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Numerical simulation of an instrumented cantilever retaining wall

Article  in  Canadian Geotechnical Journal · August 2011

DOI: 10.1139/t11-037

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Numerical simulation of an instrumentedcantilever retaining wall

Ashok K. Chugh and Joseph F. Labuz

Abstract: The field data of an instrumented cantilever retaining wall are reexamined to develop a working hypothesis forthe mechanism that explains the observed response. The field data are in terms of earth pressures and wall movements (de-flection, translation, and rotation) from the start to completion of backfilling. The observed response demonstrates strong in-teraction between the retaining wall and foundation soil. Traditional calculations based on earth pressure coefficients hadnot provided a satisfactory explanation for the measured responses during placement of backfill. In this paper, the workinghypothesis, and results from its implementation in a continuum-mechanics-based computer program are presented. The nu-merical model results, displacements and earth pressures, are in general agreement with the field data for all stages of back-fill placement and provide a clear exposition to the observed response. Practical implications of the work are included.

Key words: retaining wall, field instrumentation, earth pressure, numerical modelling and analysis, soil–structure interaction,case history.

Résumé : Les données de terrain d’un mur de soutènement cantilever instrumenté sont réétudiées afin de développer unehypothèse de travail sur le mécanisme qui expliquerait le comportement observé. Les données de terrain incluent les pres-sions des terres et les mouvements du mur (déflection, translation et rotation) depuis le début et jusqu’à la fin du rem-blayage. Le comportement observé démontre une forte interaction entre le mur de soutènement et le sol de fondation.Cependant, les calculs traditionnels basés sur le coefficient de pression des terres n’ont pas permis d’obtenir une explicationsatisfaisante des comportements mesurés durant le placement du remblai. Dans cet article, l’hypothèse de travail et les résul-tats de son implantation dans un programme informatique basé sur la mécanique des milieux continus sont présentés. Les ré-sultats de la modélisation numérique, incluant les déplacements et les pressions des terres, correspondent bien avec lesdonnées de terrain pour toutes les étapes du remblayage, et offrent une présentation claire du comportement observé. Lesimplications pratiques de ces travaux sont présentées.

Mots‐clés : mur de soutènement, instrumentation de terrain, pression des terres, modélisation et analyse numérique, inter-action sol–structure, historique de cas.

[Traduit par la Rédaction]

IntroductionIn 2002–2003, the Minnesota Department of Transporta-

tion (Mn/DOT) constructed a new 0.8 km long poured-in-place reinforced concrete cantilever retaining wall on thesouth side of I-494 near West Bush Lake Road crossing inBloomington, Minnesota (latitude N 44°51′36″, longitudeW 93°22′36″). The wall consists of eighty-three 9.3 mwide panels, designated A–CE. Individual panels are sepa-rated by 13 mm thick cork expansion joints, but they areconnected to one another through vertically spaced (in0.3 m increments) smooth, epoxy-coated steel dowels. Thepanel heights range from 3.96 to 7.92 m. The retainingwall has a spread footing and a shear key founded on soil.Figure 1 shows the location of the wall and the arrangementof panels.

As a part of the regular construction of the wall (Minne-sota Department of Transportation 2002), one of the panels,panel BJ, was fitted with instruments to measure (i) earthpressure on the wall and (ii) movement of the wall duringbackfilling. The objective of the instrumentation programwas to gain a better understanding of the design methods,construction materials, and construction procedures, whichmay reduce the cost of retaining walls, bridge abutments,and their foundations (Bentler et al. 2005). Figure 2 showsthe layout of instruments that provided the wall responsedata, and consists of nine earth pressure cells (EPC), five tilt-meters, and four survey reflectors. Data from EPCs and tilt-meters were collected every 15 min for the first week ofbackfilling and 30 min after the first week for over12 months; the survey data were collected at discrete timesduring the backfilling, which was completed in about 8 con-struction days spread over a month.Bentler et al. (2005) and Bentler and Labuz (2006) inter-

preted the measured data at select stages of backfilling to de-scribe (i) the wall behaviour (translation, rotation, lateralearth pressures on the wall stem, footing toe and shear key,and vertical stresses under the wall footing) based on classi-cal active and passive earth pressure theory and (ii) wall de-formations based on beam theory and rigid body rotation and

Received 20 August 2010. Accepted 15 June 2011. Published atwww.nrcresearchpress.com/cgj on 29 August 2011.

