NALYSIS OF STABILIZING SLOPES USING VERTICAL PILES Mahmoud S. Abdelbaki: Lecturer, Gehan E. Abdelrahman: Lecturer, Youssef G. Youssef :Assis.Lecturer, Civil Eng. Dep., Faculty of Eng., Cairo University, Fayoum Branch. Abstract This parametric study reveals the important parameters that affect the behavior and factor of safety of piles in slopes. These parameters are; the pile position, pile diameter and depth, soil properties, soil layer thickness and surcharge load. The effect of different undrained shear strength of clayey soil on the pile bending moment and the slope factor of safety are also studied. The nonlinear elasto-plastic finite element program PLAXIS is used to analyze the response of vertical piles due to the lateral soil movement generated by road surcharge. In addition an X-STABLE program is used to calculate the critical slip surface for the different cases studied before pile installation to predict the required pile length for stabilization. A comparison is made for no stabilization, stabilization using one row of piles and stabilization using two rows of piles. The studied case is for soft clayey soil overlying sandy soil. The results show that piles designed to stabilize slopes, raise the factor of safety and the allowable road surcharge in case of using one or two pile rows, for that type of soil. A comparison is made between the results of the finite element analysis and case study results from Alsalam- Canal. In many cases the results are reasonably in good agreement. Introduction Piles may be designed to restrain soil movements when used to stabilize slopes or potential landslides. The lateral loads resulting from the soil movement induce bending moments and deflections in the pile which may lead to their structural failure. Many theoretical and empirical methods were introduced for solving certain types of problems. Stewart et al. (1992), Poulos (1995), Chen and Poulos (1996),Chow (1996), Hassiotis et al. (1997) introduced other methods for the design of slopes stabilized with a single row of piles. Poulos and Chen (1996, 1997) took into account the pile group effect and the presence of a slope adjacent to two pile rows. The methods of the analysis of piles and pile groups subjected to lateral loading from horizontal soil movements, have been classified into four categories as described by Stewart et al. (1994): 1. Empirical methods, where the pile response is estimated in terms of maximum bending moment and pile cap deflection on the basis of charts developed from experimental data. 1
2. Earth pressure-based methods, where an earth pressure distribution acting against the piles is estimated in a relatively simple manner and is often used only to calculate the maximum bending moment in the piles. 3. Displacement- based methods, where the distribution of lateral soil displacement with depth is introduced and the resulting pile deflection and bending moment calculated. 4. Comprehensive finite-element analysis, where the piles are represented in the mesh and the overall soil-pile-embankment response is included. The last method is adopted here using the nonlinear elasto-plastic finite element program PLAXIS. Geotechnical Analysis Two slope profiles have been studied. The first consists of homogenous soft to medium silty clay, whereas the second is made of homogenous soft to medium silty clay followed by a sand layer as shown in Figure (1). Figure (1) Schematic drawing of the soil profile and pile rows (PLAXIS). The soft clay was assigned a rang of different values of undrained cohesion as shown in Table (1). These values are in the range of the soft to medium clay as stated in the Egyptian code of practice. The value of the Modulus of Elasticity is assumed to be 5 C u. The piles 2
