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Suggested Citation:"Appendix F - Example." National Academies of Sciences, Engineering, and Medicine. 2011. LRFD Metal Loss and Service-Life Strength Reduction Factors for Metal-Reinforced Systems. Washington, DC: The National Academies Press. doi: 10.17226/14497.
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Suggested Citation:"Appendix F - Example." National Academies of Sciences, Engineering, and Medicine. 2011. LRFD Metal Loss and Service-Life Strength Reduction Factors for Metal-Reinforced Systems. Washington, DC: The National Academies Press. doi: 10.17226/14497.
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Suggested Citation:"Appendix F - Example." National Academies of Sciences, Engineering, and Medicine. 2011. LRFD Metal Loss and Service-Life Strength Reduction Factors for Metal-Reinforced Systems. Washington, DC: The National Academies Press. doi: 10.17226/14497.
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Suggested Citation:"Appendix F - Example." National Academies of Sciences, Engineering, and Medicine. 2011. LRFD Metal Loss and Service-Life Strength Reduction Factors for Metal-Reinforced Systems. Washington, DC: The National Academies Press. doi: 10.17226/14497.
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Suggested Citation:"Appendix F - Example." National Academies of Sciences, Engineering, and Medicine. 2011. LRFD Metal Loss and Service-Life Strength Reduction Factors for Metal-Reinforced Systems. Washington, DC: The National Academies Press. doi: 10.17226/14497.
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Suggested Citation:"Appendix F - Example." National Academies of Sciences, Engineering, and Medicine. 2011. LRFD Metal Loss and Service-Life Strength Reduction Factors for Metal-Reinforced Systems. Washington, DC: The National Academies Press. doi: 10.17226/14497.
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Suggested Citation:"Appendix F - Example." National Academies of Sciences, Engineering, and Medicine. 2011. LRFD Metal Loss and Service-Life Strength Reduction Factors for Metal-Reinforced Systems. Washington, DC: The National Academies Press. doi: 10.17226/14497.
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Suggested Citation:"Appendix F - Example." National Academies of Sciences, Engineering, and Medicine. 2011. LRFD Metal Loss and Service-Life Strength Reduction Factors for Metal-Reinforced Systems. Washington, DC: The National Academies Press. doi: 10.17226/14497.
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Suggested Citation:"Appendix F - Example." National Academies of Sciences, Engineering, and Medicine. 2011. LRFD Metal Loss and Service-Life Strength Reduction Factors for Metal-Reinforced Systems. Washington, DC: The National Academies Press. doi: 10.17226/14497.
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Suggested Citation:"Appendix F - Example." National Academies of Sciences, Engineering, and Medicine. 2011. LRFD Metal Loss and Service-Life Strength Reduction Factors for Metal-Reinforced Systems. Washington, DC: The National Academies Press. doi: 10.17226/14497.
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Suggested Citation:"Appendix F - Example." National Academies of Sciences, Engineering, and Medicine. 2011. LRFD Metal Loss and Service-Life Strength Reduction Factors for Metal-Reinforced Systems. Washington, DC: The National Academies Press. doi: 10.17226/14497.
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Suggested Citation:"Appendix F - Example." National Academies of Sciences, Engineering, and Medicine. 2011. LRFD Metal Loss and Service-Life Strength Reduction Factors for Metal-Reinforced Systems. Washington, DC: The National Academies Press. doi: 10.17226/14497.
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Suggested Citation:"Appendix F - Example." National Academies of Sciences, Engineering, and Medicine. 2011. LRFD Metal Loss and Service-Life Strength Reduction Factors for Metal-Reinforced Systems. Washington, DC: The National Academies Press. doi: 10.17226/14497.
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Suggested Citation:"Appendix F - Example." National Academies of Sciences, Engineering, and Medicine. 2011. LRFD Metal Loss and Service-Life Strength Reduction Factors for Metal-Reinforced Systems. Washington, DC: The National Academies Press. doi: 10.17226/14497.
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Suggested Citation:"Appendix F - Example." National Academies of Sciences, Engineering, and Medicine. 2011. LRFD Metal Loss and Service-Life Strength Reduction Factors for Metal-Reinforced Systems. Washington, DC: The National Academies Press. doi: 10.17226/14497.
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Suggested Citation:"Appendix F - Example." National Academies of Sciences, Engineering, and Medicine. 2011. LRFD Metal Loss and Service-Life Strength Reduction Factors for Metal-Reinforced Systems. Washington, DC: The National Academies Press. doi: 10.17226/14497.
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Suggested Citation:"Appendix F - Example." National Academies of Sciences, Engineering, and Medicine. 2011. LRFD Metal Loss and Service-Life Strength Reduction Factors for Metal-Reinforced Systems. Washington, DC: The National Academies Press. doi: 10.17226/14497.
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Suggested Citation:"Appendix F - Example." National Academies of Sciences, Engineering, and Medicine. 2011. LRFD Metal Loss and Service-Life Strength Reduction Factors for Metal-Reinforced Systems. Washington, DC: The National Academies Press. doi: 10.17226/14497.
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Suggested Citation:"Appendix F - Example." National Academies of Sciences, Engineering, and Medicine. 2011. LRFD Metal Loss and Service-Life Strength Reduction Factors for Metal-Reinforced Systems. Washington, DC: The National Academies Press. doi: 10.17226/14497.
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Suggested Citation:"Appendix F - Example." National Academies of Sciences, Engineering, and Medicine. 2011. LRFD Metal Loss and Service-Life Strength Reduction Factors for Metal-Reinforced Systems. Washington, DC: The National Academies Press. doi: 10.17226/14497.
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Suggested Citation:"Appendix F - Example." National Academies of Sciences, Engineering, and Medicine. 2011. LRFD Metal Loss and Service-Life Strength Reduction Factors for Metal-Reinforced Systems. Washington, DC: The National Academies Press. doi: 10.17226/14497.
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Suggested Citation:"Appendix F - Example." National Academies of Sciences, Engineering, and Medicine. 2011. LRFD Metal Loss and Service-Life Strength Reduction Factors for Metal-Reinforced Systems. Washington, DC: The National Academies Press. doi: 10.17226/14497.
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Suggested Citation:"Appendix F - Example." National Academies of Sciences, Engineering, and Medicine. 2011. LRFD Metal Loss and Service-Life Strength Reduction Factors for Metal-Reinforced Systems. Washington, DC: The National Academies Press. doi: 10.17226/14497.
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Suggested Citation:"Appendix F - Example." National Academies of Sciences, Engineering, and Medicine. 2011. LRFD Metal Loss and Service-Life Strength Reduction Factors for Metal-Reinforced Systems. Washington, DC: The National Academies Press. doi: 10.17226/14497.
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Suggested Citation:"Appendix F - Example." National Academies of Sciences, Engineering, and Medicine. 2011. LRFD Metal Loss and Service-Life Strength Reduction Factors for Metal-Reinforced Systems. Washington, DC: The National Academies Press. doi: 10.17226/14497.
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Suggested Citation:"Appendix F - Example." National Academies of Sciences, Engineering, and Medicine. 2011. LRFD Metal Loss and Service-Life Strength Reduction Factors for Metal-Reinforced Systems. Washington, DC: The National Academies Press. doi: 10.17226/14497.
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Suggested Citation:"Appendix F - Example." National Academies of Sciences, Engineering, and Medicine. 2011. LRFD Metal Loss and Service-Life Strength Reduction Factors for Metal-Reinforced Systems. Washington, DC: The National Academies Press. doi: 10.17226/14497.
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Suggested Citation:"Appendix F - Example." National Academies of Sciences, Engineering, and Medicine. 2011. LRFD Metal Loss and Service-Life Strength Reduction Factors for Metal-Reinforced Systems. Washington, DC: The National Academies Press. doi: 10.17226/14497.
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Suggested Citation:"Appendix F - Example." National Academies of Sciences, Engineering, and Medicine. 2011. LRFD Metal Loss and Service-Life Strength Reduction Factors for Metal-Reinforced Systems. Washington, DC: The National Academies Press. doi: 10.17226/14497.
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70 Introduction This example problem demonstrates analysis and design of a MSE wall using LRFD and the corresponding metal loss mod- els and resistance factors based on recommendations described in this report. The example is adapted from Berg et al. (2009), Appendix E.3. Various designs are executed employing ribbed- steel-strip- or steel-grid-type reinforcements, that may be plain steel or galvanized, and construction that may incorporate high quality, good quality, or marginal quality fills. Both the simpli- fied and the coherent gravity methods will be used to compute reinforcement tension. Results from this example illustrate the effects that these parameters have on the amount of reinforce- ment needed to meet the demand (i.e., the applicable load case). For the purpose of this illustration it is assumed that fill quality refers to electrochemical properties, and the mechanical prop- erties of the fill (e.g., unit weight, shear strength) are the same for all of the fill qualities considered. The MSE wall has a sloping backfill surcharge and includes a segmental precast concrete panel face as shown in Figure F-1. The analysis is based on principles of MSE design described by Berg et al. (2009). Table F-1 presents a summary of steps involved in the analysis. This appendix describes details related to evaluation of the internal stability of the wall as this bears on the calculation of tension (yield) resistance and the corresponding reinforcement cross-section. Berg et al. (2009), Appendix E-3, also describes details of the external stability analysis, design of facing elements, overall and compound sta- bility analysis at the service limit state, and design of the wall drainage system. Step 1. Establish Project Requirements • Exposed wall height, He = 28 ft. • Length of wall = 850 ft. • Design life = 75 years or 50 years as appropriate in consid- eration of fill quality and whether or not reinforcements are galvanized. • No seismic considerations. • Precast panel units: 5-ft wide × 5-ft tall × 0.5-ft thick. • Type of reinforcement: Grade 65 (Fy = 65 ksi) with zinc coating of 86 μm for galvanized reinforcements. Nine cases are considered in this example with reinforcement types and sizes summarized as follows: Fill Case Quality Galvanized Type of Reinforcement 1 High Yes 50-mm wide × 4-mm thick ribbed strips 2 High Yes W11 × W11 (longitudinal × transverse, welded wire fabric) 3 Good Yes 50-mm wide × 4-mm thick ribbed strips 4 Good Yes W11 × W11 (longitudinal × transverse, welded wire fabric) 5 Marginal Yes W20 × W11 (longitudinal × transverse, welded wire fabric) 6 High No 50-mm wide × 6-mm thick ribbed strips 7 High No W20 × W11 (longitudinal × transverse, welded wire fabric) 8 Good No 50-mm wide × 8-mm thick ribbed strips 9 Good No W20 × W11 (longitudinal × transverse, welded wire fabric) Step 2. Evaluate Project Parameters • Reinforced backfill, φ′r = 34°, γr = 125 pcf, coefficient of uniformity, Cu = 7.0. • Retained backfill, φ′f = 30°, γf = 125 pcf. A P P E N D I X F Example