A.K. Chugh. US Bureau of Reclamation, Denver, CO 80225,USA.J.F. Labuz. Department of Civil Engineering, University ofMinnesota, Minneapolis, MN 55455, USA.

Corresponding author: A.K. Chugh (e-mail: Achugh@usbr.gov).

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translation of the wall footing. A discussion by Neely (2007)and closure were about peculiarities in the observed behav-iour at various stages of the backfilling. These attempts didnot provide a complete picture of wall behaviour duringplacement of backfill.The objectives of this paper are to present

1. a working hypothesis, based on the construction sequenceused in the field, for the mechanism that explains themeasured data, displacements and earth pressures, at allstages of backfilling;

2. results, deformations and earth pressures, of numerical si-mulation based on the working hypothesis implementedin a continuum-mechanics-based computer program;

3. comparisons of computed deformations and earth pressureswith the measured data; and

4. recommendations for engineering practice.For the objectives of this paper and to conserve space,

only relevant details about the project and field instrumenta-tion are included herein; other details and plots of nearly con-tinuous data are available in Bentler et al. (2005). For ease ofpresentation, the two-dimensional cross section of the wallgeometry is referenced in x–z plane, and the x, y, z coordi-nate system used follows the right-hand rule; u, v, w refer to

displacements in the x, y, z coordinate directions, respec-tively — positive displacements are in the positive coordinatedirections, and positive rotation is clockwise; EPC data andcomputed stresses are presented as positive values. Imperialunits were used on the project; field data were converted tometric units and conveniently rounded for analysis.

Site conditions and instrumentation data

From two drill holes, the following conditions were esti-mated to apply below the wall footing of panel BJ: (i) depthto ground water to be 1–1.5 m; (ii) average blow count fromstandard penetration test to be 35 blows/ft (1 ft = 30.48 cm)in sandy soils (SP–SM by the Unified Soil ClassificationSystem (ASTM 2006)) and 20 blows/ft in SC–SM soils;(iii) average moisture content to be 12%; and (iv) depth tothe bedrock to be >7 m. The soils placed behind the wall(backfill) and in front of the wall (frontfill) were poorlygraded medium to fine sand (SP) with unit weight g =18.9 kN/m3, angle of internal friction 40 = 35°–39°, and co-hesion c′ = 0.Figure 1c shows the before- and after-construction ground

levels along the wall length, including panel BJ. After site

Fig. 1. Project location map and details of the retaining wall under study: (a) state map showing the project location; (b) aerial view; (c) wallpanels.

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preparation for the wall construction, excavation of the trenchfor the wall footing extended to the bottom of the shear keyand was backfilled to the bottom of the footing using thebackfill material and compacted using a 103 kN smooth-wheel vibratory roller. A trench for the shear key was exca-vated using smaller excavation equipment (backhoe). Afterthe wall construction, the frontfill was placed prior to place-ment of the backfill and compacted (less rigorously than thebackfill). The backfill was dumped by trucks, spread by bull-dozers into 0.2 m thick layers, and compacted using the vi-bratory roller to achieve the desired density. If necessary,water was added between lifts to achieve optimum moisturecontent. A typical construction day was from 0800 to 1700Monday through Friday, with no construction on the week-end. Backfilling for panel BJ was completed during about 8construction days spread over a month. See Bentler et al.(2005) for construction activity log of panel BJ.All instruments were set to zero at the start of the backfill

placement above the top of the wall footing, i.e., starting withzero backfill against the wall stem as the null reference statefor all instrument readings. Figure 3 shows plots of the meas-ured data for the backfill placement in 0.3 m incrementsagainst the wall stem; the value for each of the 0.3 m incre-mental stage was calculated by linear interpolation between

two consecutive backfill heights in the instrumented data,and in the event of multiple readings for a particular backfillheight, the last recorded value for that backfill height wasused. For the tiltmeters and the survey reflectors located off-center (but symmetric) to the center line of the wall panel,the arithmetic mean of the measured values were used.Peculiarities in the measured data during placement of the

