Embedded Retaining Wall Design Engineering or Paradox?


 Robert Price
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1 Embedded Retaining Wall Design Engineering or Paradox? A personal viewpoint by A.Y. Chmoulian, associate at Royal Haskoning Introduction Retaining wall design theory is a complicated subject with a long history. The problem was, for a long time, solved exclusively in terms of Coulomb s approach, that is, through equilibrium calculations based on postfailure soil pressures. The geometry of the wall reflecting its equilibrium could then be enhanced to create a desired margin of safety on wall stability. In a similar way, direct factoring of the calculated stresses would ensure the necessary margin of wall structural strength. The main disadvantage of this method was its oversimplified approach to the soilstructure interaction. However, most of the sophisticated methods of soilstructure interaction analysis were not capable of dealing with the conventionally used definitions of factors of safety on wall stability. Hence, the advances in numerical analysis required modification of the safety factor approach to ensure compatibility of the results. An easy way forward was available through factoring soil strength and was often adopted. The idea is very simple and clear for wall stability: if the soil strength is reduced by a factor and the wall is still standing the problem is solved. The problem becomes less clear when dealing with structural forces induced in the by soil pressures. Common sense suggests that reducing the soil strength would cause consequential increases in soil pressures on the interface with the wall and therefore in the structural forces, providing the ultimate design loading conditions. This idea was suggested in the original (1994) edition of BS82 [2]. But it was noticed that when factored soil parameters are used, the stability requirement is for the external forces to be in equilibrium only, that is by calculation the wall may actually be as near to the point of failure as possible. For a cantilever wall or a wall with a single prop near the top this may mean that the soil on the interface with the wall has reached the point of failure and so interface stresses are lower than those in the working conditions. The amended edition of BS82 states that the earth pressures at ultimate limit state are actually lower than those under working conditions. It is noted that the British Standards for structural design, for example BS595 [1] and BS811 [2], have also introduced additional partial factors of safety on loads calculated using the BS82 design approach. This, in the author s experience, sometimes causes substantial increases in the overall structural strength demand compared with the traditional (unfactored) retaining wall design approach. While it is logical to accept that soil pressure reduces with the increasing wall deflection, it is more difficult to comprehend that a structure can deflect less under greater earth pressures. This paper will show examples from the author s experience, representing just a small sample of possible effects that may be caused by the use of factored soil parameters for designing embedded s. General The analyses presented in this paper represent real design situations. But to make the effect of different design parameters clearer, only simple geometries are presented, with the varying factors applied independently. The basic initial conditions always implied that the soil conditions are uniform and all structural elements are absolutely stiff, although the effect of finite wall stiffness was also studied. The groundwater pressures were ignored here to ensure that the primary effects caused by the soil pressures are clearer. It is a normal design practice that the majority of analyses within a single project are carried out using the same design software. It would be unusual in a routine design to find the same engineer using different analysis methods when carrying out the ultimate limit state (ULS) calculations using factored soil parameters, compared with the serviceability limit state (SLS) calculations using representative parameters. As the analyses presented here are supposed to represent normal The following notations are used here: Subscripts f and r refer to any results of f and r the analysis using respectively a factored or a representative set of design parameters ø δ d h D K a, K p, K o M R A m = Mf A r = Rf M r R r Internal friction angle of soil Adhesion angle on the interface between soil and Retaining wall embedment Retaining