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D-1 APPENDIX D Comparison of ASD- and LRFD-Based Designs of Soil Nail Walls Program Capabilities D.1 Introduction SNAILZ can model only two-dimensional wall geome- This appendix presents a comparison of SNW designs tries. It is based on the limit-equilibrium method and only based on the ASD and LRFD approaches. The comparison was achieves force equilibrium. Moment equilibrium is gener- between designs of identical cases and conditions of SNWs for ally not achieved in this program; therefore, results from both the ASD and LRFD approaches. Designs were performed SNAILZ are only approximate but are considered accept- using the computer programs SNAILZ (Caltrans, 2007) and able for design purposes. GOLDNAIL (Golder, 1993), the two most commonly used SNAILZ uses two-part planar wedges. It can model slip sur- computer programs for SNW design in the United States. faces with one wedge exiting the SNW toe and the other to the Section D.2 provides a brief description of these two computer ground surface behind the modeled wall [Figure D-1(a)]. This programs. Section D.3 provides an overview of the comparisons. is the most common scenario for SNWs. The program can also Section D.4 contains results of a parametric study conducted to model approximately a slip surface extending behind and below assess the design sensitivity to various factors. Section D.5 the wall using a simpliﬁed passive earth pressure formulation presents results of a comparison based on a design example for the section below the wall toe [Figure D-1(b)]. However, presented in the FHWA Geotechnical Engineering Circular this solution approach is only approximate. Therefore, the slid- (GEC) 7 (Lazarte et al., 2003) of a SNW using the ASD method ing and basal heave limit states can be modeled only approxi- and designs for the same wall using the LRFD method. mately with this program. SNAILZ can model up to seven soil layers. Up to three points deﬁne the water table location, which for some ground- D.2 Computer Programs Used in water conditions may not be sufﬁcient. SNAILZ allows a max- Comparative Analyses imum of two uniform surcharge distributions behind the face D.2.1 SNAILZ of the wall. Therefore, the program may have limited capa- bilities to model complex stratigraphy and load conditions. Basic Features For complex wall geometries, stratigraphy distributions, or SNAILZ, developed by the California Department of Trans- load conditions, the design engineer may need to simplify portation (Caltrans, 2007), is an updated version of the pro- actual conditions due to the program limitations. However, gram SNAIL (Caltrans, 1991) and is currently the most widely for most common conditions encountered in SNW design used program in the United States for the design of SNWs. practice, this program produces acceptable results, even in The program is available through the public domain and can relatively complex design situations. be downloaded free-of-charge from http://www.dot.ca.gov/ hq/esc/geotechlrequest.htm. Technical support is limited. Input Parameters SNAIL was originally in a Microsoft® DOS platform. SNAILZ Parameters selected for input in SNAILZ include those runs within a Microsoft Windows® environment. SNAILZ is related to reinforcement, loads, and soil. Reinforcement param- versatile as it allows the design engineer to consider various eters include nail head depth on the wall face, nail diameter, nail design scenarios and the most common elements that partic- inclination, vertical and horizontal nail spacing, bar cross- ipate in the design of a SNW. The user can input nail bond sectional area, and nail tensile resistance. These parameters can and tensile resistances, as well as the facing resistance.
