table 6.7. The induced cohesion on

the fill mate rials was calculated u s ing Eqns. 4 .55 and 4.56.

2000 f 1500

l , > ..

.!!. 1500 ; .. e · OkP •

• ; 1000 • ~ .... ~ -• .. " • II'~. 300kP. b ~ • .li 500 .. 500 .IJ " O'~ • 200kP. ..

0 0

0 5 10 15 0 500 1000 1500 Strain 1%) p '" la. + ( 3 ) I 2 IkPa)

la' Deviator stress vs. strain curve (b) Shear strength parameters Fig. 6 .12 Determination of linear elastic properties for coarse aggregate

1000

.. ' ~ 800 -f

• • > ~ 600 ~ • " • 400 ~ • .. .IJ 200

0

0 10 Strain 1%)

20

800 .-______________ , .. ~ 600

--- 400 S

6 200 • ..

. c - 0 kPa

o I--------.- ___ -----J

o 200 400 600 800

p :::: lal + 0'3)1 2 IkPa )

la' Deviator stress vs. s train curve (b) Shear strength parameter. Fig. 6.13 Determination of linear elastic p roperties for quarry dust

125

Table 6.7 Elastic properties of coarse aggregate and quarry dust

Parameters Coarse aggregate Quarry dust

Modulus of elasticity, E (kPa) 100233 32107

Poisson's ratio, ~l 0.22 0.27

Angle of internal friction, ~ (degrees) 43 40.5

Cohesion, C (kPa) 0 0

Induced cohesion (kPa) 5.72 5.4

6.8.3 Hyperbolic constants for interface

Interface elements were used for modelling regions wherever there is soil

- reinforcement contact i.e., behind wall facing and above and below steel mesh

reinforcements. To determine the interface properties (hyperbolic constants

KJ and nl) and the angle of interfacial friction, 0, a series of modified direct

shear tests were conducted under varying normal pressures.

For the tests, a wooden block was fitted inside the lower half of the direct

shear box and a steel mesh cut to the inner dimensions of the shear box was

pasted at the top of the wooden block. The arrangement was prepared in such

a manner that the top surface coincides exactly with the surface of sliding.

Sand was filled in the top half of the direct shear box at the same density as it

is filled in the model tests.

From the results of the modified direct shear tests, for each normal

stress, shear stress vs. shear displacement curves were plotted (Fig. 6.14 (a)).

I /1 The constants {/, and J, were determined using Eqns. 6.6 and 6.7 respectively.

The initial shear modulus, k" was taken as 1 / a,l. Log - log plot was prepared

with [~.' 1 vs. (;:: .. 1 an d the hyperbolic con stan ts K' and n' were d etermin ed as

in Fig. 6.14 (b). The failure ratio, RI, was taken as the average value obtained

from the four curves. The angle of interfacial friction was obtained using the

peak values of shear stresses. The modulus of elasticity of the steel mesh was

obtained by' conducting tension test u<sing universal testing machine for

126

geotextile testing (AIMIL Ltd) . The properties of the interface and the steel mesh

are listed in Tab les 6 .8 and 6.9 respect ively.

1 20r~~ 1 ,, )OOO(

.. 100 0'11 " 109 kPa

~ 80 : u 60 1 0'., "" 8 2 .75 kPa ~ , = 40 ~ ~ fJ~~~-:~~;:~~~~ O'J 20 +

r a ., - 2 7.25 kPa

a ., ,. 54.S kPa

60000

K' 40000

ii ~ 1 • 20000 ~ -J

10000 ' , .~

o 0.5 1 1.5 2 0 .1 1

Shear displa cement (_ 10.3 ml

la) Shear .tre •• n .• hear dJ.placement curve. (b) Hyperbolic con.tanh

Fig. 6.14 Determination of non Unear ela.tic properties for

.teel me. h - sand interface

Table 6 .8 Non linear elastic properties of interface

Paramete n Values

Hyperbolic constant , KI 46338

Degree of curve, n 1 0.697

Failure ratio, Rrl 0.887

Angle of interfacial friction , 8 (degrees) 32.6

Table 6 .9 Linear elastic properties of steel mesh

Paramete" Values

Modulus of elasticity, E (k Pa) 3.33x 106

Cross sectional area, A (m2) 0.0022

Strain at breaking load 3.2 %

Secant modulus, M& (kNj m) 22 .4

127

2

6.8.4 Finite element modelling

After the determination of the essential properties for FE modelling, mesh

was prepared after mesh reftnement studies (Fig. 6.15). In the figure, the

gabion facing has been shown hatched in order to distinguish this portion from

the remaining soil elements. The mesh consisted of 962 nodes, 720 soil

elements, 56 truss elements, 112 interface elements and 144 gablon facing

elements. Boundary conditions were selected as shown in Fig. 6.15. The strip

load is given as lumped loads. The input parameters for the analysis are listed

in Table 6.10.