wall height, measured from top to toe Excavation depth Respectively, active, passive and atrest earth pressure coefficients Maximum calculated bending moment in the Maximum calculated prop force Ratio between maximum bending moments calculated in retaining structures of the same geometry using factored (M f) and representative (M r) sets of soil parameters Ratio between maximum prop forces calculated for retaining structures of the same geometry using factored (R f) and representative (R r) sets of soil parameters design conditions but to allow modelling of both the elastic and plastic soil behaviour, most of the calculations for this paper were performed using a standard industry software suite that allows modelling nonlinear soil structure interaction with coupled subgrade reactions (Software Suite A). References to the results attained through other types of numerical modelling are given where necessary. All of the analyses have first been carried out using the factored sets of soil parameters to establish required wall embedment. The factored analyses would also give the structural design forces consistent with BS82 or with EC7 [4]. Analyses were then repeated using the same wall geometry but with the representative soil parameters. This would indicate the structural strength demand using the traditional design approach. It would also give the designer s best estimate of the real situation, which should attract a load factor when using structural design codes. When factoring the soil parameters in accordance with BS82 it was assumed that the critical state effective stress strength is greater than the factored representative strength value. Otherwise, the findings presented may be exaggerated even further, as the ratio between the factored and the representative values increases. Where references are made to BS82 δvalues it was assumed that δ r = 2/3ø r in the analysis using representative soil parameters and tan(δ f) =.75tan(ø f) for the factored soil parameters. The effect of factoring soil parameters is addressed here in the form of ratios A m and A r, which gives an indicative comparison of the structural strength demand when using different design approaches. Issues related to the analysis of stability are avoided if possible, although it should be acknowledged that different design approaches, for example, J.B. Burland and D.M. Potts (1981), may result in different wall embedment requirements, which can ultimately affect the structural design of the GROUND ENGINEERING JULY 27 31
2 Partial factor wall. The size of this paper does not permit inclusion of all available data. In particular, only uniform granular soil deposits are discussed. It should be noted that the design is very sensitive to the wall embedment; the calculated value was always rounded up to the nearest 1mm rather than the usual.5m to 1m. The results do not always align into smooth curves as they, like all numerical analyses, contain different types of small random errors due to various numerical inaccuracies. An example in Figure 1 shows a plot of A m versus øvalue for a cantilever in a uniform granular deposit. The values are hand calculated using a simple approximation of perfectly plastic soil behaviour, with the maximum bending moment corresponding to the zero shear point. The results of these calculations are not dependent on the depth of the excavation and the calculation errors are only caused by the inaccuracy of reading the K a and K p values from the BS82 charts. Naturally, A m values for δ = were calculated directly and contain no error so they are aligned horizontally. It can be seen that a few per cent calculation error is possible just through the rounding of chart data. To design what is meant or to mean what is designed? General analysis of cantilever walls A large sample of analyses was carried out for a simple cantilever. The analysis covered various excavation depths from 3m to 12m, øvalues from 2º to 4º, wall stiffnesses ranging from 2 x 1 4 kn.m 2 /m.run (conversion is difficult to achieve for smaller stiffnesses) to the virtual infinity and soil stiffnesses from 1MPa to 1MPa. The values of K o =.6 were used in all analyses. A sample of analysis results for 9m deep excavations in soils of different strength is presented in Figure 2. These curves are based on the analyses assuming a partial factor of on the ø values. A very similar plot can be produced for the partial factor value δvalues 2/3 ø ø BS82 6 ±.2 96 ± ±.3 6 ± ± ±.57  Table 1: A m ratios for different analysis parameters of 5, as per Table A.2 of