71 Step 3. Estimate Depth of Embedment and Length of Reinforcement Based on Table C.11.10.2.2.-1 of AASHTO (2009), the minimum embedment depth = H/20 for walls with hori- zontal ground in front of wall, in other words, 1.4 ft for exposed wall height of 28 ft. For this design, assume embed- ment, d = 2.0 ft. Thus, design height of the wall, H = He + d = 28 ft + 2.0 ft = 30 ft. Due to the 2H:1V backslope, the initial length of reinforce- ment is assumed to be 0.8 H or 24 ft. The length of the rein- forcement is assumed to be constant throughout the height to limit differential settlements across the reinforced zone because differential settlements could overstress the reinforcements. Step 4. Estimate Unfactored Loads To compute the numerical values of various forces and moments, the parameters provided in Step 2 are used. Earth pressures transferred from the retained fill are not considered for internal stability analysis with the simplified method, but are related to reinforcement tension with the Coherent Grav- ity method. Using the values of the various friction angles, the coefficients of lateral earth pressure for the retained fill are computed as follows: Coefficient of active earth pressure per Eq. 3.11.5.3-1 of AASHTO (2009) is Where, per Eq. 3.11.5.3-2 of AASHTO (2009), the various parameters in above equation are as follows: δ = friction angle between fill and wall taken as specified, β = angle (nominal) of fill to horizontal, θ = angle of back face of wall to horizontal, and φ′f = effective angle of internal friction of retained backfill. Γ = + ′ +( ) ′ −( ) −( ) +( ) ⎡ ⎣⎢ 1 sin sin sin sin φ δ φ β θ δ θ β f f ⎢ ⎤ ⎦⎥⎥ 2 Ka f = + ′( ) −( ) sin sin sin 2 2 θ φ θ θ δΓ 2 Reinforced backfill φ'r, r He H L d Retained backfill (above or behind the reinforced backfill) φ'f, f Leveling Pad Foundation Soil φ'fd, fd Figure F-1. Configuration showing various parameters for analysis of an MSE wall with sloping backfill (not-to-scale). Step Item 1 Establish project requirements 2 Establish project parameters 3 Estimate wall embedment depth and length of reinforcement 4 Estimate unfactored loads 5 Summarize applicable load and resistance factors 6 Evaluate external stability of MSE wall—not discussed, see Berg et al. (2009) 6.1 Evaluation of sliding resistance 6.2 Evaluation of limiting eccentricity 6.3 Evaluation of bearing resistance 6.4 Settlement analysis 7 Evaluate internal stability of MSE wall 7.1 Estimate critical failure surface, variation of Kr and F* for internal stability 7.2 Establish vertical layout of soil reinforcements 7.3 Calculate horizontal stress and maximum tension at each reinforcement level 7.4 Establish nominal and factored long-term tensile resistance of soil reinforcement 7.5 Establish nominal and factored pullout resistance of soil reinforcement 7.6 Establish number of soil reinforcing strips at each level of reinforcement 8 Design of facing elements—not discussed, see Berg et al. (2009) 9 Check overall and compound stability at the service limit state—not discussed, see Berg et al. (2009) 10 Design wall drainage system—not discussed, see Berg et al. (2009) Table F-1. Summary of steps in analysis of MSE wall with sloping backfill.

72 For this example problem, compute the coefficient of active earth pressure for the retained fill, Kaf, using β = 26.56° (for the 2:1 backslope), vertical backface, θ = 90°, and δ = β as follows: Step 5. Summarize Applicable Load and Resistance Factors Table F-5.1 summarizes the load factors applied to cal- culations of reinforcement load using the Simplified Method. For the internal stability analysis using the Simplified Method only the maximum values of the load factors for the Strength I load case apply. However the coherent gravity method requires consideration as to whether maximum or minimum values render the most critical loading conditions. In most cases, the proper choice can be readily identified by inspection at the onset. Appropriate resistance factors have to be used for compu- tation of factored resistances during evaluation of strength Kaf f = + ′( ) −( ) = ( )sin sin sin sin2 2 2 90θ φ θ θ δΓ ° +30° 1.563 sin 90° ° 26.56°( ) −( )[ ] = 2 90 0 750 1 563 sin . .( )( )( ) =1 0 0 894 0 537. . . Γ = + +( ) −( ) − 1 30 26 56 30 26 56 90 26 sin . sin . sin ° ° ° ° ° . sin . . . 56 90 26 56 1 0 834 0 06 2 ° ° °( ) +( ) ⎡ ⎣⎢ ⎤ ⎦⎥ = + ( ) 0 0 894 0 894 1 563 2( ) ( )( ) ⎡ ⎣⎢ ⎤ ⎦⎥ = . . . limits states. Based on Table 11.5.5-1 from AASHTO (2009) a resistance factor, φp = 0.9 is applied to the nominal pullout resistance. Table F-5.2 summarizes the applicable resistance factors for tensile resistance, φt, for galvanized, or plain steel, strip and grid reinforcements with different fill conditions as recommended in this report. These resistance factors apply to design lives (tdesign) up to 100 years unless otherwise noted. Step 6. Evaluate External Stability of MSE Wall Not included because metal loss is not relevant to these calculations. See Berg et al. (2009), Appendix E.3. Step 7. Evaluate Internal Stability Analysis of MSE Wall 7.1 Estimate critical failure surface, variation of Kr, and F* for internal stability For the simplified method the variation of Kr depends on the stiffness of the reinforcements and is different for strip- or grid-type reinforcements. For the case of inextensible steel ribbed strips, the profile of the critical failure surface, the vari- ation of internal lateral horizontal stress coefficient, Kr, and the variation of the pullout resistance factor, F, are as shown in Figure F-2 wherein other definitions, such as measurement of depths Z and Zp as well as heights H and H1 are also shown. The variation of Kr and F are with respect to depth Z that is measured from the top of the reinforced soil zone. For the computation of Kr, the value of Ka is based on the angle of internal friction of the reinforced backfill, φr, and the assump- tion that the backslope angle β = 0; thus, Ka = tan2(45° − 34°/2) Load Factors (after AASHTO, 2009, Tables 3.4.1-1 and 3.4.1-2) Load Combination EV EH Strength I (maximum) 1.35 1.5 Strength I (minimum) 1.00 0.9 Service I 1.00 1.0 Note: EV and EH = vertical earth load and horizontal earth load, respectively. Table F-5.1. Summary of applicable load factors. Fill Quality Reinforcement High Good Marginal Galvanized Strips 0.80 0.65 NA Galvanized Grids 0.70 0.55 0.301 Plain Steel Strips 0.452 0.451 NA Plain Steel Grids 0.352 0.351 NA 1 tdesign = 50 yrs 2 tdesign = 75 yrs Table F-5.2. Summary of applicable resistance factors for evaluation of tensile resistances.