H .21}-j- 0.25 -l

T o. 5

0. 5

0.5

0.5

. cm thick sand la\'er 1-- 0.40 --1-- 0.35 0.15 t- .

All dimellsions in metres

Fig. 6.15 DiscretisatioD of ,_blon faced reinforced earth wall

Table 6 .10 Input data for ,ablon fac ed reinforced soU wall

Soil ~ (degreesj c (kPaj K 11 Rr K., m

39 0 479 0.61 0.84 360 0.32 Steel E kPa A {m l

mesh 3 .33 x IOu 0 .0022 Coarse •• Ide.,.ees} c . lkPaj E (kPaj " aggregate 43 5 .72 100233 0 .22 Quarry ; • Ide.,.ees) c (kPaj E (kPaj " dust 40.5 5,4 32107 0.27

Interface B Idegrees) c. (kPaj 1( ' n ' Rr I 32 .6 0 46338 0 .697 0.887 I

128

y I (kN j m 31

16

The horizontal deflections of the top point of the facing were noted for

different load increments until the system failed . The FEM results of

FECAGREW were plotted along with the experimental results for validation

purposes. Fig. 6.16 shows the load - deflection data for gabion reinforced soil

walls with different facings obtained from experiment as well as FE analysis.

Comparing both, it can be observed that the FEM results closely follow the

experimental results even upto the failure load.

o Loacl (U)

10 20 30

I -s { o _~'

-; .10 -:: . - . I ·15 ~ g PEM .. e a ult

!!l ·20 1 .(\. E:.:periment ... ault , ·25 .r

o

-25 .!

(a ) 100% C A radn a;

Load (Io:NI 10 20 30

(e) 50% QD ... 50% CA racina;

~8acl(kN~0 o 30

I ·5 .;

J · t o ';

a · 15_

-20 f .25 1

lel 100% QD raciae

I i

~ ~

o Loed (kIf)

to 20 30

(bl 30% QD ... 70% CA r.cluI

o

I -S " g · t o t

J - 15 :

~ -20 f -2.1

Load (kM) to 20 30

Idl 70% QD • 30% C A radn e

o 0

-·5 .z:

- 10 1

Loaet IkMI 10 20

, . 30

- IS ! ...•... W it tlnte .. rec:e

i- WI te .. race .20 __ Expo en.

-2S If) Eaeet or IDterrae:.

Fig. 6.16 Validation curve. for gabion faced reinforced earth wall

with different facing. - load deflection curve.

129

Fig. 6.17 shows the deflections of the fron t facing of the walls for the

different cases studied, obtained from both the experiment and finite element

analysis . In the cases, both the curves show a very close comparison in

behaviour.

! r jr! a 40. I • t j ~ I i 20 L' &l a PEII reeult i . -- EJrptlrime."t result

o " o

60_

i " rOj ~ 20

• • 0

0

o

, , 6 Oenec:tlo." (mm)

la} 100% CA fa c:l.a,

, , 6

Oenec:tlOD (mm)

8

8

le) 50% QD + 50% CA ra dD'

, 4 6 8 10

OeO.c:tlolll_)

(e) 100% QD radq

o

.o r i " ; 40 . ~ r • • ,

t 1 0

0

il .. If

, 6 8

De nec:tlon (mm)

fb) 30% QD + 70% CA rad.D,

, , 6 8 10

aen ecUo." (mm)

(et) 70% QD + 30% CA red .",

2 , --0 With lul edaca _ 6 _ Eaperlme."t ••• " ••• W t bou Inlerrace

6 8 10

De O.ctJon Imml

(f) Err.et of I."t.dace

Fig. 6.17 VaUdation curve. for gabion faced reinforced earth wall

with different facings - bulging pattern . at 60kN I m load

130

if ! • • ::l u .l! u ... .. u ::l • • • • t:

10 o 100% CA D 30% QD + 70% CA

8 r <> 50% QD + 50% CA + 70% QC + 30% CA :«: 100% QD

6 , 0

Cl>

4 , 0 D

:I: ID

o .---~----~--~----~----

o 2 4 6 8 Experimenta l de flection (mm)

Fig. 6 .18 Load - deflection data:

Comparison between theory and experiment

10

o

0 100% CA

o 30% QC + 70% CA

0 50% QD + 50% CA

'+ 70% QD + 30% CA

X 100% QC

2 4 6 8 10 Experimental deflection (mm)

Fig. 6.19 Facing deflection data:

Comparison between theory and experiment

132

10

6.9 SUMMARY

The finite element code developed by the author was successfully tested

for its performance at each stage of its development. The details regarding the

testing have been described elaborately in this chapter. Each component of

modelling, namely, the individual performance of the different elements, the

non linear behaviour of soil and interface, the simulation of construction

phases, the confinement of gabion boxes etc., have been tested step by step

systematically. All the test results show encouraging results and hence it may

be concluded that FECAGREW may be effectively used as a prediction tool for

simulating the behaviour of gabion faced reinforced earth walls.

133