are modeled as a beam element using the moment of inertia of a single pile and distributing it on every meter to get the moment of inertia/m as shown in Table (2). Since the analysis presented here is intended for addressing the slope stability problem of Alsalam-Canal. The water level is modeled to be at the water level in the Alsalam-Canal with a seepage line 15:1 towards the inland. A paved road exists on the right bank of the canal. The width of the canal is about 32m, while the width of the road is 12m. The only external load applied is the live load on the road. Table (1) Soil properties Parameter Clay Sand Dry unit weight γ ( kn/m 3 ) 16 17 Wet unit weight γ ( kn/m 3 ) 18 2 Young's modulus E ( kn/m 2 ) 5 C 3x1 4 Poisson's ratio ν.49.3 Cohesion C ( kn/m 2 ) 1,2,3,4 Friction angle φ 31 Type of behavior Undrained Drained Table (2) Pile properties Parameter Pile Young's Modulus, E ( kn/m 2 ) 2.1x1 7 EA (kn/m) 4.75x1 6 EI (kn.m 2 /m) 1.7x1 5 Poisson's ratio, ν.3 Pile Diameter, D (m).5 Pile Length, L (m) 17 Two different approaches are adopted to study the canal bank stability. In the first, the vertical load intensity on the bank is increased up to failure. This method was used for three cases; without piles, with one row of piles, and with two rows of piles. In the second 3
approach, the value of the cohesion is decreased till failure and the respective load at failure is determined. Analytical Model The slope stability analysis is performed using the specialized finite element program, PLAXIS. The program is an elasto-plastic, plane strain, finite element program for soil modeling. The soil is modeled using 6 nodded triangular elements. The soil model is Mohr- Columb method with nonlinear failure envelope. Both vertical and lateral soil movements may occur, but only the lateral soil movement is of significance in this case. The pile is modeled as a simple elastic beam with interface elements to model the soil structure interaction. The strength ratio of the interface elements, R, is assumed to be.7. The lateral displacement of each element of the pile can be related to the pile bending stiffness and the horizontal pile-soil interaction stresses. The lateral displacement of the corresponding soil elements is related to the soil modulus or stiffness, the pile-soil interaction stresses, and the free-field horizontal soil movements. A limiting lateral pile-soil stress can be specified so that local failure of the soil can be allowed for, thus allowing a nonlinear response to be obtained. The stability of a slope can be investigated by a number of limit equilibrium methods. The program X-STABLE is used to calculate the actual slip surface plane for the different shear strength cases, using Janbu slices method before pile installation. Factors Influencing the lateral Pile Response The parametric study presented by Poulos (1993) identified some of the most important factors influencing the behavior of piles within or near an embankment on clay. The most significant factors appear to include pile position, undrained shear strength of clay, soil layer thickness, and road surcharge intensity. He also indicated that delayed installation of the pile had substantial benefit in reducing pile bending moments and lateral movements. Table (3) presents the results of the parametric study performed in the current study. 4
Table (3) The effect of clay cohesion on pile bending moment at failure. Clay underlain Cohesion Clay Clay Clay underlain by Sand by Sand One Pile One Pile Two Piles Two Piles Two Piles Canal Pile Road Pile Canal Pile Road Pile C M M1 M2 M M M1 M2 M1 M2 kn/m 2 kn.m kn.m kn.m kn.m kn.m kn.m kn.m kn.m kn.m 1 261.2 13. 23. 719.8 11. 31. 437. 344.1 48. 12 25.7 121. 24.6 537.2 814.6 312. 442.4 338.7 425. 14 268.6 14. 48.2 453. 82. 312. 366.9 342.8 34.7 15 247.4 947.1 52.2 443. 828.6 312.7 349.9 312. 327. 16 272.5 94. 59.1 456.7 733.7 36.7 335.1 277.7 319.1 17 265.9 845.1 68.5 443. 719.4 297.3 324.3 259. 31.6 18 249.2 792.7 77.5 376. 7. 284.7 315.5 242.9 34.4 25 264.6 544.6 16.6 374.7 647.3 19.8 295. 169.9 282.4 3 266.7 417.7 125.1 416.8 694.1 128.3 275. 98.9 284.1 4 268.2 38. 159. 419.6 696.7 3.4 25. 54.4 273.2 * M1 maximum negative moment * M2 maximum positive moment (a): Maximum pile moment in Clay (b): Maximum pile moment in Clay underlain by Sand Figure (2) A sample of the bending moment diagram along the pile ( PLAXIS) 5
