Comparison of Sheet Pile Wall Design According to Conventional and AASHTO LRFD Design Methodologies
Chad William Harden, P.E., S.E. Senior Associate RBF Consulting, a Company of Michael Baker Corporation 14725 Alton Parkway (MS 400) Irvine, CA 92619 Phone: 949-855-7058, Fax: 949-855-7070 Email:
[email protected]
Word Count: Text: Tables (4 x 250): Figures (4 x 250): Total:
5131 1000 1000 7131
Date of Submission: November 15, 2012
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Comparison of Sheet Pile Wall Design According to Conventional and AASHTO LRFD Design Methodologies ABSTRACT Sheet Pile wall design using methods in AASHTO LRFD Bridge Design Specifications (2010) is compared in this study to methods in United States Army Corps of Engineers (USACE) Engineering Manual 1110-2-2504 (USACE, 1994). It will be shown that AASHTO (2010) results in a greater embedment depth, mainly due to a safety factor compounded with Load Factors. Simple modifications to the current AASHTO (2010) code provisions code are suggested which have the potential for large cost savings – while achieving a relatively conservative design compared to conventional design methods (USACE) and typical load combinations. Guidance on the selection of load combinations is also provided. Finally, available centrifuge test data for sheet pile walls subjected to earthquake loading are compared to resulting moment demands derived for both AASHTO and USACE methods.
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INTRODUCTION
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The American Association of State Highway and Transportation Officials (AASHTO) Load and Resistance Factor Design (LRFD) Bridge Design Specifications (1) represents the state of the art design basis for transportation structures, including nongravity cantilevered retaining walls. In this paper “sheet pile wall” is used in lieu of the term “nongravity cantilevered wall.” However, recommendations in AASHTO (1) specific to sheet pile walls compound load and resistance factors with an additional safety factor for depth which results in an overly conservative design.
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This paper compares resulting embedment depths and moment demands for sheet piles installed in cohesionless soils using the AASHTO LRFD Bridge Design Specifications (1) with another state of the art design code for sheet pile walls – the United States Army Corps of Engineers (USACE) Engineering Manual 1110-2-2504 (2).
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A range of retained heights, H, from eight to 18 feet are considered, as well as a range of possible soil strengths; friction angles considered range from 28 degrees to 44 degrees. The study also includes a range of earthquake design accelerations.
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Section 1.0 of this article summarizes the general load cases considered in this study, which apply to both AASHTO (1) and USACE (2). Section 2.0 and 3.0 discuss specific load combinations for AASHTO (1) and USACE (2), respectively, followed by a short comparison of both codes in Section 4.0. Finally, results of analysis are compared (Section 5.0) and summarized (Section 6.0).
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1.0
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Before discussing the similarities and differences of the two codes considered in this paper, three general load cases typical for this wall type are defined, which can be considered both by AASHTO (1) and USACE (2).
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These typical load cases specific to sheet pile walls are shown graphically in Figure 1 and described as follows,
LOAD CASES CONSIDERED
Load Case (a): Drained Soil Pressures and Live Load A typical minimum load case considered in practice is drained soil with maintenance or live loading on the retained side. Active and passive pressures are derived using the Rankine (3) method for soil equivalent fluid pressures. Table 1 lists the resulting active and passive equivalent fluid pressures and coefficients.
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FIGURE 1 Load Cases Considered. Table 1 Range of Soil Strengths Considered in this Study Friction Angle ∅ (deg)
28 30 32 34 36 38 40 42 44 56 57 58 59 60 61
Active Pressure Coefficient
0.36 0.33 0.31 0.28 0.26 0.24 0.22 0.20 0.18
Passive Pressure Coefficient
Equivalent Active Fluid Pressure
Equivalent Passive Fluid Pressure
2.77 3.00 3.25 3.54 3.85 4.20 4.60 5.05 5.55
pcf (kN/m3) 43 (6.8) 40 (6.3) 37 (5.8) 34 (5.3) 31 (4.9) 29 (4.5) 26 (4.1) 24 (3.7) 22 (3.4)
pcf (kN/m3) 332 (52.2) 360 (56.5) 391 (61.3) 424 (66.6) 462 (72.6) 504 (79.2) 552 (86.6) 605 (95.0) 666 (104.6)
Load Case (b): Flooded Soil Pressures A less frequent load case occurs when the sheet pile wall retains an undrained soil condition induced by a “quick draw-down” event. In this analysis, a worst case is assumed where the soil is flooded to the top of the retained side of the wall, as well as to the grade in front of the wall.
