# FACTOR OF SAFETY IN AS : EARTH RETAINING STRUCTURES 1

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3 foundation should be sufficiently wide to prevent overturning failure. Therefore, the width of the foundation, B, was determined based on the equilibrium of moments around a rotation point at the toe of the wall foundation, point o in Figure 1, and the requirements of AS : M a - Φ nm p = 0 where M a is the overturning moment, M p is the restoring moment around point o, and Φ n is structural importance factor which was taken as 1 in all analyses. 1.5q =7.5kPa 1.5q =7.5kPa t 0.8γ s 1.25γ s H t o 0.8γ c B Figure 1: Cantilever retaining wall Figure 2: Distribution of stresses embedded wall A range of soil strength parameters, c and φ, was used in the design of the wall to estimate the overall factor of safety for different cases. The overall factor of safety of a designed wall, with known t, H and B, can be obtained using the nominal values of soil strength parameters, c and φ, and the nominal unit weight of the soil and wall, and an overburden pressure of 5 kpa on the ground L level at the back 3.2 EMBEDDED SHEET PILE WALL In this paper embedded sheet pile walls in cohesionless soils as well as cohesive soils were considered. The walls were assumed to be free earth support, so that no significant moment will be developed around the tip of the wall. The wall has a rotational failure mechanism around a point which is above the wall tip, point o in Figure 2. Active pressures form behind the wall above the rotation point and in front of the wall below the rotation point where the wall moves away from the soil mass during failure. Passive pressures form in front of the wall above the rotation point and behind the wall below the rotation point, where the wall moves toward the soil mass during failure. Figure 2 also shows the applied load on the ground level at the back of the wall and the different factors used to increase or decrease the unit weight of the soil at different locations. In general, the unit weight of the soil is increased if the soil contributes to the disturbing actions, and decreased if the soil contributes to the resisting reactions. In assessing the stability of embedded walls it is usually assumed that the active and passive earth pressures vary linearly with depth, which is a realistic assumption if the wall is rigid. In this study linear distribution of stresses, as shown in Figure 2, was assumed. For any wall height, H, the required depth of embedment, D, is the design outcome. Equations for the equilibrium of moments and horizontal forces can be formulated and solved simultaneously to obtain the depth of embedment, D, for the wall: M a - Φ nm p = 0 F a - Φ nf p = 0 where M a and F a are sum of the active moments and sum of the active horizontal forces, M p and F p are sum of the passive moments and sum of the passive horizontal forces developed in the front and back of the wall. The structural importance factor, Φ n, was taken as unity in all analyses. The design was performed for varying soil strength properties, φ (friction angle) and c (cohesion). The overall factor of safety of a designed wall, with known H and B, was obtained using the nominal values of soil strength parameter, φ, nominal unit weight of the soil, and an overburden pressure of 5 kpa on the ground level at the back of the wall. A trial and error procedure is used to evaluate the overall factor of safety for a designed wall, by varying the factor of safety until the equilibrium of moments and forces are both satisfied. 4 RESULTS 4.1 CANTILEVER RETAINING WALL Australian Geomechanics Vol 44 No 3 December