backfill include the following: (i) EPCs located at higher ele-vations on the wall stem (with smaller backfill depth) gavehigher lateral earth pressures than EPCs located at lower ele-vations (with larger backfill depth); (ii) the EPC located inthe heel area gave higher vertical pressure than the EPC inthe toe area, and the EPC located on the toe gave higher lat-eral earth pressure than the EPC in front of the shear key;(iii) tiltmeter located at the base of the wall stem showedwall rotation towards the backfill for all stages of backfilling,while the tiltmeters located near the top of the wall showedwall rotations towards the backfill during the initial 5 m ofbackfilling followed by wall rotation away from the backfillfor the rest of the backfilling. Tiltmeters located at intermedi-ate locations on the wall stem showed rotations opposite indirection than the rotations observed at the top of the wall;(iv) average of the four survey reflectors showed wall trans-lation away from the backfill for all stages of backfilling.

Fig. 2. Wall panel BJ and instrument locations (adapted from Bentler and Labuz 2006, with permission from the American Society of CivilEngineers (ASCE)): (a) front face with tiltmeter and survey reflector locations; (b) cross section with EPC locations.

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Working hypothesisThe measured wall movements and earth pressures on the

wall stem and under the footing (Fig. 3) are far too differentin trends and magnitude than those commonly understood(linear increases in earth pressure with depth, monotonicwall rotations away from the backfill, and soil pressure underthe toe to be higher than under the heel) to be due to com-paction effects during construction or relaxation during off-construction periods. A different mechanism must be respon-sible for the measured response data. This conviction for adifferent mechanism resulted in development of the followingworking hypothesis based on the wall being founded on soiland the construction sequence used:

1. Site preparation for the construction of the retaining wall(excavation of in-place soils) causes displacement re-bound (heave) and stress relief in the foundation soil.

2. Construction of the retaining wall counters (to some extent)the effects of step 1.

3. Placement of the frontfill causes the wall to rotate forward(away from the backfill).

4. Placement of the backfill in layers counters the effects ofstep 3 incrementally. However, there is a strong interac-tion between the increasing lateral force from the backfill,increasing differential vertical displacement in the founda-tion soil, increasing translation of the wall including thefoundation slab, and increasing passive force from thefrontfill.

5. Compaction of the backfill with vibratory roller adds tothe magnitude of forces and movements of the wall in-cluding the footing (envisioned in step 4).

6. Stoppage of the backfilling during no-construction durationsresults in readjustment in stresses in the backfill andfoundation soils, and in the wall movements (transla-tions, displacements, and rotations).

7. Magnitude of wall movements and forces on the wall (fromthe backfill and frontfill) are affected by the material be-haviour.

Fig. 3. Measured instrument data on the prototype wall for 0.3 m increments in backfill height (Bentler et al. 2005): (a) wall stem and backfillEPCs; (b) wall footing EPCs; (c) tiltmeters; (d) survey reflectors.

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In terms of importance, (i) items 1 and 2 of the workinghypothesis were considered unimportant because the weightof soil excavated (approximately 1550 kN/m) is counterbal-anced by the weight of the retaining wall and the fill soil (ap-proximately 1425 kN/m); (ii) items 3 and 4 were consideredimportant; (iii) items 5 and 6 were thought not to be the pri-mary contributors to the gross differences between the ob-served and expected behaviour; (iv) for item 7, materialbehaviour was assumed to be elastoplastic.

ImplementationThe working hypothesis for the prototype wall behaviour can

be implemented in essentially any continuum-based analysisprogram. For the retaining wall problem presented in this paper,the commercially available software FLAC (Itasca ConsultingGroup 2006) was used, and its adoption was for convenience.

Numerical model

Figure 4 shows the 2D FLAC model of the prototype wallpanel BJ used for analysis. Materials included in the modelare as shown in Fig. 4a. The constitutive model for the soilis elastoplastic, with a Mohr–Coulomb yield condition and anonassociative (dilation angle equals 0) flow rule; the rein-forced concrete is linearly elastic. Contacts between differentmaterials are modelled as interfaces. The water table is notincluded in the numerical model. The discretization andboundary conditions used are shown in Fig. 4b. The samplelocations shown on Fig. 4b correspond to the field instrumentlocations shown in Fig. 2. The vertical grid line passingthrough the heel of the footing is drawn darker than the restof the grid lines in Fig. 4b — computed horizontal and verti-cal stresses along this line are used in engineering practice

Fig. 4. Numerical model: (a) material identifications; (b) model details; (c) backfill placement stages.