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Load Case (c): Earthquake Loading A third load case is defined as “drained” active soil pressures plus earthquake soil pressures. There are several suggested methods in literature for estimating seismic demands on retaining walls. FEMA P-750 (4) suggests a simplified procedure which is linearly proportional to the peak ground acceleration. Other recent design guides suggest a method which modifies the Mononobe-Okabe (M-O) approach (5) to account for displacement of the wall, such as NCHRP Report 611 (6) and Appendix A11 to AASHTO (1) In this study, seismic earth pressures are estimated according to the Mononobe-Okabe analysis (5) without regard for displacement; that is, the demands are calculated in a pseudo-static approach which is widely used. This approach is presented in AASHTO (1) and USACE Engineering Manual 1110-2-2502 (7). Results for required embedment and moment demand are presented in a normalized format in terms of the design kh, for easier comparison to other methods. In this analysis a range of kh is considered, from 0.1 to 0.5. The vertical component of ground acceleration, kv, is assumed to be zero. The equation for the seismic active pressure coefficient, after AASHTO (1) is given by the following:
K AE
é cos2 (f - q - b ) = · ê1 + 2 cosq cos b cos(d + b + q ) ë
sin(f + d ) sin(f - q - i ) ù ú cos(d + b + q ) cos(i - b ) û
-2
(1)
where: g = unit weight of soil (kcf) H = height of soil face (ft) f = angle of friction of soil (degrees) q = arc tan ( k h / (1 - k v )) (degrees) d = angle of friction between soil and abutment (degrees) k h = horizontal acceleration coefficient (dim.) kv = vertical acceleration coefficient (dim.) (taken as zero in this study) i = backfill slope angle (degrees) (taken as zero in this study for level backfill) b = slope of wall to the vertical (degrees) (taken as zero in this study)
Finally, the Dynamic Increment Earth Pressure, ∆KAE, is derived: D K AE = K AE - K A
(2)
Each of these load cases will be evaluated with the applicable load factors and strength reduction factors according to the USACE (2) and AASHTO (1) methodologies, over a range of heights,
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soil friction angles and acceleration coefficients. Table 2 lists the coefficient of Dynamic Increment Earth Pressure, ∆ , for the friction angles and design kh considered in this study. Table 2 Dynamic Increment Earth Pressure Variables Friction Angle f (deg) 28 30 32 34 36 38 40 42 44
109 110 111 112 113 114 115 116 117 118 119
120 121 122
5
2.0
Dynamic Incremental Component of Earth Pressure, ∆ = 0.1 = 0.2 = 0.3 = 0.4 0.066 0.147 0.250 0.392 0.063 0.140 0.236 0.363 0.061 0.134 0.224 0.340 0.058 0.127 0.212 0.319 0.056 0.122 0.202 0.301 0.053 0.116 0.192 0.285 0.051 0.111 0.183 0.270 0.048 0.106 0.174 0.257 0.046 0.101 0.166 0.244
= 0.5 0.644 0.557 0.502 0.462 0.430 0.402 0.379 0.357 0.338
USACE (2) DESIGN METHODOLOGY
The design approach described in USACE (2) is chosen for comparison in this study because it perhaps best emulates the “conventional” design approach commonly used in industry. The conventional approach to sheet pile design consists of balancing active and passive pressures such that the sum of forces and moments about the tip of the sheet pile, or bottom of wall, are equal to zero. In the conventional approach, a large net passive pressure is developed at the retained side of the wall at the base, as shown in Figure 2(a). The embedment depth, “D”: and point, “Z” are iterated until static equilibrium is reached.