= 0.283. Hence, the value of Kr varies from 1.7(0.283) = 0.481 at Z = 0 ft to 1.2(0.283) = 0.340 at Z = 20 ft. For steel strips, F = 1.2+log10Cu. Using Cu = 7.0 as given in Step 2, F= 1.2 + log10(7.0) = 2.045 > 2.000. Therefore, use F= 2.000. For the case of inextensible grids (i.e. welded wire fabric) the value of Kr varies from 2.5Ka at Z = 0 (2.5(0.283) = 0.707) to 1.2Ka at Z = 20 ft. (1.2(0.283)=0.34). For grid-type reinforce- ments, the value of F varies from 20(t/St) at Z = 0 ft to 10(t/St) at Z ≥ 20 ft, where t is the diameter of the transverse wires and St is the transverse wire spacing. The coherent gravity method uses Kr = K0 for the top 20 feet (Z ≤ 20 ft), where K0 is the coefficient of lateral earth pressure at-rest, approximated as 1− sin φr = 1 − sin 34° = 0.441 in this example. At depths Z > 20 ft Kr = Ka = 0.283 (in this example). 7.2 Establish vertical layout of soil reinforcements Using the definition of depth Z as shown in Figure F-2 the following vertical layout of the soil reinforcements is chosen: The above layout leads to 12 levels of reinforcements. The vertical spacing was chosen based on a typical vertical spacing, Sv, of approximately 2.5 ft that is commonly used in the industry for steel ribbed strip- or grid-type reinforce- ment. The vertical spacing near the top and bottom of Z = 1 25. ft, 3.75 ft, 6.25 ft, 8.75 ft, 11.25 ft, 13.75 ft, 16.25 ft, 18.75 ft, 21.25 ft, 23.75 ft, 26.25 ft, and 28.75 ft. the walls is locally adjusted as necessary to fit the height of the wall. For internal stability computations, each layer of reinforce- ment is assigned a tributary area, Atrib as follows: where wp is the panel width of the precast facing element, and Svt is the vertical tributary spacing of the reinforcements based on the location of the reinforcements above and below the level of the reinforcement under consideration. The computation of Svt is summarized in Table F-7.1 wherein Svt =Z+ −Z−. Note that wp = 5.00 ft per Step 1. 7.3 Calculate horizontal stress and maximum tension at each reinforcement level The horizontal spacing of the reinforcements is based on the maximum tension (Tmax) at each level of reinforcements, which requires computation of the horizontal stress, σH, at each reinforcement level. The reinforcement tensile and pull- out resistances are then compared with Tmax and an appropri- ate reinforcement pattern is adopted. This section demonstrates the calculation of horizontal stress, σH, and maximum ten- sion, Tmax. For the Simplified Method the horizontal stress, σH, at any depth within the MSE wall is based on only the soil load as summarized in Table F-7.2. σ σ σH H-soil H-surcharge= + A = w Strib p vt( )( ) Z Zp Kr F*Z=0 1.7 Ka 1.2 Ka 2.000 tan (φ1) = 0.675 Z=20 ft Zp β− β =Δ tan3.01 )H3.0)((tanH Zp at start of resistant zone, Zp-s= Z + Latanβ Zp at end of resistant zone, Zp-e= Z + Ltanβ Use average Zp over the resistance zone, Zp-ave, for computing pullout resistance Zp-ave = Z + 0.5(Latanβ + Ltanβ) = Z + 0.5 tanβ (La + L) Z=0 Z=20 ft ΔH 0.3H1 Ka is computed assuming that the backslope angle is zero, i.e., β= 0 per Article C11.10.6.2.1 of AASHTO (2009) H1= H + ΔH Figure F-2. Geometry definition, location of critical failure surface, and variation of Kr and F* parameters for steel ribbed strips. 73

74 Using the unit weight of the reinforced soil mass and heights Z and S as shown in Figure F-3(b), the equation for horizontal stress at any depth Z within the MSE wall can be written as follows: Once the horizontal stress is computed at any given level of reinforcement, the maximum tension, Tmax, is computed as follows: where Atrib is the tributary area for the soil reinforcement at a given level. For the coherent gravity method the factored horizontal stress at each reinforcement level is computed as where σv is the pressure due to resultant vertical forces at the reinforcement level being evaluated, determined using a uni- form pressure distribution over an effective width (L-2e) as specified in AASHTO (2009), Article 10.6.1.3, where e is the load eccentricity. The vertical effective stress at each level of reinforcement shall consider the local equilibrium of all forces at that level only. Forces used to compute σv (EV and EH) are factored as described in Table F-5.1. The computations for Tmax using the simplified method for Case 1 are illustrated at z = 8.75 ft, which is Level 4 in the assumed vertical layout of reinforcement. Assume Strength I (max) load combination for illustration purposes and use appropriate load factors from Table F-5.1. σ σH r vK= T Amax H trib= ( )( )σ σ γ γ γ γ γ γH r r P-EV r r P-EV r r P-EVK Z K S K Z S= ( ) + ( ) = +( )[ ] • At Z = 8.75 ft, the following depths are computed: Z− = 7.50 ft (from Table F-7.1) Z+ = 10.00 ft (from Table F-7.1) • Obtain Kr by linear interpolation between 1.7Ka = 0.481 at Z = 0.00 ft and 1.2Ka = 0.340 at Z = 20.00 ft as follows: At Z− = 7.50 ft, Kr(Z−) = 0.340 + (20.00 ft − 7.50 ft)(0.481- 0.340)/20.00 ft = 0.428 At Z+ = 10.00 ft, Kr(Z+) = 0.340 + (20.00 ft − 10.00 ft)(0.481- 0.340)/20.00 ft = 0.411 • Compute σH-soil = [Kr σv-soil]γP-EV as follows: γP-EV = 1.35 from Table F-5.1 At Z− = 7.50 ft, σv-soil(Z−) = (0.125 kcf)(7.50 ft) = 0.94 ksf σH-soil(Z−) = [Kr(Zp−)σv-soil(z−)]γP-EV = (0.428)(0.94 ksf)(1.35) = 0.54 ksf At Z+ = 10.00 ft, σv-soil(Z+) = (0.125 kcf)(10.00 ft) = 1.25 ksf σH-soil(Z+) = [Kr(Zp+)σv-soil(z+)]γP-EV = (0.411)(1.25 ksf)(1.35) = 0.69 ksf σH-soil = 0.5(0.54 ksf + 0.69 ksf) = 0.62 ksf • Compute σH-surcharge = [Kr σ2]γP-EV as follows: σ2 = (1/2)(0.7Htanβ)(γf) (from Figure F-3(b)) σ2 = (1/2)(0.730 ft)[tan (26.56°)](0.125 kcf) = 0.656 ksf γP-EV = 1.35 from Table F-5.1 At Z− = 7.50 ft, σH-surcharge = [Kr(Z−) σ2]γP-EV = (0.428)(0.656 ksf)(1.35) = 0.38 ksf Level Z (ft) −Z (ft) +Z (ft) Svt (ft) 1 1.25 0 1.25+0.5(3.75–1.25)=2.50 2.50 2 3.75 3.75-0.5(3.75–1.25)=2.50 3.75+0.5(6.25-3.75)=5.00 2.50 3 6.25 6.25-0.5(6.25-3.75)=5.00 6.25+0.5(8.75-6.25)=7.50 2.50 4 8.75 8.75-0.5(8.75-6.25)=7.50 8.75+0.5(11.25-8.75)=10.00 2.50 5 11.25 11.25-0.5(11.25-8.75)=10.00 11.25+0.5(13.75-11.25)=12.50 2.50 6 13.75 13.75-0.5(13.75-11.25)=12.50 13.75+0.5(16.25-13.75)=15.00 2.50 7 16.25 16.25-0.5(16.25-13.75)=15.00 16.25+0.5(18.75-16.25)=17.50 2.50 8 18.75 18.76-0.5(18.75-16.25)=17.50 18.75+0.5(21.25-18.75)=20.00 2.50 9 21.25 21.25-0.5(21.25-18.75)=20.00 21.25+0.5(23.75-21.25)=22.50 2.50 10 23.75 23.75-0.5(23.75-21.25)=22.50 23.75+0.5(26.25-23.75)=25.00 2.50 11 26.25 26.25-0.5(26.25-23.75)=25.00 26.25+0.5(28.75-26.25)=27.50 2.50 12 28.75 28.75-0.5(28.75-26.25)=27.50 30.00 2.50 Table F-7.1. Summary of computations for Svt. Load Component Load Type Horizontal Stress Soil load from reinforced mass, v-soil EV H-soil = [Kr v-soil] P-EV Surcharge load due to backslope, 2 EV H-surcharge = [Kr 2] P-EV Table F-7.2. Summary of load components leading to horizontal stress.

At Z+ = 10.00 ft, σH-surcharge = [Kr(Z+) σ2]γP-ES = (0.411)(0.656 ksf)(1.35) = 0.36 ksf σH-surcharge = 0.5(0.38 ksf + 0.36 ksf) = 0.37 ksf • Compute σH = σH-soil + σH-surcharge as follows: σH = 0.62 ksf + 0.37 ksf = 0.99 ksf • Based on Table F-7.1, the vertical tributary spacing at Level 4 is Svt = 2.50 ft • The panel width, wp, is 5.00 ft (given in Step 1) • The tributary area, Atrib, is computed as follows: Atrib = (2.50 ft)(5.00 ft) = 12.50 ft2 • The maximum tension at Level 4 is computed as follows: Tmax = (σH)(Atrib) = (0.99 ksf)(12.50 ft2) = 12.37 k for panel of 5-ft width Using similar computations, the various quantities can be developed at other levels of reinforcements and load combinations. The computations for Tmax using the coherent method for Case 1 are similar, however σv is computed based on the equi- librium of forces and moments using a force diagram similar to Figure F-3(a) for each level of reinforcement. Equations for A (2/3)L L/2 FTV FTH h = z + Lt an (β) z V1=γrzL V2=L(h-z)γr/2 (a) (b) Figure F-3. Legend for computation of forces and moments for (a) internal stability analysis with the coherent gravity method, and (b) internal stability analysis with the simplified method (not-to-scale). 75

