Oct 6, 2008 - parameters are used for undrained analysis. ... analysis using beam element as in the case of PLAXIS, can be ... sheet pile), respectively.
th
The 12 International Conference of International Association for Computer Methods and Advances in Geomechanics (IACMAG) 1-6 October, 2008 Goa, India
Benchmarking of FEM Technique Involving Deep Excavation, Pilesoil Interaction and Embankment Construction D. E. L. Ong School of Engineering, Swinburne University of Technology (Sarawak Campus), Malaysia Keywords: excavation, pile-soil interaction, centrifuge modelling, embankment ABSTRACT: Three case studies involving the use of numerical models are presented in this paper. First, a comparison of FE modelling of a deep excavation is made using 2-D finite element software, SAGE-CRISP and PLAXIS. In the second study, benchmarking is made between results obtained from 2-D FE modelling using PLAXIS and well-established 3-D centrifuge studies for the case of an existing single pile and pile group located nearby to an excavation. Finally, practical application of FEM in the design of a 12-m high hydraulically placed sand-fill embankment is presented to demonstrate the importance of time-dependent analyses. These benchmarked studies using FEM technique will undoubtedly increase the confidence level of any designer who is involved in the challenging field of geotechnical engineering.
1 Introduction Benchmarking or verification of a designer’s numerical model to safeguard against carelessness and/or unforeseeable site condition is very important to prevent any untoward incidents. This is especially so in geotechnical engineering due to the variability of subsurface ground conditions, which are largely interpolated from known but limited numbers of soil sampling exercises. It is hoped that this paper will create greater awareness amongst numerical modellers to adopt a prudent attitude to check and re-check their numerical models so as to increase their confidence level, especially in critical geotechnical engineering projects.
2 Benchmarking of numerical models Case studies on deep excavation, pile-soil interaction and embankment construction involving the use of numerical models are presented hereinafter.
2.1 Case study 1: Deep excavation Case study 1 involves the comparison of finite element modelling of a deep excavation using 2-D finite element software, SAGE-CRISP version 5.1 and PLAXIS version 8.2. The soil profile selected for study consists of a 3.8m thick fill overlying a layer of 3.9m thick fluvial sand. Underlying the fluvial sand is a 25.4m thick S-VI and S-V residual soil of the Jurong Formation (sedimentary type of Singapore residual soil) with SPT N values varying from 6 to 62. S-III limestone is found underlying the residual soil. A typical cross-section of this problem in hand is shown in Figure 1.
(a)
(b)
Figure 1. Finite element meshes for a typical deep excavation using (a) SAGE-CRISP and (b) PLAXIS.
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Effective stress parameters are used for fully drained and coupled-consolidation analyses, while total stress parameters are used for undrained analysis. Input parameters for the selected soil profiles are presented in Table 1. For the Jurong Formation residual soil, use of the common elastic-perfectly plastic Mohr-Coulomb’s model is considered reasonable as the soil is expected to behave closer to over-consolidated clays. Appropriate use of boundary conditions, finite element meshes, in-situ stress conditions, interface or slip elements and modelling of strutting elements and preloads are considered in detail in each set of the numerical model using PLAXIS and SAGE-CRISP. The detailed construction sequence and all relevant modelling technique have been described in detail in Ong et al. (2006). Table 1. Typical soil properties for Mohr-Coulomb soil model. Soil layer 1 2 3 4 5 6 7 8 9
Soil description Fill F1 sand SVI N6 (clayey) SVI N22 (clayey) SVI N33 (clayey) SVI N62 (clayey) SVI N26 (clayey) SIII Limestone Backfill
E' (kPa) 8696 8696 10435 38261 57391 107826 45217 869565 8696
φ’ o () 28 30 28 28 28 30 28 34 28
c' (kPa) 0 0 5 10 15 15 10 50 0
K’o 0.5 0.7 0.8 0.8 0.8 0.8 0.8 0.8 0.5
γbulk 3 (kN/m ) 19 20 20 20 20 20 20 22 19
cu (kPa) 20 30 110 165 310 130 20000 20
k (m/s) -7 1x10 -6 1x10 -7 1x10 -7 1x10 -7 1x10 -7 1x10 -7 1x10 -7 1x10 -7 1x10
Figure 2(b) shows the typical bending moment and deflection profiles of the wall at four selected stages based on a typical undrained total stress analysis. The results show that if the calculations of the wall equivalent properties using solid LSQ elements are done correctly in the SAGE-CRISP analysis, reasonably good comparison to the analysis using beam element as in the case of PLAXIS, can be achieved. When these two sets of results are compared to the results obtained from the PLAXIS analysis, reasonably good agreement in the bending moment and deflection profiles are observed. This has definitely increased the level of confidence in the modelling techniques and the consistent boundary conditions used for both the PLAXIS and SAGE-CRISP analyses.