Figure 2 Conventional (a) and Simplified (b) method of design for cantilever sheet piling in granular soils (USS (8) with permission)
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USACE (2) prescribes varying levels of safety factors corresponding to each of the three load combinations considered in design; either “Usual”, “Unusual”, or “Extreme”. Factors of safety also vary depending on whether the engineer is checking for the required embedment depth or the maximum moment demand. In this approach, the engineer makes the best estimate of soil strengths and characteristics. A safety factor appropriate to each load combination is then applied to the passive capacity of the system to determine the required embedment depth. A separate load case is then analyzed for each load combination, without applying a safety factor, to determine the maximum moment demand on the system; however, an allowable stress increase is applied to the steel capacity as appropriate to each load combination. In order to compare these safety factors to the AASHTO (1) method, the inverse of safety factors are presented as “f ” factors for soil capacity in Table 3. Steel capacity in USACE (2) is estimated at allowable stress level. Similar to the safety factors, allowable stress increases are presented as “f ” factors for steel capacity in Table 3, after making the following necessary adjustments to compare with AASHTO (1) at ultimate capacity, starting with the required steel capacity according to USACE (2): ≤ 0.5 ⋅
⋅
⋅
(3)
Because sheet pile sections are comprised of generally rectangular sections, we can substitute the plastic section modulus for the elastic section modulus as follows: 1.5 ⋅
=
(4)
= ∙
(5)
149 150
= 0.5 ⋅
⋅
⋅ ∙
=∅⋅
⋅
(6)
151 152
∴∅= ⋅
153 154 155 156 157 158 159
where: Mr = Moment Demand ASI = Allowable Stress Increase fy = Steel Yield Stress S = Elastic Section Modulus Z = Plastic Section Modulus
160 161 162 163 164 165 166
(7)
The actual loads corresponding to the “Usual”, “Unusual”, and “Extreme” load combinations in USACE (2) is left to the judgment of the Engineer. However, with some consideration of code guidance, a clear breakdown of these load combinations is as follows.
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Load Case (a): USACE “Usual” Condition A typical minimum load combination considered in practice is drained soil with maintenance or live loading on the retained side. Therefore, the “Usual” condition is considered to be the sheet pile wall retaining a drained soil condition and two feet of live load surcharge pressures. Load Case (b): USACE “Unusual” Condition A “Unusual” condition is defined as the sheet pile wall retaining an undrained soil condition induced by a “quick draw-down” event. ASCE 7-10 (9) provides some guidance on selecting an appropriate loading condition where flooded backfill may govern the design of the sheet pile wall. In the following discussion and definition of this load case, consider that ASCE 7-10 is another state of the art reference for civil and structural engineers, in the absence of local building codes or design guides. ASCE 7-10 (9) is referenced by the 2012 International Building Code (10) and the AISC Steel Construction Manual, 13th Edition (AISC) (11). ASCE 7-10 (9) Chapter 2.4.2, Load Combinations Including Flood Load, indicates the following load combination shall be considered when a structure is located in a non-coastal “A-Zone” flood zone, where Fa is the flood load:
5. H + F + 0.75Fa
(Unusual Condition)
(8)
where: H = load due to lateral earth pressure or ground water pressure F = load due to fluids with well-defined pressures and maximum heights. In the above equation, the terms, D, W and E are omitted which do not apply to the load combination considered. Please note a more stringent load factor on Fa may be considered for “V-Zones” or “Coastal A-Zones”, which is not considered in the scope of this analysis. “V-Zones” and “Coastal A-Zones” correspond to loading in areas of extreme wind or flood in hurricane-prone coastal areas (9), and are determined from Flood Insurance Rate Maps (FIRM) (12) developed as part of the FEMA National Flood Insurance Program (NFIP) (13). Such loading would be highly specific to location and project conditions. ASCE 7-10 (9) Chapter C2.4.2 commentary indicates “…the multiplier on Fa aligns allowable stress design for flood load with strength design.” The 0.75 applied to the flood load is compatible with the “one-third” increase in allowable stress associated with the “Unusual” loading condition described in USACE (2) Chapter 6-3. Therefore, it is justified to define the flooded backfill condition as an “Unusual” condition for stability calculations.