unfactored vertical forces and moments for coherent gravity method are as follows: Moment arm Force LRFD (Length units) (Force/length units) Load Type @ Point A V1 = (γr)(z)(L) EV L/2 V2 = (L)(L tan β)(γf) EV (2/3)L FTV = (1/2)(γr)(h2)(Kaf)(sinβ) EH L FTH = (1/2)(γr)(h2)(Kaf)(cosβ) EH h/3 Note: h = z + Ltanβ • Compute unfactored vertical forces and moments at Z = 30 ft (about Point A in Figure F-3(a)) V1 = 90.00 k/ft MV1 = 90 × 12 = 1080.00 k-ft/ft V2 = 18.00 k/ft MV2 = 18 × 16 = 288.00 k-ft/ft FTV = 26.48 k/ft MFTV = 26.48 × 24 = 635.44 k-ft/ft FTH = 52.95 k/ft MFTH = 52.95 × 14 = 741.35 k-ft/ft • Compute factored moments and forces at Z = 30 ft. (Checks with Strength I maximum and minimum load factors are necessary. Strength I Max was determined to govern for this case and only these calculations are shown here.) Vertical load @Z = 30 ft, VAb1 = V1+V2 145.80 k/ft Vertical load @Z = 30 ft, VAb2 = FTV 39.72 k/ft Total vertical @Z = 30 ft, 185.52 k/ft ΣV = R = VAb1+VAb2 Resisting moments about Point A, 1846.80 k-ft/ft MRA1 = MV1+MV2 Resisting moments about Point A, 953.17 k-ft/ft MRA2 = MFTV Total resisting moment @ Point A, 2799.97 k-ft/ft MRA = MRA1+MRA2 Overturning moments @ Point A, 1112.03 k-ft/ft MOA = MFTH Net moment at Point A, 1687.94 k-ft/ft MA = MRA − MOA 1 2 ⎛⎝⎜ ⎞⎠⎟ 76 Location of the resultant from 9.10 ft Point A = (MRA − MOA)/VA Eccentricity of Vertical load @ 2.90 ft Z = 30 ft = 0.5L − a Effective width @ Z = 30 ft = L-2eL 18.20 ft σv @t Z = 30 ft =ΣV/(L-2eL) = σv 10.19 ksf Horizontal stress, σH, and tensile force, Tmax, are computed using Kr appropriate to the coherent gravity method, and tributary area as demonstrated for the simplified method. 7.4 Establish nominal and factored long-term tensile resistance of soil reinforcement The nominal tensile resistance of soil reinforcements is based on the design life and estimated loss of steel over the design life during corrosion. Table F-7.3 is a summary of the metal loss models recommended in this report and the esti- mated metal loss per side (i.e., sacrificial steel requirements) for each case considered in this example. For galvanized reinforce- ments it is assumed that steel corrosion is initiated subsequent to depletion of zinc. For fill materials that meet AASHTO requirements and an initial zinc thickness, zi = 86 μm, zinc life is computed as 16 years using the AASHTO metal loss model described in Table 3 of this report and per Article 11.10.6.4.2a of AASHTO (2009). Considering Case 1 (described in Step 1) and a design life of 75 years, the anticipated thickness loss is calculated as follows: Based on a 50 mm wide strip, the cross-sectional area at the end of 75 years will be equal to (50 mm) × (2.58 mm) = 129 mm2 (0.2 in.2) For Grade 65 steel with Fy = 65 ksi, the nominal tensile resistance at the end of a 75 year design life will be Tn = 65 ksi (0.200 in.2) = 13.00 k/strip. Using the resistance factor, φt = 0.75 as listed in Table F-5.2 for galvanized strip-type reinforce- ments in high quality fill, the factored tensile resistance, Tr = 13.00 k/strip (0.75) = 9.75 k/strip. E 708 m sides m 0.056 in. anR = × ( ) = ( )μ μ2 1416 , d E mm mm mm 0.102 in.C = − = ( )4 1 416 2 58. . Reinforcement FillQuality Recommended Metal Loss Model tdesign (years) X (tdesign) (μm) Galvanized, zi = 86 μm High X (μm) = (tdesign – 16 years) x 12 μm/yr 75 708 Galvanized, zi = 86 μm Good X (μm) = (tdesign – 16 years) x 12 μm/yr 75 708 Galvanized, zi = 86 μm Marginal X (μm) = (tdesign – 10 years) x 28 μm/yr 50 1120 Plain Steel High X (μm) = tdesign x 13 μm/yr 75 975 Plain Steel Good X (μm) = 80 x tdesign0.8 50 1829 Table F-7.3. Basis for computing sacrificial steel requirements.

Considering Case 2, the cross-sectional area at the end of 75 years for a Wll cold drawn wire will be equal to π(0.374 in (initial diameter of W11) − 0.056 in (loss of diameter))2/ 4 = 0.079 in2. Tn = 65 ksi (0.079 in2) = 5.14 k/wire. Using φt = 0.70 as listed in Table F-5.2 for galvanized grids in high quality fill, the factored tensile resistance, Tf = 5.14 k/wire (0.70) = 3.61 k/wire. 7.5 Establish nominal and factored pullout resistance of soil reinforcement The nominal pullout resistance, Pr, of galvanized steel, ribbed, and strip-type soil reinforcements is computed with the following equation: For Case 1, the following parameters are constant at all lev- els of reinforcements: The computations for Pr are illustrated for Case 1 at z = 8.75 ft which is Level 4 as measured from the top of the wall. Assume Strength I (max) load combination for illustration pur- poses and use appropriate load factors from Table F-5.1. • Compute effective (resisting) length, Le, as follows: Since Z < H1/2, active length La = 0.3(H1) and Le = L − La = L − 0.3(H1) H1= H + ΔH H1 = H + ΔH = 30.00 ft + 5.29 ft = 35.29 ft Active length, La = 0.3(35.29 ft) = 10.59 ft Effective (resisting) length, Le = 24.00 ft − 10.59 ft = 13.41 ft • Compute (σv)(γP-EV) As per Figure F-3(b), σv = γr(Zp-ave) Zp-ave = Z + 0.5 tanβ (La + L) = 8.75 ft + 0.5[tan(26.56°)] (10.59 ft + 24.00 ft) = 17.40 ft Per Article 11.10.6.3.2 of AASHTO (2009), use unfactored vertical stress for pullout resistance. Thus, γP-EV = 1.00 σv(γP-EV) = (0.125 kcf)(17.40 ft) (1.00) = 2.175 ksf • Obtain F at Z = 8.75 ft Obtain F by linear interpolation between 2.000 at Z = 0 and 0.675 at Z = 20.00 ft as follows: F = 0.675 + (20.00 ft − 8.75 ft)(2.000 − 0.675)/20 ft = 1.420 ΔH H 1 0.3 tan ft = ( )( ) − = ( ) ×(tan . . .β β 0 3 0 5 0 3 30 ) − ( ) =1 0.3 0.5 ft5 29. b 1.969 in. ft for inextensible = = = 0 164 1 0 . .α reinforcement per Table 11.10.6.3.2-1 of AASHTO (2009) P F 2b Lr e v P-EV= ∗( )( )( ) ( )( )[ ]α σ γ • Compute nominal pullout resistance as follows: Pr = α(F)(2)(b)(Le)[(σv-soil)(γP-EV)] Pr = (1.0)(1.420)(2)(0.164 ft)(13.41 ft)(2.175 ksf) = 13.58 k/strip • Compute factored pullout resistance as follows: Prr = φPr = (0.90)(13.58 k/strip) = 12.23 k/strip Using similar computations, the various quantities can be developed at other levels of reinforcements and load combi- nations. These calculations are similar for grid-type reinforce- ments but with the appropriate factor for F. Calculations of pullout resistance are the same using either the simplified or coherent gravity methods. 7.6 Establish number of soil reinforcements at each level of reinforcement Based on Tmax, Tr, and Prr, the number of strip reinforce- ments at any given level of reinforcements can be computed as follows: • Based on tensile resistance considerations, the number of strip reinforcements, Nt, is computed as follows: • Based on pullout resistance considerations, the number of strip reinforcements, Np, is computed as follows: Based on Tmax, Tr and Prr, the number of longitudinal wires for grid-type reinforcements at any given level of reinforce- ments can be computed as follows: • Assume spacing of the longitudinal wires, Sl = 6 in. = 0.5 ft • Based on tensile resistance considerations, the number of longitudinal wires, Nt, is computed as follows: • Based on pullout resistance considerations, the number of longitudinal wires, Np, is computed as follows: Considering Case 1 and the Level 4 reinforcement at Z = 8.75 ft, the number of strip reinforcements can be com- puted as follows: • Tmax = 12.36 k for panel of 5-ft width, Tr = 10.41 k/strip, Prr = 12.23 k/strip • Nt = Tmax/Tr = (12.36 k for panel of 5-ft width)/(10.41 k/strip) = 1.19 strips for panel of 5-ft width N 1+ T P Sp max rr= ( ) ( )1 N T Tt max r= N T Pp max rr= N T Tt max r= 77