105 100
RL (m)
95 90 85 80 75 70
Exc for S3
65 105 100 95 RL (m)
Formation level
90 85 80 75 70
Exc to formation
65 105 100
RL (m)
95 90 85 80 75
Removal of S4 strut
70
Remove S4
65 105 100
RL (m)
95 90 85 80 75 70
Remove S1
65 -600 -400 -200
0
200
400
Bending moment (kNm/m)
(a)
(b)
Final backfill to ground level
600 -0.1
-0.08
-0.06
-0.04
-0.02
0
Deflection (mm)
PLAXIS SAGE-CRISP (solid element) SAGE-CRISP (beam element)
Figure 2. Comparison of FEA (a) deformed meshes and (b) wall responses using SAGE-CRISP and PLAXIS
155
105
100
100
95
95
90
90 RL (m)
RL (m)
105
85 80
Drained Coupled consolidation Undrained
70
-1200
Program
Analysis Type
SAGE-CRISP
Drained
PLAXIS
Drained
Hydrostatic
-
85 80
75
65
Symbol
(a) -800 -400 0 400 800 Bending moment (kNm/m)
75 70 65
1200
(b)
-300 -200 -100 0 100 200 300 Pore water pressure (kPa)
400
Figure 3. Comparison of FEA results for (a) wall BM envelopes and (b) PWP distribution behind wall Figure 3(a) shows the wall bending moment envelopes resulted from the typical undrained, coupled-consolidation and drained analyses. It is distinct that the largest bending moment envelope is derived from the drained analysis, followed by the coupled-consolidation and then the undrained analysis. Undrained and drained analyses are idealized analysis of the two ends of a consolidation analyses. A coupled-consolidation analysis is therefore the most representative of the actual conditions encountered on site considering the time required for each construction stage and thus provides a more realistic assessment of the time effect than the idealized undrained and drained analyses. Figure 3(b) shows the active and passive pore water pressure distribution along the wall in contact with the surrounding soils when the excavation reaches the formation level in a typical drained analysis. It is obvious that if the modelling techniques of the excavation and the boundary conditions are applied correctly, the pore water pressure distributions for both PLAXIS and SAGE-CRISP using drained analysis show very good agreement to each other. Subsequently, various parametric studies can then be performed with greater confidence.
