Evaluation Of Group Factor Method For Analysis Of Pile Groups

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m. The pile head condition was free head. The pile group was horizontally pushed to target deflectionsof 0.006, 0.013, 0.019, 0.025, 0.038, and 0.051 m and pile head forces are measured. Christensen’s testresults are used for the continuum model validation in our study.2.1. Continuum modelThe pile group response is simulated here using FLAC3D (Itasca, 2009) as a continuum model. Mohr–Coulomb with a non-associated flow rule (ψ 0) is used as the constitutive model for soil. Christensenmodeled his pile group test in the GROUP program (Reese et al., 2010) using p–y approach. The soilprofile in our continuum model is divided into eight layers, as was suggested in the Christensen’s p–ysimulation of the test. Table 1 illustrates soil properties for the model. For elastic properties of the soil,the average soil’s Young’s modulus for each layer is derived from Christensen’s reported CPT testresults using equation Es 7qc (Bowles, 1996), where Es is soil Young’s modulus and qc is conepenetration resistance. Poisson's ratio is assumed to be 0.3 for all layers. Shear modulus and bulkmodulus are calculated using the Young’s modulus and the Poisson's ratio. Unit weight, friction angle,and cohesion for this continuum model are the same as those of Christensen’s p–y model. The soilparameters for our continuum model are shown in Table 1. Figure 2 shows the measured andcomputed total pile head force at different pile head target deflections.Table 1. Input soil properties for the continuum modelDistance from groundsurface to top of eachsoil layer (m)Unitweight(kN/m3)0Constitutive model 26154900033001400Total pile head force (kN)12001000800600400Measured200Computed000.010.02 0.03 0.04Target deflection (m)0.050.06Figure 2. Total pile head force of the pile group at different targetdeflections from the test and the continuum model

Profiles of bending moments at the target deflections of 0.006 m and 0.051 m are depicted in Fig. 3.Comparisons between the model and the full scale test results show that the continuum model for thistest is reliable enough to explore the effects of different parameters on pile group response. Forcomplete details of this model validation see Fayyazi et al. (2012).-1051 mmDepth (m)16 mm2345Measured6Computed7-50050100150Moment (kN.m)200250Figure 3. Bending moment profile for the middle pile at differenttarget deflections from the test and the continuum model2.2. p–y modelAs it was mentioned before, Christensen (2006) modeled his test in the GROUP program using API p–y approach. The computer program GROUP is widely used in practice. He also simulated his singlepile test using p–y approach. He divided the soil profile to eight layers and he only calibratedproperties of the first layer of soil in his p–y model using the results of his single pile experiment to geta match on displacement. He used these calibrated parameters for the pile group p–y simulations. Hissoil properties for the p–y model are used in this study as described in Table 2. In this table ε50 is thestrain at 50% of the undrained shear strength. The GROUP program calculates the response for agroup of piles using desired input p-multipliers. The same procedure of Christensen (2006) is used toobtain the p-multipliers. In their procedure the p-multipliers are required as input to the program andthen they are modified until the computed displacements from the GROUP program match themeasured experimental results for the same pile head force. This procedure is repeated for differenttarget deflections. In this study instead of experimental results we used our continuum analysis resultsto obtain the p-multipliers then we compare the obtained p-multipliers with Christensen’s p-multipliersto investigate reliability of our procedure for obtaining p-multipliers and also to investigate how muchdifference in p-multipliers we get. Figure 4 shows the pile arrangement in a 3 3 group. The calculatedp-multipliers for different target deflections and the average p-multipliers for each row of the pilegroup are presented in Table 3. The average p-multipliers for this pile group are 1.01, 0.74 and 0.61for row #1, row #2, and row #3, respectively. These values are in a good agreement with Christensen’s(2006) values of 1, 0.7, and 0.65 which are obtained using the pile group full scale test and theGROUP program. This confirms the fact that the p-multiplier for a leading row is higher than the pmultiplier for trailing row. It is noted that in one case the p-multiplier slightly exceeded unity. Thismeans in that case API p–y curves were softer than the continuum model so it needed to be stiffened.From these comparisons it can be concluded that our continuum and p–y models are reliable forsimulating behavior of pile groups. In the next step a parametric study has been conducted toinvestigate reliability of using group factor for pile group analysis.