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for design of retaining wall and are included in this paper. Place-ment of the backfill was modelled in 26 lifts, one lift per gridspacing in the z direction. Figure 4c shows the start of backfill-ing against the wall stem (stage_0), a typical intermediate back-filling stage (stage_j), and the end of backfilling (stage_26).Material and interface properties used in the numerical

model are shown in Tables 1 and 2, respectively. For thebackfill, the density is based on field measurements of unitweight; the angle of internal friction was set at 40°. The elas-tic properties were estimated from bender element testing ofsimilar granular soils. For the foundation soil, the propertieswere assumed. For the reinforced concrete, standard proper-ties for concrete with compression strength of 28 MPa wereadopted. All material property values were selected prior toanalysis (they were not adjusted during modelling). Paramet-ric analyses, by varying material properties values, were notconsidered necessary, considering the primary emphasis ofthe numerical model was to check the validity of the workinghypothesis in explaining the wall behaviour at intermediateheights of the backfill as observed via the field instrumentation.Numerical analyses were performed in plane strain

(3yy ¼ 0) mode (panel BJ has two adjacent panels of equaldimensions — see Fig. 1c). The model was analyzed for thefollowing three phases: phase a, the model has only the foun-dation soil without the shear key slot; phase b, the retainingwall, frontfill, and backfill to the top of the wall footingadded to phase a; phase c, placement of backfill in 26 liftsadded to phase b. For the objectives of this paper, resultsfrom phases b and c are presented in detail; for phase a, itsuffices to say that the state of stress in the model was elasticand the slope stability analyses using FLAC resulted in acomputed factor of safety (FS) of 1.40. For comparison, forphase b, the state of stress is elastic, and the computed FS =1.46; and for phase c with completed backfill, the state ofstress is essentially elastic, and the computed FS = 1.24. Inthe FLAC model, displacements are calculated at the gridpoints and stresses at the centers of the zones. The computedstresses at grid points were taken to be the average of thestresses in the adjacent zones.

Computed results

Figure 5a shows the progression of wall stem configura-tion (computed u displacements) at the end of each of the 27backfill placement stages (stage_0 to stage_26); Fig. 5bshows the corresponding progression of footing configuration(computed w displacements). These results show the overallbehaviour of the prototype wall during the backfilling asshown in Table 3.Figure 6 shows the computed results at sample locations

on the model wall, which correspond to the instrument loca-tions on the prototype wall, and similar behaviour is de-picted. Specifically, Fig. 6a is for the u displacements at foursample locations corresponding to the five tiltmeter loca-tions — only one sample location is used for tilt_25E andtilt_25W. An average of u displacements at sample locationscorresponding to the four survey reflector locations is in-cluded in Fig. 6a. Figure 6b is for the computed earth pres-sure at the sample locations corresponding to the EPClocations on the wall stem and the backfill; Fig. 6c is for thecomputed earth pressure results at the sample locations corre-sponding to the EPC locations on or below the wall footing.Noteworthy observations include the following:

• From Fig. 6a: strong soil-structure interaction between thewall and soil media occurs for backfill height from 0.5 to2.6 m during which a complete reversal of u displacementpattern occurs, i.e., for a given backfill height, u < 0 and |u|decreases in the +z direction.

• From Fig. 6b: earth pressure variations at sample locationson the wall stem are not monotonic; instead, typically, aninitial earth pressure increase is followed by a drop inearth pressure that later begins to increase again. Specifi-cally, for backfill height from 1.7 to 3.2 m, earth pressureat EPC_5 is higher than that at EPC_1. Similarly, for back-fill heights from 3.4 to 4.4 m, earth pressure at EPC_10 ishigher than that at EPC_5; and for backfill heights from5.0 to 5.9 m, earth pressure at EPC_15 is higher than thatat EPC_10. For backfill heights from 3.5 to 4.1 m, earthpressure at EPC_10 comes close to being equal to that at

Table 2. Interface properties (all interfaces were assumed to be glued).

Interface LocationNormal stiffness,kn (kPa/m)

Shear stiffness,ks (kPa/m)

1 Between backfill and foundation soil 5.0 × 103 1.0 × 103

2 Between backfill and wall stem 1.7 × 104 4.4 × 103

3 Between foundation soil and footing 1.0 × 104 1.0 × 104

4 Between frontfill and wall stem 3.5 × 104 1.0 × 104

5 Between frontfill and foundation soil 1.0 × 104 6.0 × 103

Table 1. Material properties.