EC7. It can be seen that bending moments for both representative and factored sets of parameters are dependent on the soil strength and on the adhesion factor. However, the curves are very similar in shape and as a result the A m ratios are virtually independent of the varied factors as shown in Table 1. Therefore, the designer can expect good predictability of the results whether the representative (or best guess) or the factored soil strength design is carried out in uniform ground conditions. The Table 1 values do not apply to layered soils. Effect of overexcavation on cantilever walls Figures 3 and 4 show the effect of overexcavation on the analysis results for absolutely stiff retaining walls. The depths of overexcavation were selected as the lesser of.1d or.5m and the overexcavations were only included in the analysis using the factored soil parameters, which is consistent with BS82. For all equations here, δ = ø was used. As can be seen, the effect of overexcavation depends on the depth of the main excavation, with the M fvalues between 55% and 8% greater than the M rvalues for the same wall geometry of absolutely stiff walls. This compares with about 38% when modelling the wall without overexcavation. Effect of embedment depth on cantilever walls Figure 5 shows the effect of extra depth of embedment, in excess of the stability requirement, on A mvalues for stiff walls. As the embedment depth increases, the wall gradually approaches the fixed earth condition. As a result, earth pressure on the active side becomes closer to the at rest value for both representative and factored analyses and A mratio reduces. But, this effect develops very slowly and is unlikely to affect the results unless the embedment is substantially greater than is necessary. Naturally, the effect caused by extra wall embedment will be reduced for walls of finite stiffness. The analysis results presented above for cantilever walls do not represent anything unexpected δ = δ = 2/3ϕ δ = ϕ 9 Figure 1: Errors arising from scaling Ka and Kp values from charts Mf (δ = ) Mr (δ = ) Mf (δ = 2/3ϕ) Mr (δ = 2/3ϕ) Mf (δ = ϕ) Mr (δ = ϕ) Mf (BS82) Mr (BS82) 5 Figure 2: Maximum bending moments for a cantilever with 9m upstand Mf (without overexcavation) Mf (with overexcavation) Mr (with or without overexcavation) 5 Figure 3: Effect of overexcavation for a cantilever with 9m upstand No overexcavation (all depths) Overexcavation (D = 3m) Overexcavation (D = 6m) Overexcavation (D = 9m) Overexcavation (D = 12m) Figure 4: Effect of overexcavation on A m ratios for a cantilever 32 GROUND ENGINEERING JULY 27
3 The picture changes, however, when dealing with tied or propped s. General analysis of propped walls Figures 6 and 7 show, respectively, bending moments and strut forces for an absolutely stiff wall with an absolutely stiff prop at the top. These analyses were based on a soil strength factor of. The use of absolutely stiff structural elements allows avoiding distortions of diagrams that may potentially be caused by the secondary effects. It can be seen that the plots are similar for different δvalues, but, significantly, for soils of greater strength the forces calculated in the factored analyses are smaller than those from the representative analyses. It looks as if an increase in the soil strength causes an increase in the forces in the, which sounds as paradoxal as Hambly s stool. As a result, the respective A m and A r ratios vary from about for the weaker soils to to for the stronger soils, as shown on the plot in Figure 8. A similar set of results is shown in Figure 9 for the partial soil strength factor of 5, as per EC7. The amplitude of variation of A m and A r ratios is just slightly greater than for the BS82 factor, but the overall pattern remains the same. To demonstrate that the above effects were not caused by software error, a numerical analysis of a similar supporting a 15m excavation was carried out using standard industry numerical analysis software using finite differences approach (Software Suite B). The wall was modelled with an absolutely stiff support at the top. As numerical analysis software cannot properly converge to a solution for an absolutely stiff wall, a reduced stiffness was used in the analysis. This does not allow a direct comparison between the results for Software Suites A and B. Nevertheless, the comparison of bending moments calculated for representative and factored designs was confirmed by Software Suite B analysis, as shown in Figure 1. It can be seen that factored analysis yields higher values of bending moments