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Load Case (c): USACE “Extreme” Condition Finally, an “Extreme” event is defined as “drained” active soil pressures plus earthquake soil pressures. Earthquake loading is a logical selection for an extreme load case. Load Combinations and corresponding Factors of Safety are presented in Table 3 based on the interpretation of loading conditions as described in USACE (2), Section 5-2 and Table 5-1. 3.0
AASHTO (1) DESIGN METHODOLOGY
AASHTO (1) suggests a simplified approach according to Teng (14). In this approach, the passive capacity pressure distribution of the base of wall previously described is replaced with a restoring force point load of the same aggregate results, as shown in Figure 2(b). However, the embedment depth is arbitrarily increased 20% from the calculated, required embedment depth. Practice shows this 20% does not constantly provide an expected “Factor of Safety” when compared to the conventional approach of including the Factor of Safety in the estimation of passive capacity. Calculations show that, if the desired factor of safety is accounted for in the passive capacity for both methods, the conventional and simplified approaches arrive at a similar depth and maximum moment. Therefore, for the discussions in this paper, the conventional approach will be used; that is, the method of Figure 2(a) is used. Table 3 lists load factors and strength reduction factors for the USACE (2) and AASHTO (1) load combinations. An Effective Safety Factor (U) is calculated, which is intended to roughly present the effect of both load and strength reduction factors, for comparison across codes, through the following calculation: =∅
∙∅
(9)
For example, one can see that the Effective Safety Factor between the USACE “Usual” Load Combination for Depth and the AASHTO (1) “Service I” Load Combinations are nearly identical. Not surprisingly, the resulting embedment depths and moment demands for this one load combination will be shown to be very similar across both codes.
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Table 3 Load and Resistance Factor Design – Comparison of Variables for Depth and Moment Demand Load Case
Load Combination
Load Factor, g
ff
Allowable Stress Increase
ff
Effective Safety Factor U= ∅
(Soil) USACE Combinations for Depth (a) Usual 1.00 (b) Unusual 1.00 (c) Extreme 1.00
(b) (a)
249 250 251 252 253 254 255 256 257 258
Service I (EH+LL) Service I (EH+WA) Strength I (EH+LL)
(b)
Strength I (EH+WA)
(c)
Extreme
(Steel)
0.67(1) 0.80(1) 0.91(1)
USACE Combinations for Moment Demand (a) Usual 1.00 (b) Unusual 1.00 (c) Extreme 1.00 AASHTO (a)
(Steel)
∙∅
1.50 1.25 1.10 1.00(2) 1.33(2) 1.75(2)
0.33(3) 0.44(3) 0.58(3)
3.00 2.25 1.71
1.00
0.75
0.90
1.48
1.00
0.75
0.90
1.48
1.50 (EH), 1.75 (LL), 1.54 Effective 1.50 (EH), 1.00 (WA), 1.10 Effective 1.50 (EH), 1.00 (EQ) 1.18 Effective
0.75
0.90
2.28
0.75
0.90
1.63
0.75
1.00
1.57
Notes: (1) Value is inverse of Factor of Safety (FS). FS Applied to Passive Pressure for Free-Draining Soils, per Table 5-1 of EM 1110-2-2504 (USACE, 1994) (2) Per Section 6-3 of EM 1110-2-2504 (USACE, 1994) (3) Capacity Per USACE is based on Section Modulus. See equations 3 through 7 for conversion from allowable stress design to ultimate level design. (4) Nomenclature after AASHTO (1): EH = Horizontal Earth Pressure Load, LL = Vehicular Live Load, WA = Water Load
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4.0
COMPARISON OF DESIGN CODES
Table 4 summarizes the load combinations for both codes applicable to the basic load cases defined in Section 1.0. The corresponding Effective Safety Factor, U, for each code and load combination from Table 3 is repeated for side-by-side comparison. Recall that AASHTO (1) makes no distinction between service and strength load combinations with respect to calculating the required embedment depth. Therefore, two load combinations for AASHTO (1) are compared to the corresponding load combination for depth as defined by USACE (2) for Load Cases (a) and (b). Table 4 Load and Resistance Factor Design – Comparison of Effective Load Factor (U)