Elastic constants Material strength

Material identifierDensity, r(kg/m3)

Bulk modulus,K (kPa)

Shear modulus,G (kPa)

Cohesion,c (kPa)

Friction angle,4 (°)

Concrete 2400 1.6 × 107 1.4 × 107 N/A N/ABackfill 1920 1.0 × 105 3.8 × 104 0 40Frontfill 1800 7.0 × 104 2.6 × 104 0 36Foundation soil 1600 3.5 × 104 1.3 × 104 10 30

Note: Unit weight (g), density × gravity; tensile strength, c=tan4; N/A, not applicable.

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Fig. 5. Computed results for the 27 backfill placement stages (Fig. 4c): (a) horizontal displacements of the wall stem, reference line (RL) is atu = 0; (b) vertical displacements of the wall footing, RL is at w = 0.

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EPC_1. For backfill heights from 3.0 to 4.4 m, earthpressure at EPC_10 is higher than that at EPC_bf.

• From Fig. 6c: earth pressures at sample locations on or be-low the wall footing are not monotonic; instead, initialtrends in earth pressures are reversed during additionalbackfilling. For example, initially, vertical stress atEPC_front is greater than that at EPC_back. However,this trend reverses for backfill heights from 1.3 to5.4 m, and reverses again for backfill height >5.4 m.Also, initially, earth pressure at EPC_key is greater thanthat at EPC_toe. However, this trend reverses for backfillheight >1.7 m.One set of computed results, near field instrument loca-

tions, were deduced from the FLAC model results for directcomparison with the measured responses for all stages ofbackfilling. This was accomplished by subtracting stage_0results from the corresponding stage_1 to stage_26 results.Figure 7 shows plots of the deduced and the correspondingmeasured responses. Considering the crude bases for thiscomparison, it suffices to say that the numerical results cap-ture the trends of the measured data.In summary, the numerical model provides an explanation

of the observed behaviour patterns of the prototype wallshown in Fig. 3. This favourable agreement gives credenceto the validity of the working hypothesis in understandingthe complex interaction between the wall, the foundation soil,the frontfill soil, and the backfill soil during the backfilling.

Implications for engineering practice

Figure 8 shows the FLAC results in terms of earth pressurecalculations typically performed for a cantilever retainingwall in engineering practice. Figure 8a shows the normalstress (|sn|) against the wall stem along its contact with thebackfill; and horizontal and vertical stresses (|sxx| and |szz|,respectively) along the z axis passing through the heel of thewall footing. Figure 8b shows the computed earth pressurecoefficients along the wall height. For comparison, nominalvertical stress (gz), and at-rest (K0gz, where K0 is the at-restearth pressure coefficient) and active (Kagz, where Ka is theactive earth pressure coefficient) lateral earth pressures aresketched in Fig. 8a. Similarly, the Ka and K0 for 40 = 40°,and the ratio of sxx/(gz) are sketched in Fig. 8b. Notable ob-servations include the following:

1. Horizontal stresses along the vertical plane through the heelagree well with the normal stresses along the wall–backfillinterface. This result supports the engineering practice ofcalculating earth pressure on the vertical plane throughthe heel for use in evaluation of stability of a cantileverretaining wall and in determining moments and forces for

design of reinforcement. Horizontal stress (sxx) in thebackfill deviates very little from the linear variation im-plied by the use of a single value of earth pressure coeffi-cient. Therefore, continued use of a triangular distributionof lateral earth pressure for wall design is appropriate.

2. Vertical stress (szz) in the backfill deviates significantlyfrom the geostatic distribution (gz) generally assumed,based on z direction being a principal stress direction.However, for retaining walls founded on soil, verticaldisplacements in the backfill are nonuniform, whichcause shear strains and result in rotation of principalstress directions. Thus, part of the gravity stresses in thebackfill soil is carried by shear stresses in the soil mass.However, the geostatic distribution is conservative.