2.2 Case study 2: Pile behaviour subject to lateral soil movement Case study 2 involves benchmarking of FE analysis against centrifuge modelling to study pile behaviour subject to lateral soil movement and the effect of smearing the properties of a 3-D pile in a 2-D FE environment. The centrifuge model set-up and model ground preparation have been described in detail by Ong et al. (2006a, 2007). In summary, the instrumented model pile has a prototype width of 630 mm at 50-g and the distance of pile from the model retaining wall varies accordingly. The model retaining wall is simulated using a 3-mm (prototype 150-mm) thick aluminium plate with length of 160-mm (8-m). The equivalent prototype bending rigidity, EI, of the 5 2 model pile and wall are approximately 2.2 x 10 kNm (equivalent to a 600-mm diameter Grade 35 bored pile or a 610-mm diameter steel pipe pile with 12.7-mm wall thickness) and 24 x 103 kNm2/m (equivalent to a FSP IIA sheet pile), respectively. Before test, a prescribed height of clay in front of the wall is replaced by zinc chloride contained in a latex bag. After the centrifuge model reaches 50-g, the in-flight excavation process is simulated by gradually releasing the zinc chloride from the latex bag. The pile head deflection, the bending moment profiles along the pile and the wall and soil movements are monitored at regular intervals throughout the tests. Figures 4(a) and (b) show a sketch of the centrifuge model setup and the undrained shear strength profile of the clay prior to and after excavation tested using the T-bar penetrometer in-flight, respectively. PLAXIS is attempted hereinafter to back-analyse the results obtained from the centrifuge study. Mohr-Coulomb soil model using PLAXIS “Method B” type of analysis was performed. “Method B” involves the use of effective stress analysis with a cap on the cohesion values of the soft kaolin clay to ensure that the cohesion values governed by the linearly elastic-perfectly plastic Mohr-Coulomb soil model are not over-predicted when compared to the actual non-linear soil behaviour. In 2-D plane-strain FE analysis, it is not possible to model the 3-D nature of a pile. As such, the actual properties of a 3-D pile are “smeared” in the plane-strain direction to obtain the “equivalent” pile properties per m width. Effectively, the 3-D nature of a pile is now represented by an equivalent wall. This can be done by considering the contact areas of a cylinder and a rectangular wall as shown schematically in Figures 5(a) and 5(b) for a single pile and a pile-group, respectively.
156
0 Before excavation at 3m behind wall
Depth (m)
2
After excavation at 1.5 m from wall
4
After excavation at 3 m behind wall
Main shaft
Load cell
4.5mm diameter 7mm
6
35mm Bar factor Nb=10.5
T-bar
(a)
(a)
cu/po' = 0.29OCR
0.85
(b)
8 0
4 8 12 Undrained shear strength (kPa)
16
Figure 4. (a) Sketch showing the centrifuge model set up and (b) clay undrained cu profile
2πr h
Assume all unit w length h
s b
Assume all unit length
2πr h
h
s
(b)
(a) 3-D pile
b
3-D pile group
2-D wall
2-D wall
Figure 5. Method of smearing (a) single pile and (b) pile-group to an equivalent 2-D wall for use in 2-D FEA For a single pile By assuming all unit length for parameters r, h, w and b (i.e. all with value 1), the unit contact areas of the cylinder (2*π*r*h) and the rectangular wall (2*h*w) are 2π and 2, respectively. This shows that the contact area of a 3-D cylinder is actually larger by π (=3.142) than that of a 2-D rectangular wall hence the development of Equations (1) and (2). This value is important in the case of a single pile as it represents the extent of influence imposed by the single pile. This concept is analogous to the “three pile diameters” rule of thumb theory for optimizing pile spacing for a group of piles. In general, the formulations used to obtain a 2-D equivalent wall for the case of a single pile can be written as: Axial rigidity:
(EpAp)/(3d)
(1)
Bending rigidity:
(EpIp)/(3d)
(2)
where Ep, Ap, Ip and d are the Young’s modulus, sectional area, second moment of area and diameter of the pile, respectively. For a group of piles For the case of a pile group, the 3-D single pile properties are multiplied by the number of similar piles in the plane-strain direction and smeared (divided) by the pile group centre-to-centre spacing, s, in the plane-strain direction as shown in Figure 5(b). In general, the formulations used to obtain a 2-D equivalent wall for a group of piles in the plane-strain direction can be written as: Axial rigidity:
n(EpAp)/[(n-1)(s)]
(3)
Bending rigidity:
n(EpIp)/[(n-1)(s)]
(4)
where n is the number of piles in the plane-strain direction and s is the centre-to-centre pile spacing between 2 piles in the plane-strain direction. The remaining quantities remain similar as described above.