Load Case
(a)
288
USACE (2) Load Combination
Usual – Depth Unusual – Depth
(b)
272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287
10
AASHTO (1) Load Combination
Service I (EH+LL) Strength I (EH+LL) Service I (EH+WA) Strength I (EH+WA)
USACE (2) Effective Safety Factor (U) 1.50 1.25
AASHTO (1) Effective Safety Factor (U) 1.48 2.28 1.48 1.63
(c)
Extreme – Depth
Extreme
1.10
1.57
(a)
Usual – Moment
Strength I (EH+LL)
3.00
2.28
(b)
Unusual – Moment
Strength I (EH+WA)
2.25
1.63
(c)
Extreme – Moment
Extreme
1.71
1.57
These Effective Safety Factors will be useful in interpreting the relative magnitude of the required embedment depths and moment demands resulting from the AASHTO (1) and USACE (2) design requirements. 5.0
COMPARISON OF RESULTS
Comparison of Typical Load Combinations The resulting embedment depths, D, and maximum moment demands according to the USACE (2) and AASHTO (1) Methodologies are shown in Figure 3. Solutions for multiple retained heights “collapse” into one solution when presented in a normalized format, which is consistent with Teng (14). Therefore, the embedment depth, D, is normalized by the height, H, of the wall, and increased by the variable j , in the case where live load (qLL) is present, to achieve a “Depth Ratio” as shown in the following equation: Depth Ratio =
D ×j H
(10)
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Where: =∅∙
⋅
(11)
⋅
∙
(12)
Resulting embedment depths are presented without increasing by 20% as recommended in AASHTO (1). The maximum moment demand in the wall is normalized by the moment calculated at the base of the retained height, H, to achieve a “Moment Ratio” as follows: =
303 304
where:
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1+
= ∙
302
305
11
(13)
=∅
γ H + K ⋅q
⋅H
(14)
When referring the USACE Load Combinations, it is implied that when the discussion is relative to moment demands, the load case for moment is considered (i.e. “Usual – Moment” in Table 4), whereas the load case for depth is relative to required embedment depths (i.e. “Usual – Depth” in Table 4). Finally, both the normalized depth and moment ratio are plotted against the Passive Earth Pressure Coefficient, Kp, normalized by the Active Earth Pressure Coefficient, Ka. Comparison of Service and Strength Load Combinations for Depth Figure 3 shows excellent comparison, from 1% to 10% difference, between the USACE Usual (US) Load Case and the AASHTO Service I Load Case for depth. Recall the Effective Safety Factor, U, is nearly identical for both codes. However, the AASHTO Strength I (EH+LL) load combination estimates approximately 19% to 29% greater embedment depth, compared to the USACE “Usual” load combination. Recall the normalized embedment depth is reported without the addition 20% increase that is recommended in AASHTO (1). Note also that the Effective Safety Factor associated with the AASHTO (1) Strength I (EH+LL) load combination is 52% greater than that for the USACE (2) “Usual” load combinations for depth.
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10
15
20
25
35
6
0
5
5 Usual, USACE Unusual, USACE Service I (LL), AASHTO Service I (WA), AASHTO Strength I (LL), AASHTO Strength I (WA), AASHTO
Moment Ratio 4
Depth Ratio, j • D/H
30
10
Moment Ratio 3
15
2
20
Depth Ratio
1
25
0
30 5
328 329 330 331 332 333 334 335 336 337 338
10
15
20
25
30
Moment Ratio, MMAX/MNORM
Increasing
5
Increasing
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Kp/Ka
Figure 3 Normalized Results for Typical Load Combinations Figure 3 also shows excellent comparison for embedment depth, from 1% to 10% difference, between the USACE Unusual (UN) Load Case and the AASHTO Service I (WA) Load Case for walls with flooded backfill. The AASHTO Strength I (WA) load combination estimates approximately 11% to 28% greater embedment depth compared to the USACE “Unusual” load combination. Again, note that the Effective Safety Factor associated with the AASHTO (1) Strength I (WA) load combination is 30% greater than that for the USACE (2) “Unusual” load combinations for depth.