3. The distribution of computed lateral earth pressure liesbetween the active and at-rest earth pressure lines —this is due to Poisson’s ratio of soil (y = 0.33). For de-sign of cantilever retaining wall on individual projects,appropriateness of calculating lateral earth pressurebased on Kgh for Ka ≤ K ≤ Kp should be carefully as-sessed (K is the earth pressure coefficient, h is the back-fill height, and Kp is the passive earth pressurecoefficient). For significant earth-retaining structuresfounded on soil, it is suggested that lateral earth pres-sure for design be calculated both ways, i.e., using dis-placement-based analysis and results compared with thevalues obtained using earth pressure coefficients — the fi-nal selection of design load should be a deliberate effort.

4. The calculated value of lateral earth pressure coefficient(sxx/szz) varies along the wall height because of the non-linear variation in vertical stress. Using the geostatic dis-tribution of vertical stress and the computed horizontalstress, (sxx/gz), the average value of K is 0.323. For com-parison, the at-rest earth pressure coefficient for planestrain (y/1 – y) is 0.5, and by the relation (1� sin4), it is0.357, and by the active earth pressure coefficient, it is0.217 using (1 – sin4)/(1 + sin4). The numerical model re-sults indicated that the material response is largely elastic.Figure 6c shows the FLAC analysis results for the resist-

ance to sliding and overturning typically needed in calculat-ing the corresponding factor of safety. Notable observationsinclude the following:

1. The soil in front of the footing and the shear key offersubstantial resistance against sliding. Therefore, place-ment of frontfill soil and a well-proportioned shear keyfor retaining walls with spread footings founded onwell-compacted soil are good engineering practices(Teng 1962). However, this is contrary to the responsemeasured in the field, as the actual construction detailsare critical.

Table 3. Overall behaviour of the prototype wall during the backfilling.

Stage_Backfillheight (m) Movement mode

0 0 Wall and base translate and tilt forward (away from the backfill)1–2 0.2–0.5 Heel of the base settles and the wall rotates backward (towards the backfill)3–11 0.8–3.2 Above mechanism continues, but the wall also starts to translate away from the backfill12–15 3.5–4.4 Base essentially horizontal and continues to settle; wall flexure and translation dominate16–26 4.7–7.92 Base and wall rotate forward; settlement, flexure, and translation continue

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2. The vertical stress in the foundation soil is uniform acrossthe footing width. Therefore, use of common proportionsof cantilever retaining walls is a good engineering prac-tice (Teng 1962).

General comments

Based on the analyses presented, the following commentscan be made:

1. The results included in Figs. 5 and 6 demonstrate that asimple elastoplastic model for soil behaviour withMohr–Coulomb failure criterion and nonassociative flowrule is successful in explaining the fairly complex inter-action between the concrete retaining wall and the sur-rounding soil media using tested or commonly acceptedpublished property values for soils and reinforced con-crete. Earth pressure calculations based on earth pressurecoefficients are the simplest but fail to explain the ob-served response at the various stages of backfilling.This comment serves as a reminder of the importanceof starting a numerical model study of a geotechnical pro-blem with the simplest procedure and incrementally add-ing to the complexity of the solution procedure, if needed.

2. Earth pressure calculations based on linear distribution ofvertical stress (szz = gh for 0 < h ≤ H, where H is thewall height) and corresponding horizontal stress on theretaining wall based on earth pressure coefficient (sxx =Kgh for Ka ≤ K ≤ Kp) is the simplest and commonlyused procedure for estimating earth pressure loads for re-taining wall design. However, this procedure does not ac-count for the incremental loading from the placement ofthe backfill. For such problems, a resort to numericalmodelling that takes account of the retaining wall, sur-rounding soils, and soil placement sequence is essential(Goodman and Brown 1963). The observed behaviourshown in Fig. 3 demonstrates complex soil-structure interac-tions for a seemingly simple retaining wall founded on soil.

3. No attempt was made to calibrate the numerical model toachieve a match with the field data. Instead, (i) a workinghypothesis was developed on the basis of the constructionsequence; (ii) material properties for use in numericalanalysis were selected based on site-specific field mea-surements of unit weights, laboratory tests for soil grada-tion (sieve analysis) and strength (triaxial tests), andavailable data for similar soils; (iii) one complete set ofanalyses using a continuum-based analysis procedure(FLAC) was performed; and (iv) the results of numericalanalysis were interpreted to assess the validity of theworking hypothesis and for comparison with the field in-strumented data.