for a relatively weak soil (ø = 25º), whereas for stronger soil (ø = 4º) representative bending moments were marginally higher than those from the factored analysis. A sensitivity analysis for the wall embedment can help to explain the apparent paradox of greater soil strength causing greater structural loads. This was carried out using Software Suite A, assuming an absolutely stiff wall and using soil parameters as above and δ = ø. The results are presented below. Effect of embedment depth on propped walls A plot of maximum bending moments calculated for different wall embedments is presented in Figure 11. It can be seen that relatively small increases in the wall embedment cause significant increases in the bending moments. This effect, which is particularly transparent for the soils of greater strength, is caused by relative stiffening of the embedded part of the wall. This effect occurs similarly to the cantilever walls but is much more pronounced for the propped walls. A stiffer toe response would, naturally, reduce wall deflections and increase the bending moments. A plot of the respective strut forces is very similar and is not presented here. Therefore, the phenomenon of increased soil strength resulting in greater structural forces is caused by a combination of effects of the increased soil strength and the Mf (δ = ) Mr (δ = ) Mf (δ = 2/3ϕ) Mr (δ = 2/3ϕ) Mf (δ = ϕ) Mr (δ = ϕ) Mf (BS82) Mr (BS82) Figure 6: Bending moments diagram for a tied with 15m upstand Strut force, kn/m run Rf (δ = ) 9 Rr (δ = ) Rf (δ = 2/3ϕ) 8 Rr (δ = 2/3ϕ) Rf (δ = ϕ) 7 Rr (δ = ϕ) 6 Rf (BS82) Rr (BS82) Figure 7: Strut forces diagram for a tied with 15m upstand and Ar (δ = ) (δ = 2/3ϕ) (δ = ϕ) (BS82) Ar (δ = ) Ar (δ = 2/3ϕ) Ar (δ = ϕ) Ar (BS82) Figure 8: A m and A r ratios for a tied (partial factor) and Ar (δ = 2/3ϕ) (δ = ϕ) Ar (δ = 2/3ϕ) Ar (δ = ϕ) Embedment = d Embedment = 2d Embedment = 3d Embedment = 4d Figure 5: Effect embedment depth on A m ratios for a cantilever reataining wall Figure 9: A m and A r ratios for a tied (partial factor5) GROUND ENGINEERING JULY 27 33
4 relatively increased wall embedment. Had two different walls been analysed separately, using either factored or representative strength for both stability and structural loads calculations, the one using the representative soil strength would have a smaller embedment and smaller design bending moments. The above effect seems only to be encountered when using software capable of numerical modelling of soilstructure interaction. The software suites that use a simplified analysis approach, even those based on noncoupled subgrade reaction analysis, just show a conventional increase in structural forces with reduced soil strength. Figure 12 shows the effect of extra wall embedment on A m and A r. It can be seen that for wall embedment just twice the design value, the ratios are very close to 1. Naturally, as wall stiffness reduces, A m and A r ratios become less dependent on the relative increase in the wall embedment. It should be noted that the relative wall stiffness depends on the depth of excavation. Figure 13 shows the effect of wall stiffness on the calculated Mvalues for a propped supporting a 15m deep excavation. It can be seen from Figure 14 that for a sufficiently soft wall A m is about to, that is, similar to the values calculated for cantilever walls. The A m values for soft walls do not seem to be affected by the soil strength or by the depth of excavation. To put the above sensitivity analysis into perspective of real walls, Figure 15 shows a sensitivity analysis for wall stiffness. Stiffnesses of some real walls are shown on the same plot for comparison. It should be noted that AZ12 sheet pile section is the lightest available from its manufacturer. It can be seen that A mratios may be close to or even less than 1 for quite real structures. Strut force plots are similar and not presented here. This phenomenon can be found in real design situations. For example, the author has been involved in reviewing designs in ground conditions comprising sands over completely weathered sandstone, where an increase in design values of sandstone strength caused an increase in the design bending moments. Effect of overexcavation on propped walls The above effect will be exaggerated by other factors increasing the relative embedment of the wall. Figure 16 shows the effect of including an overexcavation in the analysis. Although it was carried out for an absolutely stiff wall, similar effects will be encountered for walls of finite stiffness. It can be seen that M f