• Np = Tmax/Prr = (12.36 k for panel of 5-ft width)/(12.23 k/ strip) = 1.01 strips for panel of 5-ft width • Since Nt > Np, tension breakage is the governing criteria and therefore the governing value, Ng, is 1.19. Round up to select two strips at Level 4 for each panel of 5-ft width. The computations in Sections 7.4 to 7.6 are repeated at each level of reinforcement. Tables of results from the com- putations at all levels of reinforcement for Strength I (max) load combination and Cases 1–9 are included at the end of this appendix. The last column of the tables for Cases 1, 3, 6, and 8 provides horizontal spacing of the reinforcing strips, which is obtained by dividing the panel width, wp, by the gov- erning number of strips, Ng. Tables F-7.4(a) and (b) summarize the steel requirements computed using the Simplified and Coherent Gravity Meth- ods, respectively, for Cases 1–9 in terms of the steel area (As) required for each 5-ft width of the wall (corresponding to the width of the precast concrete facing panel). Both Models I and II are used to compute nominal steel requirements for Case 5. As described in the report, Model II renders twice the nominal sacrificial steel compared to Model I, but resistance factors are calibrated to render the 78 same probability that reinforcement resistance may fall below acceptable levels before the end of the design life (pf = 0.01). This example demonstrates that the designs executed with Models I or II and corresponding resistance factors are indeed similar. These results demonstrate the advantages of using galvanized steel to reduce the sacrificial steel requirements. Reinforcement requirements for plain steel are between 1.5 and 2.0 times higher in terms of cross-sectional area (As) compared to when galvanized steel reinforcements are used in similar fill condi- tions (e.g., Case 1 compared to Case 6, Case 2 compared to Case 7, Case 3 compared to Case 8, and Case 4 compared to Case 9). Designs achieved using the simplified method of analy- sis are close to those rendered with the coherent gravity method when the same resistance factors are applied. This is expected because the simplified method was calibrated to render results similar to the coherent gravity method. However, when com- paring details of the designs achieved with the coherent gravity compared to the simplified methods, the distributions of the reinforcements are different. Use of the coherent gravity method results in fewer reinforcements placed near the top of the wall and more reinforcements placed near the bottom com- pared to designs achieved with the simplified method. Case Fill Quality Galvanized Reinforcement Type tdesign (years) As per 5-ft. wide panel (in.2) 1 High Yes Strip 75 8.1 2 High Yes Grid 75 7.1 3 Good Yes Strip 75 9.0 4 Good Yes Grid 75 8.9 5 Marginal Yes Grid 50 17.0/16.4 1 6 High No Strip 75 13.0 7 High No Grid 75 13.8 8 Good No Strip 50 16.7 9 Good No Grid 50 19.2 Table F-7.4 (a). Simplified method—computed reinforcement requirements. Case FillQuality Galvanized Reinforcement Type tdesign (years) As per 5 ft. wide panel (in2) 1 High Yes Strip 75 9.0 2 High Yes Grid 75 7.3 3 Good Yes Strip 75 10.2 4 Good Yes Grid 75 8.9 5 Marginal Yes Grid 50 17.6/17.01 6 High No Strip 75 14.4 7 High No Grid 75 14.0 8 Good No Strip 50 18.0 9 Good No Grid 50 19.6 1 Model I/Model II— demonstrates that resistance factors are calibrated with respect to different models to render similar designs. Table F-7.4 (b). Coherent gravity method—computed reinforcement requirements.

CASE 1 H= 30 ft Ka= 0.283 p= 0.9 X= 708 m = 0.027874 in L= 24 ft P-EV = 1.35 t= 0.8 t= 75 yrs tan 0.5 2= 0.65625 ksf b= 0.164 ft zi= 86 m H= 5.294118 ft F*min=tan( r)= 0.674502089 CRz0-z2= 15 m/yr H1= 35.29412 ft F*max= 2 CRz2+= 4 m/yr La= 10.58824 ft CRsteel= 12 m/yr r= 125 pcf s= 4 mm = 0.15748 in Cu= 7 Fy= 65 ksi Level Z Zp-ave H Tmax F* Le pPr tTn Np Nt Ng Sh (ft) (ft) ksf k/ 5 ft wide panel dim (ft) k/strip k/strip - - - (ft) 1 1.25 9.90 0.52 6.45 1.917 13.41 9.39 10.41 0.7 0.6 2 2.50 2 3.75 12.40 0.69 8.61 1.751 13.41 10.75 10.41 0.8 0.8 2 2.50 3 6.25 14.90 0.85 10.57 1.586 13.41 11.69 10.41 0.9 1.0 2 2.50 4 8.75 17.40 0.99 12.36 1.420 13.41 12.23 10.41 1.0 1.2 2 2.50 5 11.25 19.90 1.12 13.95 1.254 13.41 12.35 10.41 1.1 1.3 2 2.50 6 13.75 22.19 1.23 15.36 1.089 14.25 12.70 10.41 1.2 1.5 2 2.50 7 16.25 24.31 1.33 16.58 0.923 15.75 13.04 10.41 1.3 1.6 2 2.50 8 18.75 26.44 1.41 17.62 0.757 17.25 12.74 10.41 1.4 1.7 2 2.50 9 21.25 28.56 1.52 18.98 0.675 18.75 13.33 10.41 1.4 1.8 2 2.50 10 23.75 30.69 1.66 20.77 0.675 20.25 15.47 10.41 1.3 2.0 2 2.50 11 26.25 32.81 1.81 22.56 0.675 21.75 17.76 10.41 1.3 2.2 3 1.67 12 28.75 34.94 1.95 24.36 0.675 23.25 20.22 10.41 1.2 2.3 3 1.67 Asum = 8.06 GALVANIZED STEEL STRIPS AND HIGH QUALITY FILL ( min >10,000 cm) SIMPLIFIED METHOD

CASE 2 H= 30 ft Ka= 0.283 p= 0.9 X= 708 m = 0.027874016 in L= 24 ft P-EV = 1.35 t= 0.7 t= 75 yrs tan 0.5 2= 0.65625 ksf St= 1 ft zi= 86 m H= 5.294118 ft F*min= 0.311666667 Sl= 0.5 ft CRz0-z2= 15 m/yr H1= 35.29412 ft F*max= 0.623333333 Tranverse W11 0.374 in diameter CRz2+= 4 m/yr La= 10.58824 ft CRsteel= 12 m/yr r= 125 pcf Longitudinal W11 0.374 in diameter Fy= 65 ksi Level Z Zp-ave H Tmax F* Le pPr tTn Np Nt Ng Bar Mat (ft) (ft) ksf k/ 5 ft wide panel dim (ft) k/ft k/wire - - - - 1 1.25 9.90 0.75 9.32 0.604 13.41 18.03 3.62 2.0 2.6 3 3W11 + W11 x 1.0' 2 3.75 12.40 0.96 12.06 0.565 13.41 21.13 3.62 2.1 3.3 4 4W11 + W11 x 1.0' 3 6.25 14.90 1.15 14.31 0.526 13.41 23.64 3.62 2.2 4.0 4 4W11 + W11 x 1.0' 4 8.75 17.40 1.29 16.08 0.487 13.41 25.57 3.62 2.3 4.4 5 5W11 + W11 x 1.0' 5 11.25 19.90 1.39 17.36 0.448 13.41 26.90 3.62 2.3 4.8 5 5W11 + W11 x 1.0' 6 13.75 22.19 1.45 18.16 0.409 14.25 29.10 3.62 2.2 5.0 6 6W11 + W11 x 1.0' 7 16.25 24.31 1.48 18.47 0.370 15.75 31.89 3.62 2.2 5.1 6 6W11 + W11 x 1.0' 8 18.75 26.44 1.46 18.30 0.331 17.25 33.98 3.62 2.1 5.1 6 6W11 + W11 x 1.0' 9 21.25 28.56 1.52 18.98 0.312 18.75 37.56 3.62 2.0 5.2 6 6W11 + W11 x 1.0' 10 23.75 30.69 1.66 20.77 0.312 20.25 43.58 3.62 2.0 5.7 6 6W11 + W11 x 1.0' 11 26.25 32.81 1.81 22.56 0.312 21.75 50.05 3.62 1.9 6.2 7 7W11 + W11 x 1.0' 12 28.75 34.94 1.95 24.36 0.312 23.25 56.96 3.62 1.9 6.7 7 7W11 + W11 x 1.0' Asum = 7.14 GALVANIZED GRIDS AND HIGH QUALITY FILL ( min > 10,000 -cm) SIMPLIFIED METHOD

CASE 3 H= 30 ft Ka= 0.283 p= 0.9 X= 708 m = 0.027874 in L= 24 ft P-EV = 1.35 t= 0.65 t= 75 yrs tan 0.5 2= 0.65625 ksf b= 0.164 ft zi= 86 m H= 5.294118 ft F*min=tan( r)= 0.674502089 CRz0-z2= 15 m/yr H1= 35.29412 ft F*max= 2 CRz2+= 4 m/yr La= 10.58824 ft CRsteel= 12 m/yr r= 125 pcf s= 4 mm = 0.15748 in Cu= 7 Fy= 65 ksi Level Z Zp-ave H Tmax F* Le pPr tTn Np Nt Ng Sh (ft) (ft) ksf k/ 5 ft wide panel dim (ft) k/strip k/strip - - - (ft) 1 1.25 9.90 0.52 6.45 1.917 13.41 9.39 8.46 0.7 0.8 2 2.50 2 3.75 12.40 0.69 8.61 1.751 13.41 10.75 8.46 0.8 1.0 2 2.50 3 6.25 14.90 0.85 10.57 1.586 13.41 11.69 8.46 0.9 1.3 2 2.50 4 8.75 17.40 0.99 12.36 1.420 13.41 12.23 8.46 1.0 1.5 2 2.50 5 11.25 19.90 1.12 13.95 1.254 13.41 12.35 8.46 1.1 1.6 2 2.50 6 13.75 22.19 1.23 15.36 1.089 14.25 12.70 8.46 1.2 1.8 2 2.50 7 16.25 24.31 1.33 16.58 0.923 15.75 13.04 8.46 1.3 2.0 2 2.50 8 18.75 26.44 1.41 17.62 0.757 17.25 12.74 8.46 1.4 2.1 3 1.67 9 21.25 28.56 1.52 18.98 0.675 18.75 13.33 8.46 1.4 2.2 3 1.67 10 23.75 30.69 1.66 20.77 0.675 20.25 15.47 8.46 1.3 2.5 3 1.67 11 26.25 32.81 1.81 22.56 0.675 21.75 17.76 8.46 1.3 2.7 3 1.67 12 28.75 34.94 1.95 24.36 0.675 23.25 20.22 8.46 1.2 2.9 3 1.67 Asum = 8.99 GALVANIZED STRIPS AND GOOD QUALITY FILL (3000 -cm< min < 10,000 -cm) SIMPLIFIED METHOD