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D-2 Figure D-1. Slip surfaces used in SNAIL: (a) two wedges through toe and (b) two wedges under toe. be assigned either to individual nails or globally to all nails. Up The ASD and “LRFD” modes would be equivalent in SNAILZ only for γ = 1.0. If load factors different than 1.0 were to two uniform surcharge distributions can be input. Pseudo- used in the “LRFD” format in SNAILZ, inconsistent results static seismic loads can be considered in SNAILZ by entering between the ASD and LRFD “modes” would be obtained. In horizontal and vertical seismic coefficients. Soil parameters addition, affecting soil loads with load factors different than include soil unit weight, soil cohesion, friction angle, and bond 1.0 is not possible in SNAILZ. For example, an attempt to affect resistance. Soil nominal resistance is modeled in SNAILZ using the soil unit weight by earth load factors (in general > 1.0) the Mohr-Coulomb failure envelope model. Another input would also affect earth load effects on the resistance side and parameter that must be included is the facing resistance. Input would ultimately produce inconsistent results between the ASD data can be entered in the English or SI unit systems. and the LRFD-equivalent analyses in SNAILZ. In summary, the only practical way to use SNAILZ with a Use of Computer Programs for LRFD Method Analyses LRFD format is to set all load factors equal to 1.0, which is con- SNAILZ is ASD based; therefore, SNAILZ strictly provides cal- sistent with a service limit state for overall stability as is currently culated global factors of safety, FSG, for overall stability. The adopted in the LRFD Bridge Design Speciﬁcations (AASHTO, program cannot be used to perform an analysis using LRFD 2007). For, load factors > 1.0, inconsistent results are obtained. methodologies unless simplifying assumptions are made and intermediate calculations are performed. The user may manually D.2.2 GOLDNAIL input reduced values of nail tensile, pullout, and facing resistances Basic Features (i.e., nominal values multiplied by the corresponding resistance factors) before the program executes any computations. The GOLDNAIL is a Windows-based proprietary program user must use the “pre-factored” option available in SNAILZ developed by Golder Associates (Golder, 1993). Although for reduced values of nail tensile, pullout, and facing resist- GOLDNAIL is not as commonly used as SNAILZ, the program ances. By selecting this option, only soil parameters (cohesion offers more advanced analysis capabilities and options that and tangent of friction angle) are affected by FSG, while the allow considering a wider range of scenarios and material prop- other resistances remain constant throughout the analysis. erties than SNAILZ. The program is commercialized and some External loads (i.e., two uniform loads available in SNAILZ) can technical support can be obtained for a fee. be entered pre-multiplied by a resistance factor. Earth loads cannot be entered pre-multiplied by a resistance factor. Program Capabilities When the “pre-factored” option is selected and factored val- ues for resistance are entered, SNAILZ can provide equivalent This program is two-dimensional and satisﬁes moment and results in ASD format or in a format resembling LRFD. How- force equilibriums. GOLDNAIL uses circular failure surfaces ever, this is limited to the condition of load factor γ = 1.0. When and analyzes SNWs as a series of slices instead of wedges. In SNAILZ is used to perform an LRFD-equivalent analysis for GOLDNAIL, the sliding soil mass is divided into vertical slices, γ = 1.0, factored values of the nominal resistances must be like is typically done in most slope-stability methods. The pro- entered. For this step, the nominal resistances of soil cohesion, gram iteratively modiﬁes the normal stresses distribution at cs, and the friction angle, ϕs, must be affected by multiplying the base of the slices until force and moment equilibriums are obtained. The program constrains circular slip surfaces to pass manually these values by soil resistance factors. Note that in SNAILZ, ϕs, not the tangent of the angle (tan ϕs) is input. There- through or above the SNW toe. Input data can be entered in the fore, an equivalent reduced friction angle (ϕs red) is computed English or SI unit systems, or any other compatible unit system. as ϕs red = tan−1 [tan (ϕs) × φ] and entered. With these factored Sliding and basal heave cannot be assessed using this program. nominal resistances entered, the condition FSG = 1.0 in SNAILZ GOLDNAIL may also be used to analyze unreinforced slopes and anchored walls. would represent a limit state for global stability.