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These comparisons suggest that only service level load combinations should be considered for estimating embedment depth in the AASHTO methodology. As well, the 20% increase in depth as suggested in AASHTO (1) should be deleted from the specification. Comparison of Strength Load Combinations for Moment Demand Figure 3 shows the USACE (2) “Usual” load combinations for moment provides a moment demand approximately 10% to 30% greater than the AASHTO (1) Strength I (EH+LL) load combination for earth and live loads. Similarly, the USACE (2) “Unusual” load combinations for moment provides a moment demand approximately 10% to 30% greater than the AASHTO (1) Strength I (EH+WA) load combination for walls with flooded backfill. The Effective Safety Factor associated with the USACE (2) “Usual” and “Unusual” load combinations for moment are approximately 30% greater than the AASHTO (1) Strength I (EH+LL) and Strength I (EH+WA) load combinations. These comparisons suggest that USACE (2) methodology is slightly conservative for moment demands with respect to AASHTO (1). Comparison of Extreme (Earthquake) Load Combinations for Depth and Moment The resulting embedment depths, D, and maximum moment demands according to the USACE (2) and AASHTO (1) Methodologies, for the Extreme load combination considering earthquake effects, are shown in Figure 4. It is desirable to present multiple solutions in a normalized format similar to the static comparisons. To this end normalizing variables for soil characteristics and wall depth and moment demand in terms of kn are found by observation and detailed following. The embedment depth, D, is normalized by the height, H, of the wall, and increased by the variable cy for earthquake loading, in order to present solutions of multiple wall heights and soil properties, as shown in the following equation: = 1 + 10
(15)
Similarly, the normalized maximum moment demand as presented in Equation 3, is increased by the variable cy for earthquake loading. Finally, both the normalized depth and moment ratio are plotted against the Passive Earth Pressure Coeffecient, Kp, normalized by the Active Earth Pressure Coeffecient, Ka, and the product of the variable cx: =1+k
(16)
Again, resulting embedment depths are presented without increasing by 20% as recommended in AASHTO (1). Compared to USACE Extreme load combinations, Figure 4 shows the AASHTO Extreme combination estimates within unity to approximately 30% greater moment demand, and 32% to
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56% greater embedment depth. This may be expected, noting that the Effective Safety Factor associated with the AASHTO (1) “Extreme” load combination is 10% and 43% greater than that for the USACE (2) “Extreme” load combinations for moment and depth, respectively. It would appear both AASHTO (1) and USACE (2) predict similar moment demands for retaining walls subject to earthquake loading. Recently, several studies have published centrifuge test data which include flexural demands on sheet pile wall subjected to earthquake loading. Madabhushi and Zeng (15) present centrifuge test data for a sheet pile scale model considering three different accelerations on a dry sand: 0.12g, 0.22g and 0.23g (or kh = 0.09, 0.165 and 0.173, respectively). The soil friction angle was 33 degrees, and the embedment depth was equal to the retained height of the model. Ueda, Tobita and Iai (16) also present centrifuge test data for earthquake loading for accelerations of 0.06g, 0.20g and 0.26g (kh = 0.04, 0.15 and 0.20, respectively) on a dry sand with a soil friction angle of 41 degress. Tests on saturated loose and dense sands were also considered. The embedment depth was approximately two times the retained height. Finally, Khan, Hayano and Kitazume (17) provide centrifuge test data for accelerations of 0.21g to 0.33g (kh = 0.16 to 0.25, respectively). The depth of embedment is fairly deep at four time the height of the wall. The test considered various soil types, including a compacted sand fill over a thick layer of clay on both sides of the wall. The effect of cement mixing in front of the wall was also considered. The resulting normalized moment demands for the centrifuge test data are also shown in Figure 4. Only results for tests with drained backfill are presented for straight-forward comparison with the earthquake load case considered in this study. It is noted that comparing the results of the centrifuge test data together on Figure 4 ignores certain variables which may influence moment demand on the wall, such as depth of embedment and soil type used in the test data. However, given the limited quantity of data available it is expected the comparisons are of a coarse nature, but still provide some insight with respect to the magnitude of demands on a sheet pile wall. The demand predicted by AASHTO (1) and USACE (2) methodologies show on Figure 4 at approximately 28% to 60% higher than the earthquake demands observed in literature (15, 16, 17). Recall that both the AASHTO (1) and USACE (2) methodologies include a 1.57 Effective Factor of Safety for moment demands. Therefore, based on the limited test data available, it would appear both procedures provide an adequate Factor of Safety for moment demands induced by earthquake loading. However, there is still much debate on a proper method for estimating seismic demands on retaining walls, as well as the proper seismic stress distribution on the back face of the wall. Even recently, Sitar and Al Atik (18) suggest a monotonically increasing (triangular distribution) seismic earth pressure distribution, as opposed to the monotonically decreasing (inverted triangular distribution) seismic earth pressure distribution used for many years. Sitar and Al Atik (18) also suggest that the M-O method may overestimate seismic demands, as the observed demand is a function of “…magnitude and intensity of shaking, the density of backfill soil, and the flexibility of the retaining structures.”