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By converting 3-D piles to equivalent 2-D wall, the magnitudes of bending moment and forces (axial or shear) will be output as kNm/m and kN/m, respectively. In order to obtain the “actual” pile bending moment and forces, multiplication of smeared dimensions is necessary. Tables 3 and 4 show the methods of converting response of equivalent wall to that of a pile for a single pile and group of piles, respectively. Nevertheless, the resulted deflections and rotations remain similar. Table 3. Method of converting response of equivalent wall to that of a pile for the case of a single pile. Pile response Bending moment (BM) Axial or shear forces (F)
Quantity per linear m of wall as output by PLAXIS BM in kNm/m
Conversion to quantity per pile BM*3d to obtain kNm
F in kN/m
F*3d to obtain kN
Table 4. Method of converting response of equivalent wall to that of a pile for the case of a group of piles. Pile response Bending moment (BM) Axial or shear forces (F)
Quantity per linear m of wall as output by PLAXIS BM in kNm/m
Conversion to quantity per pile BM*[(n-1)*s]/n to obtain kNm
F in kN/m
F*[(n-1)*s]/n to obtain kN
0
Centrifuge (3-D)
Distance of pile behind wall (m)
PLAXIS (2-D)
3
2.5
5
Depth (m)
7
5 7.5 10 12.5 -40
0 40 80 Bending moment (kNm)
120 -10
0
10 20 Deflection (mm)
30
Figure 7. Measured and predicted results from centrifuge tests and 2-D FE modelling for the case of a single pile 0
3m
Depth (m)
2.5 5
5m
7.5
1.2m
10 12.5
Distance of pile Centrifuge PLAXIS behind wall (m) (3-D) (2-D) 3
-60 -40 -20 0
20 40 60 80 100 -10 -5 5
0
5
10 15 20 25 30
Uninstrumented pile Instrumented pile
Deflection (mm)
Bending moment (kNm)
Figure 8. Measured and predicted results from centrifuge tests and 2-D FE modelling for the case of a 4-pile group
Figures 7 and 8 show the measured and predicted results from FE and centrifuge modelling for the case of a single pile and a 4-pile group, respectively. It is noted that the bending moment profiles show particularly good match compared to the deflection profiles, which are over-predicted, thus erring on the conservative side in design. Ong et al. (2007) provides comparison for various other pile group sizes. Nonetheless, the main advantage of using a 2-D analysis is that it is less time-consuming as compared to the more rigorous analysis of 3-D analysis if better accuracy of pile response prediction is desired.
158
2.3 Case study 3: Hydraulic sand-fill embankment The proposed hydraulic sand-fill embankment was located in a valley. The hydraulic sand-fill was pumped from a nearby river. As foundation treatment, the weaker natural overlying strata was excavated and replaced with sand. When the embankment reached 4m in height, toe failure occurred. Subsequent hydraulic sand-filling work was temporarily suspended to prevent more toe failures from occurring at different locations of the embankment. The possibility of rapid and considerable build up of pore water pressure within the embankment during hydraulic sand-filling therefore needs to be investigated and a remedial proposal is to be recommended. Detailed description of this project is discussed in Ting et al. (2004). The proposed channel transporting the hydraulic sand-fill is modelled at the middle of the crest of the embankment. The depth of the channel is approximated to be about 3m and the hydraulic sand-fill is expected not to exceed a height of 2m at all times. Proper drainage is an important design consideration. In view of this, it is proposed that a highly permeable rock toe with an extended berm of 4m be constructed at the toe of the existing embankment. This design consideration is modelled in SEEP/W. The input soil properties for the seepage and slope stability analyses are found in Table 5. The partially saturated compacted sand-fill can be modelled using volumetric water content functions so that transient analyses can be performed. From site observation, it was noted that the deposited hydraulic sand-fill would take about 1 hour to reach a height of 2m in the approximately 600m long channel. Likewise, the drawdown rate of the channel was also noted to be about 2m/hour from the onset of suspension of sand-filling. Table 5. Input parameters for seepage and slope stability analyses.