1. Effect of Soil Layer Thickness Two types of soils are used, The first type consisted of extended homogeneous clay, while the other consisted of homogeneous clay underlain by a bearing stratum of sand. A relation is obtained between pile bending moment and the undrained shear strength of clayey soil C for the two soil types. As shown in Figure (3) the maximum negative bending moment, M1, decrease as the undrained shear strength increases in case the pile extend in underlying bearing stratum. For the extended homogeneous clay, the pile bending moment is not affected by the increase in the undrained shear strength as shown in Figure (3). MOMENT M, (kn.m) 14 12 1 8 6 4 (M Pile In Clay) (M1 Pile In Sand) (M2 Pile In Sand) 2 UNDRAINED COHESION C, (kn/m2) Figure (3) Comparison between one pile row floating in clayey soil and another ending in sandy soil. 2. Pile Arrangement (Piles in One and Two Rows.) In the finite-element analysis, the pile-soil-pile system is simplified to a twodimensional plain strain study, and is loaded by a soil movement due to road surcharge, which is applied incrementally until the system reaches an ultimate plastic state. Chen et al. (1997) studied the group effect, f p, on the ultimate pile load, p u, in case of floating pile. In this study the transverse pile spacing as shown in Figure (1) S h = 3D while in the longitudinal direction the pile spacing S v = 6D, where D is the pile diameter. According to Chen et al, f p equals 1.1 in case of one long row. In case of two long rows, for the pile located close to the dredged side, f p, equals to 1.4, while for the pile located close to road side, f p, equals to 1.2. 6
Consistent with the above-mentioned results, in case of two pile rows, the pile near the canal side has bending moment less than the pile that lies near the road side as shown in Figure (4). In case of one pile row the pile bending moment is less than that of two pile rows. This is attributed to the greater moment of inertia of two pile rows compared to the single row of piles. MOMENT M, (kn.m) 14 12 1 8 6 4 One Pile Canal Pile Road Pile 2 UNDRAINED COHESION C, (kn/m2) Figure (4) Comparison between one and two pile rows floating in clay. 3. Pile Size and Position In all analysis cases, the pile length has been chosen deeper than the slip failure surface. XSTABLE program was used to calculate the position of the slip surface before pile installation. This slip surface was calculated to be at 12.65m from the berm level. Thus the selected pile length of 17m, is suitable. Poulos (1976) found that piles installed within the embankment are subjected to significantly larger bending moments than piles at the toe, due to both larger horizontal movements and also the effect of the embankment fill moving past the pile. The maximum moment appears to be developed for piles located near the middle of slope, and is more than twice the value for piles at the embankment toe. In this study the pile is locate at the berm level which is considered at the mid-slope according to Poulos (1976). Piles floating in clayey soil had maximum bending moment double that for those ending in the sand layer. The existence of underlying bearing stratum of sand decreases the bending moment on the pile as shown in Figure (5). 7
MOMENT M, (kn.m) 14 12 1 8 6 4 2 (M Piles In Clay) (M1 Piles In Sand) (M2 Piles In Sand) UNDRAINED COHESION C, (kn/m2) Figure ( 5 ) Bending moment of pile near the canal side. MOMENT M, (kn.m) 14 12 1 8 6 4 2 (M Piles In Clay) (M1 Piles In Sand) (M2 Piles In Sand) UNDRAINED COHESION C, (kn/m2) Figure ( 6 ) Bending moment of pile near the road side. In case of two pile rows and according to group effect, the pile near canal side had bending moment less than the pile which lies near the road side as shown in Figures (5 and 6) in case of piles floating in clayey soil. In case of two pile rows ending in sandy layer, both piles had the same bending moment and equal value for both maximum negative bending moment, M1, and maximum positive bending moment, M2, along the pile length as shown in Figure (6). 8