Table 2. Input soil properties for the p–y model (Christensen, 2006)Distance from groundsurface to top of each soillayer (m)EffectiveUnit .5E433--Row #3Row #2Row #1Middle pilesSide pilesLoadFigure 4. Pile group arrangementTable 3. Calculated p-multipliers for each row of the pile group using the p–y model and the continuummodelRow#1Row#2Row#3Pile headdeflection (m)Force (kN)0.0250.0380.051258327369Pm1.001.030.99Avg. :1.01Force (kN)PmForce 630.613. PARAMETRIC STUDYAs discussed in Section 1, rather than defining p-multipliers row by row, a group factor is used inpractice for the pile group analysis. Different 3 3 pile groups with different Spacing over pileDiameter ratios (S/D) of 3, 4 and 5 are analyzed using both continuum model and p–y model. Pilegroup dimensions are depicted in Fig. 5. The soil profile for this study is the same as soil profiledescribed in Section 2. Spacings in both directions are the same for each pile group. In the continuummodel, the same target deflection at the pile head is applied on all of the piles. Total force at the pilehead is calculated and then this force is applied on the head of the pile group in p–y model. The groupfactor is introduced as input to the GROUP program and then it is modified until the computed totalpile head deflection for that spacing matches the applied pile head deflection in the continuum model.This procedure is repeated for 3 pile head target deflections (0.03, 0.04 and 0.05 m). In the next stepthe average of the group factors is calculated and introduced as group factor for that pile group.Calculated group factors for the pile groups with S/D of 3, 4 and 5 are presented in Table 4. The groupfactor increases with the increase of pile spacing; this happens because the group effect decreases withthe increase of pile spacing in the pile group.

02244Depth (m)Depth (m)06p-y model using group factor86p-y model using group factor8Continuum - Row #1Continuum - Row #210Continuum - Row #1Continuum - Row #210Continuum - Row #304080Moment (kN.m)Continuum - Row #312004080Moment (kN.m)120(a)(b)Figure 6. Bending moment profile at target deflections of (a) 0.03 m and (b) 0.05 m for the side piles of a pilegroup with the spacing of 3DRow #170Maximum bending moment difference (%)Maximum bending moment difference (%)Figure 7 depicts the differences between calculated maximum bending moment using continuummodel and using p–y model for different piles in the pile groups with different pile spacings.Comparing the amount of these differences at different target deflections shows that with increasingthe pile head deflection this difference decreases for almost all of the piles in the group. This reductionis more significant for pile groups with lower spacing. In all cases trailing rows (rows #2 and #3) havehigher differences than leading row (rows #1). In all of the pile group configurations with differentlevels of loading, maximum bending moments are overestimated for trailing rows. However, for row#1 the difference is within fairly acceptable range. As it is shown in Figure 6 leading row always hasthe highest bending moment, therefore in practice engineers design the piles for maximum bendingmoment of the leading row.Row #260Row #350403020100-10234S/D ratio(a)56Row #170Row #260Row #350403020100-10234S/D ratio56(b)Figure 7. Difference of maximum bending moment at target deflections of (a) 0.03 m and (b) 0.05 m versus pileSpacing/Diameter ratio

Figure 7 illustrates that the amount of difference for piles in the leading row is less than other piles andit is within fairly acceptable range, therefore it can be concluded that the group factor can predict themaximum bending moment for the leading row with acceptable difference. Figure 7 also shows thatwith increase of spacing, the difference of maximum bending moment between two models decreasesfor the row #3 at lower deflection. For row #2 at lower deflection this difference does not changesignificantly with increasing of pile spacing but for higher deflection this difference increases. FromFig. 7 (a,b) it can be concluded that with increase of spacing the amount of difference in maximumbending moment between p–y model and continuum model for trailing rows (rows #2 and #3) reachesto the similar value for different target deflections.4. SUMMARY AND CONCLUSIONA continuum model is validated based on a full scale test which was conducted by Christensen(2006). Group factor for pile groups with different spacings are then calculated based on this validatedcontinuum model approach and the corresponding p–y models. The results are used for study thereliability of using group factor for analysis of pile groups with different pile spacings. The same pilehead deflection is applied on the p–y model and the continuum model and pile head force and bendingmoment along the pile shafts are calculated for each pile. It is observed that with increase of theloading level the difference of maximum bending moment between continuum model and thecorresponding p–y model decreases. This evaluation also shows that f

The nonlinear springs are defined using API p–y curves at regular depth . intervals, where p represents the lateral soil resistance per unit length of the pile and y is the lateral deflection of the pile (API, 2007). As it was discussed before response of a single pile is different from response of a pile in a pile group due to group effect. One of the most common methods of accounting for .

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