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D-4 Table D-1. Soil nail wall input parameters comparable using both the LRFD and ASD methods. For all (baseline case). cases considered, the calculated nail length is, on average, approximately 4 percent larger in the LRFD method. No single Description Quantity factor appears to have a signiﬁcantly greater inﬂuence on the Wall height (ft) 30 results. Slightly larger differences were obtained for large loads Wall batter (deg) 0 and for high nominal pullout or bond resistances. The largest Number of soil nail levels 6 difference obtained for nail length was approximately 8 percent. Nail diameter (in.) 1.128 The soil nail loads calculated via the ASD or LRFD modes Diameter of grouted hole (in.) 6 were similar, with differences on average less than 3 percent. Nail inclination (deg) 15 As a result, it is expected that the differences in calculating the Nail vertical spacing (ft) 5 Nail horizontal spacing (ft) 5 necessary nail cross sectional area and required facing resist- Soil unit weight (pcf) 120 ance would be almost identical using either the ASD or LRFD Soil friction angle (deg) 35 methods for γ = 1.0. Bond stress (psi) 15 D.5 Example Design of a SNW nail yield resistance and facing resistance. However, this is not a typical manner of analyzing SNWs. D.5.1 Design Conditions Because the calibrated pullout resistance factors are values In this design example (Figure D-3), the soil proﬁle behind that are close to 0.5 (a value that would have been derived the proposed SNW and the project requirements are similar through a calibration with safety factors), the results between to those of the design example presented in Appendix D of the LRFD and ASD methods are expected to be similar. FHWA GEC No. 7 (Lazarte et al., 2003). The objective of this exercise is to compare the results obtained from the two most D.4.2 Results common SNW software programs in the design of a wall with Results for the over 30 analyzed design cases are summarized realistic conditions. in Table D-2. Results conﬁrm what was expected: using the The wall conditions are as follows. A 10-m (33-ft) high reliability-calibrated resistance factors of Chapter 3, the calcu- SNW is to be constructed as part of a roadway project. The road adjacent to the proposed wall is of low-to-medium lated nails length that are required to satisfy design criteria are Table D-2. Comparison of required nail length using ASD and LRFD approaches. Required Length, L (ft) LRFD to ASD Percent Difference (w/ respect to baseline case, %) Variable Compared Case Variable Value ASD LRFD φPO = 0.49 φPO = 0.47 φPO = 0.49 φPO = 0.47 FSG = 1.5 H = 30 ft, ϕs = 35° – Baseline 23.43 24.14 24.48 3.03 4.48 qu = 15 psi, Q = 0 1 H = 40 ft 31.24 32.18 32.63 3.01 4.45 Wall Height 2 H = 20 ft 15.62 16.16 16.31 3.46 4.42 ϕs = 28 ° 1 27.59 28.43 28.99 3.04 5.07 ϕs = 32 ° Friction Angle 2 25.22 25.99 26.51 3.05 5.11 ϕs = 38 ° 3 21.64 22.29 22.74 3.00 5.08 1 qu = 10 psi 26.28 27.59 28.42 4.98 8.14 Bond Resistance 2 qu = 20 psi 18.93 19.39 19.78 2.43 4.49 3 qu = 25 psi 17.14 17.67 17.83 3.09 4.03 1 Q = 250 psf 36.09 37.18 38.69 3.02 7.20 Surcharge 2 Q = 500 psf 40.67 41.91 43.61 3.05 7.23 Note: φ PO were calibrated for a reliability factor of 2.33
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D-7 Table D-4. Resistance factors for overall stability. Resistance Factor Value Soil Shear Resistance φs 0.65 Nail Pullout Resistance, φPO 0.49 Nail Tendon Resistance, φT 0.56 Nail Head Resistance (flexure and punching shear), φFF (controls) 0.67 Nail Head Resistance (headed-stud in tension), φFH 0.50 D.5.2 Design Procedures Upper Silty Sand Deposit: ϕs = 33 degrees Based on the recommendation of AASHTO (2007), the c′ = 0 overall stability of the SNW is assessed using the load combi- γs = 115 pcf nation for service limit state. The resistance factors in Table D-4 are used based on the Lower Silty Sand Deposit: recommendation of AASHTO (2007). For the pullout ϕs = 39 degrees resistance factor, the values calibrated in Chapter 3 for sand c′ = 0 are used. γs = 125 pcf The overall stability of the SNW system is evaluated using 3) Input the following load and resistance factors: SNW design software. The following are examples of design In the safety factor screen, select LRFD mode. The load analysis results obtained using the programs SNAILZ and factors for water weight, soil weight surcharge, and seismic GOLDNAIL. load are all selected to be 1.0. Input the resistance factors as shown in Table D-4. 