4. Maximum Bending Moment with Undrained Shear Strength Figure (7) shows that the increase in undrained shear strength decreases the pile bending moment. This may be due to the smaller lateral movements which are developed in the stronger soils. In case of one pile row the maximum negative bending moment, M1, is much higher than maximum positive bending moment, M2, as shown in Figures (7and 8), while in case of two piles M1 and M2 had the same value for both canal and road piles. Pile position has no effect on the value of bending moment. MOMENT M1,(kN.m) 14 12 1 8 6 4 2 One Pile Canal Pile Road Pile UNDRAINED COHESION C, (kn/m2) Figure (7) Comparison between maximum negative pile moment, M1, in one and two pile rows socket in sandy soil. MOMENT M2, (kn.m) 14 12 1 8 6 4 2 UNDRAINED COHESION C, (kn/m 2 ) One Pile Canal Pile Road Pile Figure (8) Comparison between maximum positive pile moment, M2, in one and two pile rows socket in sandy soil. 9
5. Surcharge Load The increase in failure (surcharge) load with the shear strength of the soil is shown in Figure (9). It is seen that the percentage of improvement increases as the shear strength of the soil decreases. At higher values of cohesion (more than 4 kn/m 2 ), the increase in the percentage of improvement decreases significantly and the need to use piles for stabilization is thus diminished. FAILURE SURCHARGE LOAD Q, kn/m2 175 15 125 1 75 5 25 NO PILE (CLAY) ONE PILE (CLAY) TWO PILES (CLAY) NO PILE (SAND) ONE PILE (SAND) TOW PILES (SAND) UNDRAINED COHESION, C, kn/m2 Figure (9) Road surcharge with different undrained shear strength ( F.O.S. =1) It may be seen that the single row and two pile rows ending in sand layer increased the failure load on the road to a value of about 28kN/m 2. One or two pile rows had the same effect either floated in clay or ended in sand on the surcharge causing failure as shown in Figure (9). Factors Influencing Factor of Safety The geotechnical analysis is concerned with calculating the value of the safety factor for the different cases and the comparison between the performances of the system in the different cases. The safety factor may be calculated by two different methods. The first is the safety factor in terms of the surcharge load. This was calculated as the ratio between the value of 1
the maximum load at failure for each case and the value of the applied load. The second method of safety factor calculation is in terms of the shear strength of the soil; that s the ratio between the actual value of shear strength and the value of shear strength at failure. Both the presence of sand layer underlying the clay strata, or the existence of one or two pile rows floating in clayey soil had no effect on the factor of safety. However with the increase of undrained shear strength, a slight increase occurs in the factor of safety, in case of one or two pile rows floating in clay. In case of piles ending in the sand layer, factor of safety increased as shown in Figure (1). The two pile rows give higher factor of safety than that for the one pile row. Table (3) Calculated factor of safety in different cases Cohesion Clay Clay underlain by Sand kn/m 2 No Pile One Pile Two Piles No Pile One Pile Two Piles 1.8 1.6 1.5 1.1 1.47 1.65 12 1.8 1.13 1.15 1.1 1.56 1.76 14 1.27 1.35 1.34 1.28 1.77 1.94 15 1.36 1.42 1.43 1.36 1.87 2.4 16 1.45 1.54 1.53 1.45 1.95 2.14 17 1.54 1.63 1.63 1.54 2.4 2.23 18 1.63 1.7 1.72 1.63 2.13 2.33 25 2.26 2.4 2.4 2.27 2.81 3.2 3 2.72 2.88 2.87 2.73 3.28 3.53 4 3.61 3.84 3.83 3.65 4.23 4.54 FACTOR OF SAFETY FOS 5. 4.5 4. 3.5 3. 2.5 2. 1.5 1..5 NO PILES(CLAY) ONE PILE(CLAY) TWO PILES(CLAY) NO PILES (SAND) ONE PILE(SAND). UNDRAINED COHESION (C) kn/m 2 Figure (1) Factor of safety with different undrained shear strength. 11