4 A series of analyses was performed to design the required foundation widths for walls of different heights in soils of varying strength parameters and the overall factor of safety of each designed wall was evaluated. Figure 3 shows variation of the overall factor of safety with wall height when a nominal friction angle of φ =30 is used while the cohesion of the soil varies from 0 to 40 kpa. The soil condition at the back of the wall was assumed to be of Class 1 fill according to AS The tensile active stresses developed close to the ground level at the back of walls in cohesive soils were ignored in the analyses. Figure 3 shows that the overall factor of safety of walls in cohesionless soil varies between 2.3, for walls height of 1 m, to 1.7 for a wall height of 10 m. However, the overall factor of safety is considerably larger for walls in cohesive soils. A wall with a height of 6 m in a soil with φ =30 o and c =20 kpa and designed based on AS has an overall factor of safety of 5.8. The main reason for the high value of the overall factor of safety in cohesive soil is the difference between the depth of tension crack obtained using the reduced value of cohesion, based on AS , and the depth of tension crack obtained using the nominal value of cohesion applicable in the calculation of the overall factor of safety. The overall factor of safety method gives a deeper tension crack compared to that obtained for the partial factors of safety method and the reduced cohesion. Figure 3: Effect of varying cohesion, c, on factor of safety of cantilever retaining walls in Class 1 fill soil. Figure 4 shows the overall factor of safety for walls in cohesionless soils (c =0) and different values of friction angle. It can be seen that the overall factor of safety varies between 2.3 for short walls to 1.65 for tall walls. It indicates that the overall factor of safety does not vary much when the soil is cohesionless. The overall factor of safety is marginally larger for soil with higher friction angles. Figure 4: Effect of varying friction angle, φ, on factor of safety of cantilever retaining walls in Class 1 fill soil. Figures 5 and 6 show the effect of different classes of soil, as defined by AS and given in tables 1 and 2, on the overall factor of safety of the walls. Both figures show that the overall factor of safety is higher for uncontrolled fill, compared to those of class 1 fill and class II fill. Figure 5: Effect of different soil classes on the overall factor of safety of walls in cohesive soils. Figure 6: Effect of different soil classes on the overall factor of safety of walls in cohesionless 4.2 EMBEDDED SHEET PILE WALL Figure 7 shows the effect of varying friction angle on the overall factor of safety of embedded sheet pile wall in cohesionless soil. The factor of safety varies from 2 to 2.5 for friction angle varying from 20 to 45. The overall factor of safety remains the same for a particular type of soil, regardless of the wall height. It also shows that soil with higher friction angle has higher factor of safety. Figure 7: Effect of varying friction angle, φ, on the overall factor of safety of embedded walls in cohesionless soil. Figure 8 shows the effect of varying cohesion on the overall factor of safety of embedded sheet pile walls in cohesive soils. The factor of safety varies from 2.2 and reaches generally to a large value, as large as 10. This result is consistent with the overall factor of safety obtained for the cantilever retaining walls in cohesive soils where the overall factor of safety is generally higher. Figure 8: Effect of varying cohesion, c, on the overall factor of safety of embedded walls 5 CONCLUSIONS In this paper, the overall factor of safety inherent in design of retaining walls based on AS was evaluated. Walls of different heights in different soils were designed based on the requirements of AS , and the overall factors of safety of the designed walls were evaluated. The results of this study show that the overall factor of safety of cantilever retaining walls varies from 1.7 to 2.3 for cohesionless soils. However, the overall factor of safety is considerably larger for walls in cohesive soils. Shorter walls have very large factor of safety, as large as 5.0 for a wall height of 4 m. For practical heights of cantilever walls, the factor of safety is well above Australian Geomechanics Vol 44 No 4 December 2009

5 For embedded sheet pile walls in cohesionless soil, the overall factor of safety increases from 2 to 2.5 when the friction angle increases from 20 to 45. The height of the wall does not have any influence on the factor of safety. Results also indicate that the overall factor of safety is much higher for walls in cohesive soils. The higher overall factor of safety is mainly due to different depths of tension crack obtained by the two methods, the overall factor of safety and the partial factors of safety. 6 REFERENCES Clausen, J., Hansson, S.O., Nillson, F.(2006) Generalizing the safety factor approach, Reliability Engineering and System Safety, 91, PP Committee BD 002, (2001) AS Concrete Structures, Standards Australia International. Committee CE-032 (2002) AS Earth Retaining Structures, Standards Australia International. Meyerhof, D. G. G. (1994) Evolution of Safety Factors and Geotechnical Limit State Design, Technical University of Nova Scotia, Canada Simpson, B. (2000) Partial factors : where to apply them?, LS2000 : International Workshop on Limit State Design in Geotechnical Engineering, ISSMGE, TC23, Melbourne. Australian Geomechanics Vol 44 No 3 December

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