4) Compute the necessary nail length and head resistance: GOLDNAIL In GOLDNAIL, run analysis using the design analysis mode. The required nail lengths to achieve a resistance-to- 1) Deﬁne geometry of wall. Trial nail lengths are selected as load ratio greater than 1.0 are calculated. follows: Nail Layers Required Nail Length (ft) Nail Layers Trial Nail Length (ft) 1 through 3 32.7 1 through 3 30 4 and 5 22.9 4 and 5 21 6 and 7 16.3 6 and 7 15 The maximum force occurs in the lowermost nail at Due to the limitations in the program, the nail inclination 32,070 kip (as obtained from the nail service mode in of nail layer #1 is selected to be the same as other layers GOLDNAIL). (i.e., 15° instead of 20° as shown in Figure D-4). Figure D-5 shows the calculated critical failure surface. 2) Input the following parameters: To ensure that pullout failure controls over tensile or punching-shear failure, artiﬁcially large values of nail diam- SNAILZ eter and nail head resistance can be entered in GOLDNAIL. In order to perform an analysis that resembles the LRFD for- For consistency with the example in GEC No. 7, the follow- mat in SNAILZ, resistances must be modiﬁed. Note that in this ing nail bar and head resistances are selected: example, the service limit state is analyzed and all load factors • Threaded bar: No. 8, 25 mm diam., cross-sect. area = are equal to 1.0. Below is a summary of the modiﬁed input 510 mm2 (0.79 in.2) parameters using a FS = 1.0 (i.e., an equivalent of the LRFD): • Nail nomin. tensile resist. = 0.79 in.2 × 75 ksi = 59.3 kips • Nail head nominal resistance (for permanent facing) = Upper Silty Sand Deposit: ϕs = tan−1(0.65 tan33°) = 22.9° 92 kip, from page D-28 (Lazarte et al., 2003) c′ = 0 × 0.65 = 0 • Nail pullout nominal resistance (per linear ft): Upper silty sand: π × 6 in. × 1 ft × 12 in./ft × 14.5 psi = γs = 115 × 1.0= 115 pcf qu = 14.5 psf (nominal value) 3,280 lbs; and Lower silty sand: π × 6 in. × 1 ft × 12 in./ft × 21.8 psi = BSF = 0.49 (Bond Stress Factor, equivalent to pullout 4,931 lbs. resistance factor) q = 14.5 psf × 0.49 = 7.11 psf (factored value) • Soil Design Parameters:
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D-8 Figure D-5. Critical failure surface calculated using GOLDNAIL. Lower Silty Sand Deposit: Note that these values are almost identical to those obtained ϕs = tan−1(0.65 tan39°) = 27.8° using the ASD method according to GEC 7 (and using the pre- c′ = 0 × 0.65 = 0 factored mode in SNAILZ). γs = 125 × 1.0 = 125 pcf The comparison indicates that SNAILZ requires nails that qu = 21.8 psf (nominal value) are approximately 4 percent longer than those obtained BSF = 0.49 (Bond Stress Factor) using GOLDNAIL. The maximum nail forces in SNAILZ are q = 21.8 psf × 0.49 = 10.7 psf (factored value) approximately 2 percent larger than with GOLDNAIL. Nail Head and Nail Tensile Resistances: D.6 Discussion of Results Facing resistance = 92 (nominal) × 0.67 = 61.3 (kips); and Tensile resistance (force) = 59.3 (nominal) × Comparative analyses show that both the LRFD and ASD 0.56 = 32.9 (ksi). method provide comparable design values for soil nail walls Tensile resistance (stress) = 75 (nominal) × under various conditions. Overall, the comparisons indicate 0.56 = 41.7 (ksi). that the required soil nail length calculated using the LRFD method and the proposed resistance factors are compara- Nail lengths need to be computed in SNAILZ iteratively in ble with those obtained with the ASD method. For all cases different runs until a target factor of safety of 1.0 (i.e., a con- considered, the length difference is on average approxi- dition equivalent to the limit state) is achieved. Figure D-6 mately 4 percent larger in the LRFD method. No factor shows the critical failure surface calculated by SNAILZ. The appears to have greater influence than others do. Slightly required nail lengths as calculated with this procedure are larger differences were obtained for large loads and for high listed below. nominal pullout or bond resistances. The largest difference obtained in the comparative analysis was approximately Nail Layers Required Nail Length (ft) 8 percent. In all cases, soil-nail loads calculated using either 1 through 3 34.1 method are comparable, with a difference of less than about 4 and 5 23.9 3 percent. 6 and 7 17 The analyses using the LRFD method with SNAILZ and The maximum calculated nail force is 32.7 kip (in the low- GOLDNAIL show that the differences and nail loads are very small, 4 and 2 percent, respectively. ermost nail).