CASE 4 H= 30 ft Ka= 0.283 p= 0.9 X= 708 m = 0.027874016 in L= 24 ft P-EV = 1.35 t= 0.55 t= 75 yrs tan 0.5 2= 0.65625 ksf St= 1.0 ft zi= 86 m H= 5.294118 ft F*min= 0.311666667 Sl= 0.5 ft CRz0-z2= 15 m/yr H1= 35.29412 ft F*max= 0.623333333 Tranverse W11 0.374 in diameter CRz2+= 4 m/yr La= 10.58824 ft CRsteel= 12 m/yr r= 125 pcf Longitudinal W11 0.374 in diameter Fy= 65 ksi Level Z Zp-ave H Tmax F* Le pPr tTn Np Nt Ng Bar Mat (ft) (ft) ksf k/ 5 ft wide panel dim (ft) k/ft k/wire - - - - 1 1.25 9.90 0.75 9.32 0.604 13.41 18.03 2.84 2.0 3.3 4 4W11 + W11 x 1.0' 2 3.75 12.40 0.96 12.06 0.565 13.41 21.13 2.84 2.1 4.2 5 5W11 + W11 x 1.0' 3 6.25 14.90 1.15 14.31 0.526 13.41 23.64 2.84 2.2 5.0 6 6W11 + W11 x 1.0' 4 8.75 17.40 1.29 16.08 0.487 13.41 25.57 2.84 2.3 5.7 6 6W11 + W11 x 1.0' 5 11.25 19.90 1.39 17.36 0.448 13.41 26.90 2.84 2.3 6.1 7 7W11 + W11 x 1.0' 6 13.75 22.19 1.45 18.16 0.409 14.25 29.10 2.84 2.2 6.4 7 7W11 + W11 x 1.0' 7 16.25 24.31 1.48 18.47 0.370 15.75 31.89 2.84 2.2 6.5 7 7W11 + W11 x 1.0' 8 18.75 26.44 1.46 18.30 0.331 17.25 33.98 2.84 2.1 6.4 7 7W11 + W11 x 1.0' 9 21.25 28.56 1.52 18.98 0.312 18.75 37.56 2.84 2.0 6.7 7 7W11 + W11 x 1.0' 10 23.75 30.69 1.66 20.77 0.312 20.25 43.58 2.84 2.0 7.3 8 8W11 + W11 x 1.0' 11 26.25 32.81 1.81 22.56 0.312 21.75 50.05 2.84 1.9 7.9 8 8W11 + W11 x 1.0' 12 28.75 34.94 1.95 24.36 0.312 23.25 56.96 2.84 1.9 8.6 9 9W11 + W11 x 1.0' Asum = 8.90 GALVANIZED GRIDS AND GOOD QUALITY FILL (3000 -cm< min < 10,000 -cm) SIMPLIFIED METHOD

CASE 5(a) - Model I H= 30 ft Ka= 0.283 p= 0.9 X= 1120 m = 0.044094488 in L= 24 ft P-EV = 1.35 t= 0.3 t= 50 yrs tan 0.5 2= 0.65625 ksf St= 1.0 ft zi= 86 m H= 5.294118 ft F*min= 0.311666667 Sl= 0.5 ft CRz0-z2= 8.6 m/yr H1= 35.29412 ft F*max= 0.623333333 Tranverse W11 0.374 in diameter CRz2+= 8.6 m/yr La= 10.58824 ft CRsteel= 28 m/yr r= 125 pcf Longitudinal W20 0.505 in diameter Fy= 65 ksi Level Z Zp-ave H Tmax F* Le pPr tTn Np Nt Ng Bar Mat (ft) (ft) ksf k/ 5 ft wide panel dim (ft) k/ft k/wire - - - - 1 1.25 9.90 0.75 9.32 0.604 13.41 18.03 2.66 2.0 3.5 4 4W20 + W11 x 1.0' 2 3.75 12.40 0.96 12.06 0.565 13.41 21.13 2.66 2.1 4.5 5 5W20 + W11 x 1.0' 3 6.25 14.90 1.15 14.31 0.526 13.41 23.64 2.66 2.2 5.4 6 6W20 + W11 x 1.0' 4 8.75 17.40 1.29 16.08 0.487 13.41 25.57 2.66 2.3 6.0 7 7W20 + W11 x 1.0' 5 11.25 19.90 1.39 17.36 0.448 13.41 26.90 2.66 2.3 6.5 7 7W20 + W11 x 1.0' 6 13.75 22.19 1.45 18.16 0.409 14.25 29.10 2.66 2.2 6.8 7 7W20 + W11 x 1.0' 7 16.25 24.31 1.48 18.47 0.370 15.75 31.89 2.66 2.2 6.9 7 7W20 + W11 x 1.0' 8 18.75 26.44 1.46 18.30 0.331 17.25 33.98 2.66 2.1 6.9 7 7W20 + W11 x 1.0' 9 21.25 28.56 1.52 18.98 0.312 18.75 37.56 2.66 2.0 7.1 8 8W20 + W11 x 1.0' 10 23.75 30.69 1.66 20.77 0.312 20.25 43.58 2.66 2.0 7.8 8 8W20 + W11 x 1.0' 11 26.25 32.81 1.81 22.56 0.312 21.75 50.05 2.66 1.9 8.5 9 9W20 + W11 x 1.0' 12 28.75 34.94 1.95 24.36 0.312 23.25 56.96 2.66 1.9 9.2 10 10W20 + W11 x 1.0' Asum = 17.03 GALVANIZED GRIDS AND MARGINAL QUALITY FILL (1000 -cm< min < 3,000 -cm) SIMPLIFIED METHOD

CASE 5(b) - Model II H= 30 ft Ka= 0.283 p= 0.9 X= 2240 m = 0.088188976 in L= 24 ft P-EV = 1.35 t= 0.5 t= 50 yrs tan 0.5 2= 0.65625 ksf St= 1.0 ft zi= 86 m H= 5.294118 ft F*min= 0.311666667 Sl= 0.5 ft CRz0-z2= 8.6 m/yr H1= 35.29412 ft F*max= 0.623333333 Tranverse W11 0.374 in diameter CRz2+= 8.6 m/yr La= 10.58824 ft CRsteel= 56 m/yr r= 125 pcf Longitudinal W20 0.505 in diameter Fy= 65 ksi Level Z Zp-ave H Tmax F* Le pPr tTn Np Nt Ng Bar Mat (ft) (ft) ksf k/ 5 ft wide panel dim (ft) k/ft k/wire - - - - 1 1.25 9.90 0.75 9.32 0.604 13.41 18.03 2.76 2.0 3.4 4 4W20 + W11 x 1.0' 2 3.75 12.40 0.96 12.06 0.565 13.41 21.13 2.76 2.1 4.4 5 5W20 + W11 x 1.0' 3 6.25 14.90 1.15 14.31 0.526 13.41 23.64 2.76 2.2 5.2 6 6W20 + W11 x 1.0' 4 8.75 17.40 1.29 16.08 0.487 13.41 25.57 2.76 2.3 5.8 6 6W20 + W11 x 1.0' 5 11.25 19.90 1.39 17.36 0.448 13.41 26.90 2.76 2.3 6.3 7 7W20 + W11 x 1.0' 6 13.75 22.19 1.45 18.16 0.409 14.25 29.10 2.76 2.2 6.6 7 7W20 + W11 x 1.0' 7 16.25 24.31 1.48 18.47 0.370 15.75 31.89 2.76 2.2 6.7 7 7W20 + W11 x 1.0' 8 18.75 26.44 1.46 18.30 0.331 17.25 33.98 2.76 2.1 6.6 7 7W20 + W11 x 1.0' 9 21.25 28.56 1.52 18.98 0.312 18.75 37.56 2.76 2.0 6.9 7 7W20 + W11 x 1.0' 10 23.75 30.69 1.66 20.77 0.312 20.25 43.58 2.76 2.0 7.5 8 8W20 + W11 x 1.0' 11 26.25 32.81 1.81 22.56 0.312 21.75 50.05 2.76 1.9 8.2 9 9W20 + W11 x 1.0' 12 28.75 34.94 1.95 24.36 0.312 23.25 56.96 2.76 1.9 8.8 9 9W20 + W11 x 1.0' Asum = 16.42 GALVANIZED GRIDS AND MARGINAL QUALITY FILL (1000 -cm< min < 3,000 -cm) SIMPLIFIED METHOD

CASE 6 H= 30 ft Ka= 0.283 p= 0.9 X= 975 m = 0.038386 in L= 24 ft P-EV = 1.35 t= 0.45 t= 75 yrs tan 0.5 2= 0.65625 ksf b= 0.164 ft H= 5.294118 ft F*min=tan( r)= 0.674502089 H1= 35.29412 ft F*max= 2 La= 10.58824 ft r= 125 pcf s= 6 mm = 0.23622 in Cu= 7 Fy= 65 ksi Level Z Zp-ave H Tmax F* Le pPr tTn Np Nt Ng Sh (ft) (ft) ksf k/ 5 ft wide panel dim (ft) k/strip k/strip - - - (ft) 1 1.25 9.90 0.52 6.45 1.917 13.41 9.39 9.18 0.7 0.7 2 2.50 2 3.75 12.40 0.69 8.61 1.751 13.41 10.75 9.18 0.8 0.9 2 2.50 3 6.25 14.90 0.85 10.57 1.586 13.41 11.69 9.18 0.9 1.2 2 2.50 4 8.75 17.40 0.99 12.36 1.420 13.41 12.23 9.18 1.0 1.3 2 2.50 5 11.25 19.90 1.12 13.95 1.254 13.41 12.35 9.18 1.1 1.5 2 2.50 6 13.75 22.19 1.23 15.36 1.089 14.25 12.70 9.18 1.2 1.7 2 2.50 7 16.25 24.31 1.33 16.58 0.923 15.75 13.04 9.18 1.3 1.8 2 2.50 8 18.75 26.44 1.41 17.62 0.757 17.25 12.74 9.18 1.4 1.9 2 2.50 9 21.25 28.56 1.52 18.98 0.675 18.75 13.33 9.18 1.4 2.1 3 1.67 10 23.75 30.69 1.66 20.77 0.675 20.25 15.47 9.18 1.3 2.3 3 1.67 11 26.25 32.81 1.81 22.56 0.675 21.75 17.76 9.18 1.3 2.5 3 1.67 12 28.75 34.94 1.95 24.36 0.675 23.25 20.22 9.18 1.2 2.7 3 1.67 Asum = 13.02 PLAIN STEEL STRIPS AND HIGH QUALITY FILL ( min >10,000 cm) SIMPLIFIED METHOD