4. The results reported in this paper capture the essence of thefield data about the wall behaviour; although the matchcould be improved. A better understanding of the foun-dation conditions is required to improve the numericalresults. Additional analyses that incorporate initial exca-vation, wall construction, compaction during backfilling,and relaxations during overnight hours and weekendsshall be an improvement. However, these details willadd to the complexity of the analysis and are not con-sidered in this paper.

Fig. 6. Computed results at sampled locations (Fig. 4b): (a) horizon-tal displacements near tiltmeter and survey reflector locations;(b) lateral earth pressures near wall stem and backfill EPCs; (c) lat-eral and vertical earth pressures near wall footing EPCs.

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ConclusionsThe results of the numerical simulation of the prototype wall

show that it is essential to implement significant aspects of ageotechnical problem in a numerical model in order for theanalysis results to be useful. For the cantilever wall, the signifi-cant aspects were (i) soil foundation, (ii) placement of frontfillprior to start of backfilling, and (iii) incremental backfilling.

For significant earth-retaining structures founded on soil,lateral earth pressure for design should be calculated using dis-placement-based analysis and results compared with the valuesobtained using earth pressure coefficients — the final selectionof design load should be a deliberate effort. Continuum-mechanics-based numerical analysis procedures provideeffective and efficient means to study complex interactions

Fig. 7. Comparison of deduced results with the measured responses: (a) EPC_1 and EPC_5; (b) EPC_10 and EPC_15; (c) EPC_bf;(d) EPC_toe and EPC_key; (e) EPC_front and EPC_back; (f) survey reflectors.

1312 Can. Geotech. J. Vol. 48, 2011

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between different components of a geotechnical problem.For the cantilever retaining wall, FLAC analysis results pro-vided a clear exposition to the observed responses. For ex-perimental work, it would be helpful to make a numericalmodel study along with the instrument calibration work togain an insight into the expected response of the structure.

AcknowledgementsThe authors would like to express their sincere thanks to the

Minnesota Department of Transportation (Mn/DOT), especiallyDavid Van Duesen and Michael Beer for providing the con-struction drawings; Richard Lamb for providing the soil borings;Jihshya Lin, Gary Peterson, and Eric Wolhowe for providing thestructural details. The findings and conclusions expressed in thispaper are those of the authors and not necessarily those of Mn/DOT. Also, the authors would like to thank Professors PeterCundall and Michel Aubertin for their prompt responses to au-thors’ enquiries on the general subject matter of this paper.

ReferencesASTM. 2006. Standard practice for classification of soils for engineering

purposes (Unified Soil Classification System). ASTM standardD2487.American Society for Testing and Materials, West Conshohocken, Pa.

Bentler, J.G., and Labuz, J.F. 2006. Performance of a cantilever retainingwall. Journal ofGeotechnical andGeoenvironmental Engineering, 132(8): 1062–1070. doi:10.1061/(ASCE)1090-0241(2006)132:8(1062).

Bentler, J.G., Labuz, J.F., and Schultz, A.E. 2005. Earth pressurebehind a retaining wall. Report No. 2005-14 [online]. MinnesotaDepartment of Transportation, St. Paul, Minn. Available fromwww.lrrb.org/pdf/200514.pdf [accessed 21 July 2011].

Goodman, L.E., and Brown, C.B. 1963. Dead load stresses andinstability of slopes. Journal of the Soil Mechanics and Founda-tions Division, SM3: 103–134.

Itasca Consulting Group. 2006. FLAC — Fast Lagrangian Analysisof Continua [computer program]. Itasca Consulting Group,Minneapolis, Minn.

Minnesota Department of Transportation. 2002. Construction plan forState Project No. 2785-332. Minnesota Department of Transporta-tion (Mn/DOT), Eden Prairie, Minn.

Neely, W.J. 2007. Discussion: Performance of a cantilever retaining wall.Journal of Geotechnical and Geoenvironmental Engineering, 133(12):1631–1634. doi:10.1061/(ASCE)1090-0241(2007)133:12(1631).

Teng, W.C. 1962. Foundation design. Prentice Hall, Inc., EnglewoodCliffs, N.J.

Fig. 8. Computed results in terms of earth pressure calculations inengineering practice: (a) earth pressure on the model wall and verti-cal pressure in the backfill; (b) earth pressure coefficients.

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