FACTOR OF SAFETY IN AS : EARTH RETAINING STRUCTURES 1

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1 FACTOR OF SAFETY IN AS : EARTH RETAINING STRUCTURES 1 Jocelin Wijaya 1 and Hossein Taiebat 2 1 Undergraduate Student and 2 Senior LectureSchool of Civil and Environmental Engineering, University of New South Wales ABSTRACT Factor of safety is used to provide safety margin over the theoretical design capacity to allow for uncertainties in loading, material strength and design process. Design of earth retaining structures has traditionally been based on the overall factor of safety method. However, the current Australian Standard for Earth Retaining Structures, AS , is based on partial factors of safety method. In this paper, cantilever retaining walls and embedded sheet pile walls have been designed based on the recommendations of AS to examine the overall factor of safety inherent in the standard. Various wall heights and soil parameters are used in the designs. The overall factor of safety is then back-calculated for each wall based on its designed dimensions. The results of analysis are presented in the form of the overall factor of safety associated with the dimension of the walls and soil properties. The overall factor of safety of walls in cohesionless soils varies between 1.7 and 2.3; shorter walls have higher factor of safety. However, when the backfill soil has some cohesion, the overall factor of safety is generally higher than 2 and becomes more than 5 for soil cohesion greater than 30 kpa. For embedded sheet pile walls in cohesionless soils, the factor of safety remains constant for one particular type of soil, regardless of the height of the wall. The results of analyses of these walls in cohesionless soils also show that the factor of safety increases slightly as the friction angle of the soil increases. For the walls embedded in cohesive soils, the overall factor of safety is higher compared to those in cohesionless soils and this behavior is consistent with the one observed in cantilever retaining walls. INTRODUCTION There are always uncertainties in engineering design. In geotechnical engineering, the uncertainties may be due to variability in applied loads, soil parameters, design approximations such as resistance and action effects and construction tolerances (Meyerhof, 1994). Factor of safety is applied to account for these uncertainties and also to lead to designs in which both geometry and strength are adequate and compatible (Simpson, 2000). There are mainly three approaches in considering safety margins in geotechnical design. Two of them have been used in the design of retaining walls. They are the overall factor of safety method, which will be referred to here as traditional method, and the partial factors of safety method. The traditional method for the design of earth retaining structures ensures that the resisting forces or moments will be greater than the disturbing forces or moments. The ratio of the resisting reactions to the disturbing actions is called overall factor of safety. In this method the design values of loads and soil parameters are assumed to be the nominal values. It is also assumed that all soil parameters such as friction angle, unit weight and cohesion are spatially constant (Clausen et al, 2005). Higher factor of safety should be selected if more uncertainties are involved in the loads, soil parameters or construction quality control. In the partial factors of safety method, various factors are applied to increase the effect of disturbing actions (load factors) and to reduce the resistance of the soil-structure system (capacity reduction factors). Different reduction factors are applied to different soil properties such as cohesion, friction angle and density. 2 REQUIREMENT OF AS In this section the requirements of AS which are directly related to design will be outlined briefly. The standard requires that for each limit state design considered, the design effect (S*) must not exceed the design resistance (R*), or Φ nr* S* where Φ n is a factor that includes the importance of structure and varies between 0.9 and 1.1, R* is the design resistance which is calculated using the design strength parameters obtained by reducing the characteristic strength values of the soil with partial factors of safety, and S* is the design action effect obtained by increasing the nominal loads and disturbing action forces. 1 This paper was presented at the Sydney Chapter YGP night September Australian Geomechanics Vol 44 No 4 December

2 The requirement of AS for dead load (including soil self weight) is that a partial factor of 1.25 is to be applied when the load contributes to the disturbing action and a partial factor of 0.8 is to be applied when the load provides resistance. For live load a partial factor of 1.5 is to be applied. A minimum live load of q=5 kpa is specified by the standard that is applicable to the ground at the back of walls, if the ground is horizontal. The standard also recommends material strength reduction factors, Φ uc and Φ uφ, which are to be applied to the nominal cohesion, c, and friction angle, φ, of the soil to obtain the design strength parameters, c * and φ *. The design strength parameters will be: c * = Φ uc c and φ * = tan -1 (Φ uφ tan φ) The designed strength parameters are used to evaluate both active and passive lateral earth pressures. The strength reduction factors recommended by AS are summarized in Tables 1 and 2 for analyses performed under drained and undrained conditions. Drained conditions are assumed in all analyses performed in this study. Table 1: Strength reduction factors for soil behaving under drained conditions (based on peak values of c and φ ) Strength reduction factor Φ uφ Φ uc Soil or fill conditions Controlled fill Uncontrolled Class I Class II fill In situ material Table 2: Strength reduction factors for soils behaving under undrained conditions (based on c u and φ u) Strength reduction factor Φ uφ Φ uc Soil or fill conditions Controlled fill Uncontrolled Class I Class II fill In situ material 3 DESIGN METHODOLOGY This research is based on a series of analyses and designs of cantilever retaining walls as well as embedded sheet pile walls. The retaining walls were initially designed based on the partial factors of safety method and the requirements of AS The overall factors of safety of the designed structures were then back calculated and presented here. A unit weight of γ s=18 kn/m 3 was assumed for the soil, as it is the average unit weight for in situ or lightly compacted soil. In order to achieve consistency and for comparisons to be valid, the same unit weight was used in all calculations. The material in the stem and foundation of cantilever walls is assumed to have a unit weight of γ c=25 kn/m 3. The weight of the embedded walls was ignored in the analysis. The forces acting on the wall are typically determined using the Rankine s or Coulomb s theories of earth pressure. In this paper, Rankine s theory of earth pressure was used to determine the active and passive earth pressures. 3.1 CANTILEVER RETAINING WALL Design of retaining walls was performed based on overturning failure only. It was assumed that if sliding and bearing failures are predominant, they could be prevented by shear keys or by extending the foundation width in front of the wall. A general geometry of the retaining wall is shown in Figure 1. The wall has a height of H, a uniform thickness t, and a foundation width of B. The surface loading at the back of the wall, the unit weights of the soil and the wall, and the load factors for different loading components are also shown in Figure 1. The weights of the wall and the soil on top of the wall foundation provide resistance to overturning, and therefore are reduced. The weight of the soil away from the foundation and its overburden pressure which contribute to overturning of the wall are increased according to the requirements of AS For any wall height, H, the thickness of the wall, t, and the required width of the foundation, B, are the design outcomes. The thickness of the wall was estimated by considering the maximum shear stress in the concrete section of the wall and the requirements of AS : Concrete Structures. The compressive strength and the minimum reinforcement ratio of the concrete was assumed to be 32 MPa and 0.2%, respectively. The wall Australian Geomechanics Vol 44 No 4 December 2009

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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