Material type
Hydraulic fill Foundation 1 Foundation 2 Stone toe
Permeability (m/s)
Effective angle of friction (deg)
Cohesion (kPa)
Volumetric water content (Porosity x Saturation)
Used in
5.4 x 10-5 1 x 10-3
37.5 26 0
0 0 25 -
0.39 0.05
SEEP/W, SLOPE/W SLOPE/W SLOPE/W SEEP/W
-
These rates are thus used as boundary conditions for the filling and drawdown of the channel in the SEEP/W transient analyses. An appropriate time interval for the transient analyses is used to capture the fluctuations of the phreatic surfaces during and after the sand-filling process. The pre-determined phreatic surfaces are then exported to the sister programme, SLOPE/W so that limit stability analyses can be performed. Figure 9(a) shows a simulated embankment, whose height (H) and width from the side of the flow channel to the edge of the slope (W) are 12 m and 8 m, respectively. It is observed that after just 30 minutes of continuous sand pumping, the phreatic surface rises rapidly so that it intercepts the slope surface at embankment height of about 4.0 m from the existing ground level. This phreatic surface is then exported to SLOPE/W so that slope stability analyses can be performed. The result reveals that the embankment shoulder yields a factor of safety of just 0.96 against failure, as shown in Figure 10(a). The factor of safety after 12 hours of continuous sand-filling is noted to have reduced to 0.84, as shown in Table 6. The flow channel for hydraulic transport of material at the crest of the embankment is shown in Figure 11(a). If W is increased to 12 m for the same embankment height, 30 minutes of continuous sand-filling will produce a phreatic surface as shown in Figure 9(b). Using this phreatic surface as input to SLOPE/W, a higher FOS of 1.21 is obtained as shown in Figure 10(b), as opposed to 0.96 if W is 8 m. Therefore, it is evident that the FOS can be increased by lengthening the flow path from the flow channel to the rock toe of the embankment. However, after 12 hours of continuous sand-filling, the FOS would reduce to 0.98 (see Table 6), which shows that the critical phreatic surface has been reached. As such, the sand-filling process must be suspended so that the critical phreatic surface is allowed to drop to a safer level before the sand-filling process is allowed to resume.
159
After 30 minutes of pumping
Elevation (m)
Elevation (m)
After 30 minutes of pumping
20 After 12 hours of pumping 8m 16 12 5m 2m (a) 8 7m 4 0 -4 -8 -12 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 35 40 45 50 55 60
20 After 12 hours of pumping 12 m 16 12 5m 2m (b) 8 7m 4 0 -4 -8 -12 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 35 40 45 50 55 60
Distance (m)
Distance (m)
16 12 8 H 4 0 -4 -8 -12 -25 -20 -15 -10 -5
W 0.956
0
(a)
16
Elevation (m)
Elevation (m)
Figure 9. Development of phreatic surfaces due to hydraulic sand-filling after 30 minutes and after 12 hours, respectively, for berm width (a) 8m and (b) 12m.
5 10 15 20 25 30 35 40 45 50 55 60
1.211
W
(b)
12 8 4
H
0 -4 -8 -12 -20 -15 -10 -5
0
5
10 15 20 25 30 35 40 45 50 55
Distance (m)
Distance (m)
Figure 10. FOS after 30 minutes of hydraulic sand-filling for width of berm (a) H=12m, W=8m and (b) H=12m, W=12m.
(b)
(a)
Figure 11. Photographs showing (a) channel at middle of embankment and (b) successful completion of the 12m hydraulic sand-fill embankment By suspending the sand-filling process for 12 hours, the corresponding FOS is noted to have increased to 1.27 as shown in Table 6. Water standpipes were installed in the sand-fill embankment to monitor the fluctuation of the phreatic surface during sand-filling. The instrumentation programme was carried out to ensure that the design criteria based on the FE time-dependent analysis were within working limits to prevent embankment slope failure. Figure 12(a) shows the data from the extracted data from the SEEP/W analysis. It is observed that the interruption of pumping of 12 hours would cause uneven drop in phreatic surface along the section of the embankment. The phreatic surface would not reduce much for locations nearer to the toe of the embankment, despite showing relatively larger reduction nearer to the centre of the embankment. This highlights the susceptibility of embankment toe and shoulder failure. If pumping is suspended indefinitely with an assumption that persistent rainfall would sustain a “steady” head, a much lower “steady-state” phreatic surface would be achieved. Figure 12(b) shows the computed and measured drop in phreatic levels. It is observed that the computed data for distances 7 m and 22 m away from the embankment toe generally gives values that are about the average of the measured values.