values do indeed increase as a result of overexcavation. But due to the excess embedment, M r values increase to an even greater extent. Figure 17 shows the respective ratios A m and A r for different overexcavation scenarios. There is very little variation of the ratio values for different depths of excavation checked here, that is, within the range of 9m to 24m upstands. Comparing the A m and A r ratios for analyses with and without overexcavation, it can be seen that introduction of overexcavation increases the relative factored structural forces for weaker soils. For stronger soils the effect is the opposite introduction of overexcavation causes A m and A r ratios to reduce further compared with the results without overexcavation. In the same way, structural forces developing during gradual excavation of soil on the passive side of the may be greater than when the excavation is completed. This is only relevant for relatively stiff walls in stronger soils, but ignoring this factor in the design cases when it is actually applicable will certainly not increase the conservatism of the design. Similarly to the cantilever wall analyses, sensitivity to soil stiffness was checked for Emoduli range from 1MPa to 1MPa and no effect on the analysis results was encountered. No sensitivity analysis for strut stiffness is presented here. But this factor rarely causes a significant effect on the bending moments. The greatest effect is normally caused by introduction of prestressed anchors, which increases the stiffness of the system, thus reducing the deflections and increasing the anchor forces. This is similar to the way it works in prestressed concrete. Discussion & concluding remarks When designing a the designer would be concerned to provide a safe as well as efficient design. It is also usually desirable to ensure that differences between various designs of the same structure done by different designers are not just governed by their willingness to take risks. Based just on the limited analysis presented in this paper, it is possible to evaluate the range of structural design forces that are implied by current design codes. This is only a sample of the possible design outcomes. Depth, m   Mr Mr 2 Mf 2 Mf (a) 22 (b) Figure 1: Bending moment diagrams from Software Suite B analysis: (a) for uniform soil strata with ø = 25, (b) for uniform soil strata with ø = Mf (Embedment = d) Mr (Embedment = d) Mf (Embedment = d) Mr (Embedment = d) Mf (Embedment = 5d) Mr (Embedment = 5d) Mf (Embedment = 2d) Mr (Embedment = 2d) Figure 11: Effect of embedment depth on bending moments for a tied with 15m upstand and Ar Rf/Rr (Embedment = d) Rf/Rr (Embedment = d) Rf/Rr (Embedment = 5d) Rf/Rr (Embedment = 2d) Mf/Mr (Embedment = d) Mf/Mr (Embedment = d) Mf/Mr (Embedment = 5d) Mf/Mr (Embedment = 2d) Figure 12: Effect of embedment depth on A m and A r ratios for a tied 6 Md (all stiffnesses) Mr (stiffness 2 x 1^8) Mr (stiffness 2 x 1^7) Mr (stiffness 2 x 1^6) Mr (stiffness 2 x 1^5) Mr (stiffness 2 x 1^4) Figure 13: Effect of wall stiffness on bending moments for a tied with 15m upstand 34 GROUND ENGINEERING JULY 27
5 s D = 6 (stiffness 2 x 1^8) D = 15 (stiffness 2 x 1^8) D = 24 (stiffness 2 x 1^8).6 D = 6 (stiffness 2 x 1^7) D = 15 (stiffness 2 x 1^7) D = 6 (stiffness 2 x 1^5).4 D = 24 (stiffness 2 x 1^7) D = 15 (stiffness 2 x 1^5) D = 6 (stiffness 2 x 1^6) D = 24 (stiffness 2 x 1^5).2 D = 15 (stiffness 2 x 1^6) D = 6 (stiffness 2 x 1^4) D = 24 (stiffness 2 x 1^6) D = 15 (stiffness 2 x 1^4) Figure 14: Effect of wall stiffness on A m ratios for a tied retaining wall with 15m upstand Mf (No overexcavation) Mr (No overexcavation) Mf (Overexcavation) Mr (Overexcavation) Figure 16: Effect of overexcavation on bending moments for a tied retaing wall with 15m upstand Contiguous RC pile wall d6mm at 9mm c/c Sheet pile wall AZ12.7 E +4 E +5 E +6 The Table 2 values are quoted directly from the results presented in this paper, for walls in a uniform granular stratum. There are other recommendations on the selection partial load factors that are currently available, however, some of them are not sufficiently explicit and some others imply Y f values lower than those applied to the self weight of the structures. The author believes that a comparison based on the above three options would give a sufficient review here. Just to make the designer s task more challenging, it is interesting to see how the understanding of a conservative design translates into a paradox: a geotechnical engineer interpreting the ground conditions may believe that by ascribing ø = 4º to a soil whose real øvalue is 45º, makes the design conservative. That would translate into a factored øvalue of about 35º using a mobilisation factor of. m thick RC diaphragm wall RC Tdiaphragm wall: flange 4x1m, web 3.6x1m D = 6m (ϕ = 2 ) D = 6m (ϕ = 4 ) D = 15m (ϕ = 2 ) E +7 D = 15m (ϕ = 4 ) D = 24m (ϕ = 2 ) D = 24m (ϕ = 4 ) E +8 E +9 Wall stiffness, kn m^2 Figure 15: A m ratios versus wall stiffness for a tied For a cantilever, for a wide range of input parameters For very stiff s propped near the top For propped wall of finite stiffness BS595 (1) (Clause 2.2.4) Yf = on nominal loads determined in accordance with CP2 BS811 (3) (Table 2.1 without BS811 (Table 2.1 with overexcavation) and BS595 (Table 2) Yf = on earth pressures obtained from BS82 including appropriate mobilisation factors 51.7, depending on the δvalue 5, depending on the ø and δvalues, but converges to about for walls with excessively large embedment 1.8, depending on the øvalues overexcavation) Yf = on earth pressures obtained from BS82, when unplanned excavation is included in the calculation 51.8, depending on excavation depth.75, depending on the excavation depth (variation of δvalues not addressed in this paper) Not addressed in this paper Using this value, the design engineer will find the required embedment through analysis and then round it up to make the design more conservative. The detailer will then increase the wall strength (and stiffness too) for the same reason. The result may be that the wall embedment will be two to three times what was actually required for the real soil conditions and the bending moment may be up to twice greater than that calculated by design. Introduction of overexcavation into the design may increase the underdesign in structural strength by a further 1% to 15%. It should be remembered that the above refers just to the designs capable of modelling variation in soil structure interface stresses, depending on the relative deflections. The use of simpler types of analysis may introduce much different results. The progress in computer development has created the and Ar.7 environment when design can be done by engineers and managers with a very basic understanding of geotechnics, who just follow the published design recommendations. This creates a large variety of designs, some of which may be more pragmatic than desired. It is hoped that the above analysis gives some understanding of the difficulties arising from direct application of standard requirements for the use of factored soil parameter designs. The author suggests that when using a factored soil strength design approach (whether BS82, or EC7, or other) the designer may wish to ensure that: They understand that the analysis based on factored soil parameters may result in a set of structural design loads little related to the real working conditions. They understand the assumptions implied by the method of analysis or type of software employed, together with the consequences caused to the structural design of the wall. The comparative increase in structural strength demand against the analysis based on best estimate reflects the factual design uncertainties faced. (No overexcavation  all depths) (Overexcavation  all depths) Ar (No overexcavation  all depths) Ar (Overexcavation  all depths) Figure 17: Effect of overexcavation on A m and A r ratios for a tied Table 2: Ratio of the structural design moments to the serviceability moments (soil strengh factor M=) Any conservative changes made to the geometry of the structure after the design is completed are not causing an increase in the structural forces (this includes, for example, increasing embedment of the wall, its crosssection). The conservative assumptions made with regard to, for example, soil strength or construction staging are indeed conservative. The issues discussed in this paper will not disappear when using EC7 unless engineers understand the importance of using a combination of several design approaches in their practice. References 1. BS5951:. Structural use of steelwork in building Part 1: Code of practice for design rolled and welded sections. 2. BS82:1994. Code of practice for earth retaining structures. 3. BS8111:1997. Structural use of concrete Part 1: Code of practice for design and construction. 4. BS EN :24, Eurocode 7: Geotechnical design Part 1: General rules. 5. J.B. Burland, D.M. Potts. The overall stability of free and propped embedded cantilever s. Ground Engineering, 1981, July, pp GROUND ENGINEERING JULY 27 35
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