Comparison with Field Measurement A case history of a stabilizing system for the embankment of Alsalam-Canal was presented by Al-Shaal et al. (2). The embankments of the large canal were made of un-compacted marine deposits, and was founded over soft clay soil in the north of Egypt. The stability of the embankment slopes was studied. In many sections of the canal, the factor of safety of the side slopes did not meet the requirements of the Egyptian code. The stabilizing system consisted of reinforced concrete piles with a diameter of.5 m spaced center-to-center at 1.25m parallel to the canal. The monitoring system included inclinometers, sondex rings, and strain gauges to measure the lateral movements, vertical movements, and the straining actions, respectively. The measurements prove the efficiency of the stabilizing system in reducing significantly the lateral movements of the embankment mass. The strains measured in the pile reinforcement bars show that the critical factor of safety of the pile is 1.63 during either the construction or loading process. Abdel-Motalab (25) concluded that the stabilizing system has efficiently controlled the sliding of the embankment side slopes under the most critical loading conditions. The maximum negative moment, M1, occurred near the bed level. Below the bed level, where the major resisting forces exist, the moment started to reverse to reach the maximum positive moment, M2, at the surface of the lower layer. Furthermore, the bending moment diminished near the surface of the continuous sand layer where the pile is embedded for at least 2. m. The maximum bending moment was about 163.76 kn.m, which is about 61% of its maximum bending capacity 267 kn.m. That means that the factor of safety of the pile is 1.63 during both the construction and loading process, Abdel-Motaleb (25). By comparing the finite element results (in Figure 1) for the case of extended clay layer or clay underlain by sand without piles with the case of using two pile rows, the factor of safety increased from 1 to 1.6 as shown in Table (3). Finite element analysis using PLAXIS program, shows good agreement with that measured in the field in the case when using two pile rows. 12
COCLUSIONS The benefit of using piles in stabilizing clay slop is more apparent at lower values of cohesion, (C>4 kn/m 2 ). The presence either of one or two pile rows floating in clayey soil caused slight increases to failure surcharge on the road, and no effect on the factor of safety. The presence of one pile or two piles rows in case of a firm sand layer below the soft clay, increased the failure load on the road. The safety factor also increased by 6%. Two double rows of piles is more effective in this case than one pile row. Finite element analysis using PLAXIS program, shows good agreement with that measured in the field in case of using two pile rows. REFERENCES 1. Stewart, D. P., Analysis of Piles Subjected to Embankment Induced Lateral Soil Movements. Journal of Geotechnical and Geo-environmental Engineering, May 1999, pp. 425-435. 2. Chen, L.T. and Poulos, H.G. Piles Subjected to Lateral Soil Movements. Journal of Geotechnical and Geo-environmental Engineering, September 1997, pp. 82-811. 3. Poulos, H.G., Behavior of Laterally Loaded Piles Near a Cut or Slope. Australian Geomechanics, July 1976, Vol. C6, No.1, pp1-12. 4. Stewart, D. P., Jewell, R. J. and Randolph, M.F. Design of Piled Bridge Abutments on Soft Clay for Loading From Lateral Soil Movements. Geotechnique 44, No.2, pp.277-296. 5. Poulos, H.G., Analysis and Design of Piles Through Embankments. Design and Construction of Deep Foundation, December 1994, Vol. III, pp143-1421. 6. Chow, Y.K. Analysis of Piles Used for Slope Stabilization. International Journal for Numerical and Analytical Methods in Geomechanics, 1996, Vol.2, pp.635-646. 7. Hassiotis, S., Chameau, J.L., and Gunaratne, M. Design Method for Stabilization of Slopes with Piles. Journal of Geotechnical and Geo-environmental Engineering, ASCE, September 1997, Vol.123, No. 4, pp. 314-323. 8. Abdel-Motaleb, A.A. Monitoring of A Stabilizing Embankment Using Reinforced Concrete Piles. The Fifth International Geotechnical Engineering Conference-Cairo University, January 25, pp. 183-199. 9. El-Ashaal, A.A., Abdel-Motaleb, A.A. and Haggag, H.A. Stabilizing Embankments Made of and Founded Over Weak Soil Using Piles; A Case History. The Fourth International Geotechnical Engineering Conference-Cairo University, January 2, pp. 415-426. 13