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D-9 Figure D-6. Critical failure surface calculated using SNAILZ. D.7 Summary bility. However, it is expected that slightly different results and design quantities would be obtained for conditions other than The comparative analyses conﬁrm that the calculated quan- load factors = 1.0. tities, including soil nail lengths and cross-sectional areas (as a function of the maximum soil nail force), as obtained using the References LRFD and ASD methods are very similar. The reason for these similar trends, which were already apparent in Chapter 3, stem AASHTO (2007). LRFD Bridge Design Speciﬁcations, 4th Edition, Amer- ican Association of State Highway and Transportation Ofﬁcials, from the fact that the calibrated resistance factors for pullout are Washington, D.C. very similar to those that could have been obtained directly Caltrans (1991). “A User’s Manual for the SNAIL Program, Version from a calibration using factors of safety. The differences were 2.02—Updated PC Version.” Division of New Technology, Material small between LRFD and ASD methods using the same pro- and Research, Office of Geotechnical Engineering, California Department of Transportation, Sacramento, California. gram (i.e., GOLDNAIL) and between different programs using Caltrans (2007). “A User’s Manual for the SNAILZ Program, Version LRFD and ASD methods. Therefore, the calibration and com- 2.02—Updated PC Version.” Division of New Technology, Mate- parison demonstrate that the parameters currently used in rial and Research, Ofﬁce of Geotechnical Engineering, California practice should not be altered. Adopting the LRFD method and Department of Transportation, Sacramento, California. http:// the calibrated resistance factors used herein would only result www.dot.ca.gov/hq/esc/geotech Golder (1993). “GOLDNAIL Soil Nailing Design Program.” Golder in a change of design format. However, the design would result Associates, Seattle, Washington. in essentially the same quantities. A limitation of these compar- Lazarte, C. A., V. Elias, R. D. Espinoza, and P. J. Sabatini (2003). “Soil isons is that analyses have been performed for load factors equal Nail Walls.” Geotechnical Engineering Circular No. 7, No. FHWA- to 1.0, per the current AASHTO LRFD practice of overall sta- IF-03-017, Federal Highway Administration, Washington, D.C.
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Abbreviations and acronyms used without deﬁnitions in TRB publications: AAAE American Association of Airport Executives AASHO American Association of State Highway Officials AASHTO American Association of State Highway and Transportation Officials ACI–NA Airports Council International–North America ACRP Airport Cooperative Research Program ADA Americans with Disabilities Act APTA American Public Transportation Association ASCE American Society of Civil Engineers ASME American Society of Mechanical Engineers ASTM American Society for Testing and Materials ATA Air Transport Association ATA American Trucking Associations CTAA Community Transportation Association of America CTBSSP Commercial Truck and Bus Safety Synthesis Program DHS Department of Homeland Security DOE Department of Energy EPA Environmental Protection Agency FAA Federal Aviation Administration FHWA Federal Highway Administration FMCSA Federal Motor Carrier Safety Administration FRA Federal Railroad Administration FTA Federal Transit Administration HMCRP Hazardous Materials Cooperative Research Program IEEE Institute of Electrical and Electronics Engineers ISTEA Intermodal Surface Transportation Efficiency Act of 1991 ITE Institute of Transportation Engineers NASA National Aeronautics and Space Administration NASAO National Association of State Aviation Officials NCFRP National Cooperative Freight Research Program NCHRP National Cooperative Highway Research Program NHTSA National Highway Traffic Safety Administration NTSB National Transportation Safety Board PHMSA Pipeline and Hazardous Materials Safety Administration RITA Research and Innovative Technology Administration SAE Society of Automotive Engineers SAFETEA-LU Safe, Accountable, Flexible, Efficient Transportation Equity Act: A Legacy for Users (2005) TCRP Transit Cooperative Research Program TEA-21 Transportation Equity Act for the 21st Century (1998) TRB Transportation Research Board TSA Transportation Security Administration U.S.DOT United States Department of Transportation