CASE 7 H= 30 ft Ka= 0.283 p= 0.9 X= 975 m = 0.038385827 in L= 24 ft P-EV = 1.35 t= 0.35 t= 75 yrs tan 0.5 2= 0.65625 ksf St= 1 ft H= 5.294118 ft F*min= 0.311666667 Sl= 0.5 ft H1= 35.29412 ft F*max= 0.623333333 Tranverse W11 0.374 in diameter La= 10.58824 ft r= 125 pcf Longitudinal W20 0.505 in diameter Fy= 65 ksi Level Z Zp-ave H Tmax F* Le pPr tTn Np Nt Ng Bar Mat (ft) (ft) ksf k/ 5 ft wide panel dim (ft) k/ft k/wire - - - - 1 1.25 9.90 0.75 9.32 0.604 13.41 18.03 3.28 2.0 2.8 3 3W20 + W11x 1.0' 2 3.75 12.40 0.96 12.06 0.565 13.41 21.13 3.28 2.1 3.7 4 4W20 + W11x 1.0' 3 6.25 14.90 1.15 14.31 0.526 13.41 23.64 3.28 2.2 4.4 5 5W20 + W11x 1.0' 4 8.75 17.40 1.29 16.08 0.487 13.41 25.57 3.28 2.3 4.9 5 5W20 + W11x 1.0' 5 11.25 19.90 1.39 17.36 0.448 13.41 26.90 3.28 2.3 5.3 6 6W20 + W11x 1.0' 6 13.75 22.19 1.45 18.16 0.409 14.25 29.10 3.28 2.2 5.5 6 6W20 + W11x 1.0' 7 16.25 24.31 1.48 18.47 0.370 15.75 31.89 3.28 2.2 5.6 6 6W20 + W11x 1.0' 8 18.75 26.44 1.46 18.30 0.331 17.25 33.98 3.28 2.1 5.6 6 6W20 + W11x 1.0' 9 21.25 28.56 1.52 18.98 0.312 18.75 37.56 3.28 2.0 5.8 6 6W20 + W11x 1.0' 10 23.75 30.69 1.66 20.77 0.312 20.25 43.58 3.28 2.0 6.3 7 7W20 + W11x 1.0' 11 26.25 32.81 1.81 22.56 0.312 21.75 50.05 3.28 1.9 6.9 7 7W20 + W11x 1.0' 12 28.75 34.94 1.95 24.36 0.312 23.25 56.96 3.28 1.9 7.4 8 8W20 + W11x 1.0' Asum = 13.82 PLAIN STEEL GRIDS AND HIGH QUALITY FILL ( min > 10,000 -cm) SIMPLIFIED METHOD

CASE 8 H= 30 ft Ka= 0.283 p= 0.9 X= 1829.22 m = 0.072017 in L= 24 ft P-EV = 1.35 t= 0.45 t= 50 yrs tan 0.5 2= 0.65625 ksf b= 0.164 ft H= 5.294118 ft F*min=tan( r)= 0.674502089 H1= 35.29412 ft F*max= 2 La= 10.58824 ft r= 125 pcf s= 8 mm = 0.314961 in Cu= 7 Fy= 65 ksi Level Z Zp-ave H Tmax F* Le pPr tTn Np Nt Ng Sh (ft) (ft) ksf k/ 5 ft wide panel dim (ft) k/strip k/strip - - - (ft) 1 1.25 9.90 0.52 6.45 1.917 13.41 9.39 9.84 0.7 0.7 2 2.50 2 3.75 12.40 0.69 8.61 1.751 13.41 10.75 9.84 0.8 0.9 2 2.50 3 6.25 14.90 0.85 10.57 1.586 13.41 11.69 9.84 0.9 1.1 2 2.50 4 8.75 17.40 0.99 12.36 1.420 13.41 12.23 9.84 1.0 1.3 2 2.50 5 11.25 19.90 1.12 13.95 1.254 13.41 12.35 9.84 1.1 1.4 2 2.50 6 13.75 22.19 1.23 15.36 1.089 14.25 12.70 9.84 1.2 1.6 2 2.50 7 16.25 24.31 1.33 16.58 0.923 15.75 13.04 9.84 1.3 1.7 2 2.50 8 18.75 26.44 1.41 17.62 0.757 17.25 12.74 9.84 1.4 1.8 2 2.50 9 21.25 28.56 1.52 18.98 0.675 18.75 13.33 9.84 1.4 1.9 2 2.50 10 23.75 30.69 1.66 20.77 0.675 20.25 15.47 9.84 1.3 2.1 3 1.67 11 26.25 32.81 1.81 22.56 0.675 21.75 17.76 9.84 1.3 2.3 3 1.67 12 28.75 34.94 1.95 24.36 0.675 23.25 20.22 9.84 1.2 2.5 3 1.67 Asum = 16.74 PLAIN STEEL STRIPS AND GOOD QUALITY FILL (3000 -cm< min < 10,000 -cm) SIMPLIFIED METHOD

CASE 9 H= 30 ft Ka= 0.283 p= 0.9 X= 1829.22 m = 0.072016544 in L= 24 ft P-EV = 1.35 t= 0.35 t= 50 yrs tan 0.5 2= 0.65625 ksf St= 1.0 ft H= 5.294118 ft F*min= 0.311666667 Sl= 0.5 ft H1= 35.29412 ft F*max= 0.623333333 Tranverse W11 0.374 in diameter La= 10.58824 ft r= 125 pcf Longitudinal W20 0.505 in diameter Fy= 65 ksi Level Z Zp-ave H Tmax F* Le pPr tTn Np Nt Ng Bar Mat (ft) (ft) ksf k/ 5 ft wide panel dim (ft) k/ft k/wire - - - - 1 1.25 9.90 0.75 9.32 0.604 13.41 18.03 2.33 2.0 4.0 5 5W20 + W11 x 1.0' 2 3.75 12.40 0.96 12.06 0.565 13.41 21.13 2.33 2.1 5.2 6 6W20 + W11 x 1.0' 3 6.25 14.90 1.15 14.31 0.526 13.41 23.64 2.33 2.2 6.1 7 7W20 + W11 x 1.0' 4 8.75 17.40 1.29 16.08 0.487 13.41 25.57 2.33 2.3 6.9 7 7W20 + W11 x 1.0' 5 11.25 19.90 1.39 17.36 0.448 13.41 26.90 2.33 2.3 7.5 8 8W20 + W11 x 1.0' 6 13.75 22.19 1.45 18.16 0.409 14.25 29.10 2.33 2.2 7.8 8 8W20 + W11 x 1.0' 7 16.25 24.31 1.48 18.47 0.370 15.75 31.89 2.33 2.2 7.9 8 8W20 + W11 x 1.0' 8 18.75 26.44 1.46 18.30 0.331 17.25 33.98 2.33 2.1 7.9 8 8W20 + W11 x 1.0' 9 21.25 28.56 1.52 18.98 0.312 18.75 37.56 2.33 2.0 8.2 9 9W20 + W11 x 1.0' 10 23.75 30.69 1.66 20.77 0.312 20.25 43.58 2.33 2.0 8.9 9 9W20 + W11 x 1.0' 11 26.25 32.81 1.81 22.56 0.312 21.75 50.05 2.33 1.9 9.7 10 10W20 + W11 x 1.0' 12 28.75 34.94 1.95 24.36 0.312 23.25 56.96 2.33 1.9 10.5 11 11W20 + W11 x 1.0' Asum = 19.23 PLAIN STEEL GRIDS AND GOOD QUALITY FILL (3000 -cm< min < 10,000 -cm) SIMPLIFIED METHOD