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15 5
10
15
20
25
30
35
40
45
50 0
5
4
3
8
Depth Ratio 2
12
Extreme, USACE
1
16
Extreme, AASHTO Madabhushi and Zeng (2007) Ueda, Tobita and Iai (2008)
Moment Ratio, Cy•MMAX/MNORM
4
Increasing
Depth Ratio, C y•D/H
Increasing
Moment Ratio
Khan, Hayano and Kitazume (2009) Power (Extreme, AASHTO) 0
20 0
430 431 432 433 434 435 436 437 438 439 440
5
10
15
20
25
30
35
40
45
50
Cx•Kp /Ka Figure 4 Normalized Results for Extreme Load Combinations
The problem is exacerbated for more exotic cut walls such as soldier pile walls, king pile walls and cut walls with tieback anchors; however, Madabhushi and Zeng (15) are able to satisfactorily simulate the response of a sheet pile wall with more advanced numerical techniques. Based on the lack of more test data, it is uncertain how accurate either USACE (2) or AASHTO (1) methodologies may estimate seismic demands in a static analysis. Obviously, much more test data would be needed to fully validate an acceptable approach for seismic design of cut walls.
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6.0
16
SUMMARY AND CONCLUSIONS
A static analysis of nongravity cantilevered walls, or sheet pile walls, in cosionless soils is considered in this study over a range of load cases (live loading, flooded backfill and earthquake loads), retained heights (H = 8 to 18 ft), soil strengths (f = 28 to 44 degrees) and design ground acceleration coefficients (kh = 0.1 to 0.5). Resulting embedment depths and moment demands are compared using both the AASHTO Load and Resistance Factor Design (LRFD) Bridge Design Specifications (1) and the United States Army Corps of Engineers (USACE) Engineering Manual 1110-2-2504 (2) – both offering state of the art approaches to sheet pile wall design. The study results in the following observations and suggestions: ·
The recommended increase of 20% for embedment depth should be deleted from the AASHTO (1) specifications. The 20% increase is a carry-over from legacy, service level approaches to shoring design, and is not applicable to an LRFD methodology.
·
Only service level load combinations should be considered for estimating embedment depth in the AASHTO (1) methodology.
·
The AASHTO (1) requirements may be further refined according to the above suggestions, while still achieving a conservative design relative to conventional design methods.
·
Additional test data is required to validate a static design approach for nongravity cantilevered walls in an extreme (earthquake) loading condition.