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Table 6. FOS of embankment shoulder against failure during hydraulic sand-filling. Embankment Configuration (m) H=12, W=8
10
0
8
0.5 Drop in phreatic level (m)
Water head (m)
H=12, W=12
Duration of continuous sand-filling 30 mins 12 hours 30 mins 12 hours After suspension for 12 hrs After suspension indefinitely
6
4
(a) 2
After 12 hours of pumping After 12 hours of suspension of pumping After indefinite suspension of pumping
0 0
5 10 15 20 25 Distance from embankment toe (m)
0.96 0.84 1.21 0.98 1.27 1.82
1 1.5 Drop after 12 hours of suspension of pumping Drop after suspension of pumping indefinitely Measured drop
2 2.5
(b) 3 0
30
FOS
5 10 15 20 25 Distance from embankment toe (m)
30
Figure 12. (a) Extracted water head data from SEEP/W analysis and (b) comparison between computed and measured drop in phreatic level. The discrepancies between the computed and measured values could be due to persistent rainfall that might have prevented the phreatic surface from dropping further. For this reason, hydraulic sand-filling had to be suspended immediately on several occasions as the head difference between the phreatic surface and ground level was less than 0.5m. With the successful implementation of the instrumentation programme coupled with the in-sight provided by the time-dependent FE analysis, the embankment was successfully constructed without any further incidents as shown in Figure 11(b).
3 Conclusions Three benchmarked case studies involving deep excavation, pile-soil interaction and hydraulic sand-fill embankment have been presented. In the first case study, comparison of FE modelling of a deep excavation using 2-D finite element software, SAGE-CRISP and PLAXIS have been carried out successfully where both sets of results yield very similar responses. Subsequently, SAGE-CRISP was used to perform a fully coupledconsolidation analysis to reflect actual construction scenario. In the second study, benchmarking is made between results obtained from 2-D FE modelling using PLAXIS and well-established 3-D centrifuge studies for the case of an existing single pile and a fixed-headed 4-pile group subject to excavation-induced soil movement. Postulation of smearing the properties of a 3-D pile into an equivalent wall in a plane-strain was examined. It has been found that the predicted pile bending moment profile shows reasonable good match, but the pile deflection profiles errs on the conservative side in design. Finally, a case study involving a 12-m high hydraulically placed sand-fill embankment was presented and this demonstrated the importance of FE analyses in performing timedependent analyses so that a field instrumentation programme could be executed to prevent recurring slope stability problems during construction. These benchmarked studies using FEM technique have undoubtedly increase the confidence level of any designer who may be involved in the challenging field of geotechnical engineering.
4 Acknowledgements The author would like to thank Swinburne University of Technology (Sarawak Campus), Jurutera Jasa (Sarawak) Sdn. Bhd, CPG Consultants Pte. Ltd (Singapore), National University of Singapore, Dr. D. Q. Yang of Coffey Geosciences, Brisbane Office and Dr. W. H. Ting for their respective contribution to this paper.
5 References Ong, D.E.L., Leung, C.F. and Chow, Y.K. 2006a. Pile behaviour due to excavation-induced soil movement in clay: I: Stable wall. Journal of Geoenvironmental and Geotechnical Engineering, American Society of Civil Engineers (ASCE), Vol. 132, No. 1, 36-44.
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Ong, D.E.L., Leung, C.F., and Chow, Y.K. 2007. Effect of horizontal limiting soil pressures on pile behaviour. 16th South-East Asian Geotechnical Conference (SEAGC), 8-11 May 2007, Kuala Lumpur, Malaysia, 427-437. Ong, D.E.L., Yang, D.Q., and Phang, S.K. 2006. Comparison of finite element modelling of a deep excavation using SAGECRISP and PLAXIS. Int. Conf. on Deep Excavations, 28-30 June 2006, Singapore. Ting, W.H., Ong, D.E.L. and Tai, L.Y. 2004. Construction of a 12m high embankment in hydraulic sand-fill. Proc. 15th SouthEast Asian Geotechnical Conference (SEAGC), Bangkok, Thailand, 319-324.
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