The simple modifications suggested in the first three summary points would yield a significant cost savings for sheet pile walls, with reduced embedment lengths and required steel areas for moment demands. In the author’s opinion, the design would still be reliable and conservative for the typical load cases considered in this paper. 7.0
SUGGESTIONS FOR FURTHER WORK
Although a few direct conclusions with respect to sheet pile design within the AASHTO (1) framework can be made from this study, additional work is needed to further refine safe, reliable and efficient sheet pile design recommendations. The following suggests directions for future work: ·
The conventional methods for sheet pile design are based on logical, but theoretical, stress distributions which are over 50 years old. These design methods are acceptable for static earth pressures and live loads, but refined methods could be developed to reliably incorporate dynamic loading within a static analysis framework. A model test program, considering a range of soil types and combinations, wall heights, embedment depth
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ratios, and earthquake ground motions is needed to provide a suite of static and dynamic test data for both anchored and cantilevered walls. Centrifuge testing is an extremely cost-effective approach to achieving this type of data. ·
8.0
A further set of static and dynamic modeling, validated against said needed test data, will help structural and geotechnical engineers communicate for code revisions as necessary. Simplified (p-y) springs with dashpots, or continuum modeling – or both – may be advantageous in this regard. ACKNOWLEDGEMENTS
The author wishes to thank Kimberlee Wertens for her help in editing and preparing this article for publication. Professors Ueda, Tobita and Iai graciously extended additional data from their testing (16), for which the author is extremely grateful. Thank you also to Mr. Brad Mielke for donating his time in reviewing and improving the article, and to Faye Stroud for creating the wonderfully clear visual of the loading diagram. 9.0
REFERENCES
1. American Association of State Highway and Transportation Officials. AASHTO LRFD Bridge Design Specifications, Fifth Edition. Washington, DC: American Association of State Highway and Transportation Officials, 2010. 2. USACE. EM 1110-2-2504: Design of Sheet Pile Walls. US Army Corps of Engineers, 1994. 3. Rankine, W.J.M. "On the Stability of Loose Earth." Philosophical Transactions of the Royal Society 147 (1857). 4. Building Seismic Safety Council. NEHRP Recommended Seismic Provisions for New Buildings and Other Structures (FEMA P-750), 2009 Edition. Washington, D.C.: Federal Emergency Management Agancy (FEMA), 2009. 5. Mononobe, Nagaho, and Haruo Matsuo. "On the Determination of Earth Pressure during Earthquake." Proceedings World Engineering Congress. Tokyo, Japan, 1929. 177-185. 6. Anderson, Donald G., Geoffrey R. Martin, Ignatius (Po) Lam, and J. N. (Joe) Wang. NCHRP Report 611: Seismic Analysis and Design of Retaining Walls, Buried Structures, Slopes and Embankments. Washington, D.C.: Transportation Research Board, 2008. 7. USACE. EM 1110-2-2502: Retaining and Flood Walls. US Army Corps of Engineers, 1989. 8. United States Steel (USS). Steel Sheet Piling Design Manual. Updated and reprinted by U.S. Department of Transportation / FHWA with permission, 1984. 9. ASCE. "ASCE/SEI 7-10: Minimum Design Loads for Buildings and Other Structures." Reston, Virginia: American Society of Civil Engineers, 2010.
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10. International Code Council. "2012 International Building Code (IBC)." 2012. 11. American Institute of Steel Construction (AISC). "ANSI/AISC 360-05: Specification for Structural Steel Buildings." Chicago, Illinois: American Institute of Steel Construction (AISC), 2005. 12. Federal Emergency Management Agency (FEMA). Flood Map Information. http://www.fema.gov/national-flood-insurance-program/flood-map-information (accessed October 30, 2012). 13. Federal Emergency Management Agency (FEMA). Flood Insurance Rate Map (FIRM). http://www.fema.gov/national-flood-insurance-program-2/flood-insurance-rate-map-firm (accessed October 30, 2012). 14. Teng, Wayne C. Foundation Design. Englewood Cliffs, New Jersey: Prentice-Fall, Inc., 1962. 15. Madabhushi, S. P. G., and X. Zeng. "Simulating Seismic Response of Cantilever Retaining Walls." Journal of Geotechnical and Geoenvironmental Engineering, 2007: ASCE, ISSN 1090-0241/2007/5-539-549. 16. Ueda, Kyohei, Tetsuo Tobita, and Susumu Iai. "A Numerical Study of Dynamic Behavior of a Self-Supported Sheet Pile Wall." The 14th World Conference on Earthquake Engineering. Beijing, China, 2008. 17. Khan, M. Ruhul Amin, Kimitosho Hayano, and Masaki Kitazume. "Behavior of Sheet Pile Quay Wall Stabilized by Sea-Side Ground Improvement in Dynamic Centrifuge Tests." Soils and Foundations, Vol. 49, No. 2 (April 2009): 193-206. 18. Sitar, Nicholas, and Al Atik, Linda. "Dynamic Centrifuge Study of Seismically Induced Lateral Earth Pressures on Retaining Structures." Geotechnical Earthquake Engineering and Soil Dynamics IV. American Society of Civil Engineers (ASCE), 2008.