CASE 1 H= 30 ft Kaf= 0.283 p= 0.9 X= 708 m = 0.027874 in L= 24 ft k0f= 0.440807097 t= 0.8 t= 75 yrs tan 0.5 P-EV = 1.35 b= 0.164 ft zi= 86 m H= 5.294118 ft V2= 18 k/ft CRz0-z2= 15 m/yr H1= 35.29412 ft F*min=tan( r)= 0.674502089 CRz2+= 4 m/yr La= 10.58824 ft F*max= 2 CRsteel= 12 m/yr r= 125 pcf Kab = 0.537 s= 4 mm = 0.15748 in Cu= 7 b= 125 pcf Fy= 65 ksi P-EH = 1.5 Level Z Zp-ave H Tmax F* Le pPr tTn Np Nt Ng Sh (ft) (ft) ksf k/ 5 ft wide panel dim (ft) k/strip k/strip - - - (ft) 1 1.25 9.90 0.47 5.86 1.917 13.41 9.39 10.41 0.6 0.6 2 2.50 2 3.75 12.40 0.65 8.07 1.751 13.41 10.75 10.41 0.8 0.8 2 2.50 3 6.25 14.90 0.82 10.21 1.586 13.41 11.69 10.41 0.9 1.0 2 2.50 4 8.75 17.40 0.98 12.26 1.420 13.41 12.23 10.41 1.0 1.2 2 2.50 5 11.25 19.90 1.14 14.24 1.254 13.41 12.35 10.41 1.2 1.4 2 2.50 6 13.75 22.19 1.29 16.13 1.089 14.25 12.70 10.41 1.3 1.5 2 2.50 7 16.25 24.31 1.44 17.94 0.923 15.75 13.04 10.41 1.4 1.7 2 2.50 8 18.75 26.44 1.57 19.65 0.757 17.25 12.74 10.41 1.5 1.9 2 2.50 9 21.25 28.56 1.77 22.10 0.675 18.75 13.33 10.41 1.7 2.1 3 1.67 10 23.75 30.69 2.04 25.51 0.675 20.25 15.47 10.41 1.6 2.5 3 1.67 11 26.25 32.81 2.35 29.36 0.675 21.75 17.76 10.41 1.7 2.8 3 1.67 12 28.75 34.94 2.70 33.73 0.675 23.25 20.22 10.41 1.7 3.2 4 1.25 Asum = 8.99 GALVANIZED STRIPS AND HIGH QUALITY FILL ( min > 10,000 -cm) COHERENT GRAVITY METHOD

CASE 2 H= 30 ft Kaf= 0.283 p= 0.9 X= 708 m = 0.027874016 in L= 24 ft k0f= 0.440807097 t= 0.7 t= 75 yrs tan 0.5 P-EV = 1.35 St= 1.0 ft zi= 86 m H= 5.294118 ft V2= 18 k/ft Sl= 0.5 ft CRz0-z2= 15 m/yr H1= 35.29412 ft F*min= 0.311666667 Tranverse W11 0.374 in diameter CRz2+= 4 m/yr La= 10.58824 ft F*max= 0.623333333 CRsteel= 12 m/yr r= 125 pcf Kab = 0.537 Longitudinal W11 0.374 in diameter b= 125 pcf Fy= 65 ksi P-EH = 1.5 Level Z Zp-ave H Tmax F* Le pPr tTn Np Nt Ng Sh (ft) (ft) ksf k/ 5 ft wide panel dim (ft) k/ft k/wire - - - - 1 1.25 9.90 0.47 5.86 0.604 13.41 18.03 3.62 1.7 1.6 2 2W11 + W11 x 1.0' 2 3.75 12.40 0.65 8.07 0.565 13.41 21.13 3.62 1.8 2.2 3 3W11 + W11 x 1.0' 3 6.25 14.90 0.82 10.21 0.526 13.41 23.64 3.62 1.9 2.8 3 3W11 + W11 x 1.0' 4 8.75 17.40 0.98 12.26 0.487 13.41 25.57 3.62 2.0 3.4 4 4W11 + W11 x 1.0' 5 11.25 19.90 1.14 14.24 0.448 13.41 26.90 3.62 2.1 3.9 4 4W11 + W11 x 1.0' 6 13.75 22.19 1.29 16.13 0.409 14.25 29.10 3.62 2.1 4.5 5 5W11 + W11 x 1.0' 7 16.25 24.31 1.44 17.94 0.370 15.75 31.89 3.62 2.1 5.0 5 5W11 + W11 x 1.0' 8 18.75 26.44 1.57 19.65 0.331 17.25 33.98 3.62 2.2 5.4 6 6W11 + W11 x 1.0' 9 21.25 28.56 1.77 22.10 0.312 18.75 37.56 3.62 2.2 6.1 7 7W11 + W11 x 1.0' 10 23.75 30.69 2.04 25.51 0.312 20.25 43.58 3.62 2.2 7.0 8 8W11 + W11 x 1.0' 11 26.25 32.81 2.35 29.36 0.312 21.75 50.05 3.62 2.2 8.1 9 9W11 + W11 x 1.0' 12 28.75 34.94 2.70 33.73 0.312 23.25 56.96 3.62 2.2 9.3 10 10W11 + W11 x 1.0' Asum = 7.25 GALVANIZED GRIDS AND HIGH QUALITY FILL ( min > 10,000 -cm) COHERENT GRAVITY METHOD

CASE 3 H= 30 ft Kaf= 0.283 p= 0.9 X= 708 m = 0.027874 in L= 24 ft k0f= 0.440807097 t= 0.65 t= 75 yrs tan 0.5 P-EV = 1.35 b= 0.164 ft zi= 86 m H= 5.294118 ft V2= 18 k/ft CRz0-z2= 15 m/yr H1= 35.29412 ft F*min=tan( r)= 0.674502089 CRz2+= 4 m/yr La= 10.58824 ft F*max= 2 CRsteel= 12 m/yr r= 125 pcf Kab = 0.537 s= 4 mm = 0.15748 in Cu= 7 b= 125 pcf Fy= 65 ksi P-EH = 1.5 Level Z Zp-ave H Tmax F* Le pPr tTn Np Nt Ng Sh (ft) (ft) ksf k/ 5 ft wide panel dim (ft) k/strip k/strip - - - (ft) 1 1.25 9.90 0.47 5.86 1.917 13.41 9.39 8.46 0.6 0.7 2 2.50 2 3.75 12.40 0.65 8.07 1.751 13.41 10.75 8.46 0.8 1.0 2 2.50 3 6.25 14.90 0.82 10.21 1.586 13.41 11.69 8.46 0.9 1.2 2 2.50 4 8.75 17.40 0.98 12.26 1.420 13.41 12.23 8.46 1.0 1.4 2 2.50 5 11.25 19.90 1.14 14.24 1.254 13.41 12.35 8.46 1.2 1.7 2 2.50 6 13.75 22.19 1.29 16.13 1.089 14.25 12.70 8.46 1.3 1.9 2 2.50 7 16.25 24.31 1.44 17.94 0.923 15.75 13.04 8.46 1.4 2.1 3 1.67 8 18.75 26.44 1.57 19.65 0.757 17.25 12.74 8.46 1.5 2.3 3 1.67 9 21.25 28.56 1.77 22.10 0.675 18.75 13.33 8.46 1.7 2.6 3 1.67 10 23.75 30.69 2.04 25.51 0.675 20.25 15.47 8.46 1.6 3.0 4 1.25 11 26.25 32.81 2.35 29.36 0.675 21.75 17.76 8.46 1.7 3.5 4 1.25 12 28.75 34.94 2.70 33.73 0.675 23.25 20.22 8.46 1.7 4.0 4 1.25 Asum = 10.23 GALVANIZED STRIPS AND GOOD QUALITY FILL (3000 -cm< min < 10,000 -cm) COHERENT GRAVITY METHOD

CASE 4 H= 30 ft Kaf= 0.283 p= 0.9 X= 708 m = 0.027874016 in L= 24 ft k0f= 0.440807097 t= 0.55 t= 75 yrs tan 0.5 P-EV = 1.35 St= 1.0 ft zi= 86 m H= 5.294118 ft V2= 18 k/ft Sl= 0.5 ft CRz0-z2= 15 m/yr H1= 35.29412 ft F*min= 0.311666667 Tranverse W11 0.374 in diameter CRz2+= 4 m/yr La= 10.58824 ft F*max= 0.623333333 CRsteel= 12 m/yr r= 125 pcf Kab = 0.537 Longitudinal W11 0.374 in diameter b= 125 pcf Fy= 65 ksi P-EH = 1.5 Level Z Zp-ave H Tmax F* Le pPr tTn Np Nt Ng Sh (ft) (ft) ksf k/ 5 ft wide panel dim (ft) k/ft k/wire - - - - 1 1.25 9.90 0.47 5.86 0.604 13.41 18.03 2.84 1.7 2.1 3 3W11 + W11 x 1.0' 2 3.75 12.40 0.65 8.07 0.565 13.41 21.13 2.84 1.8 2.8 3 3W11 + W11 x 1.0' 3 6.25 14.90 0.82 10.21 0.526 13.41 23.64 2.84 1.9 3.6 4 4W11 + W11 x 1.0' 4 8.75 17.40 0.98 12.26 0.487 13.41 25.57 2.84 2.0 4.3 5 5W11 + W11 x 1.0' 5 11.25 19.90 1.14 14.24 0.448 13.41 26.90 2.84 2.1 5.0 6 6W11 + W11 x 1.0' 6 13.75 22.19 1.29 16.13 0.409 14.25 29.10 2.84 2.1 5.7 6 6W11 + W11 x 1.0' 7 16.25 24.31 1.44 17.94 0.370 15.75 31.89 2.84 2.1 6.3 7 7W11 + W11 x 1.0' 8 18.75 26.44 1.57 19.65 0.331 17.25 33.98 2.84 2.2 6.9 7 7W11 + W11 x 1.0' 9 21.25 28.56 1.77 22.10 0.312 18.75 37.56 2.84 2.2 7.8 8 8W11 + W11 x 1.0' 10 23.75 30.69 2.04 25.51 0.312 20.25 43.58 2.84 2.2 9.0 9 9W11 + W11 x 1.0' 11 26.25 32.81 2.35 29.36 0.312 21.75 50.05 2.84 2.2 10.3 11 11W11 + W11 x 1.0' 12 28.75 34.94 2.70 33.73 0.312 23.25 56.96 2.84 2.2 11.9 12 12W11 + W11 x 1.0' Asum = 8.90 GALVANIZED GRIDS AND GOOD QUALITY FILL (3000 -cm< min < 10,000 -cm) COHERENT GRAVITY METHOD

CASE 5(a). Model I H= 30 ft Kaf= 0.283 p= 0.9 X= 1120 m = 0.044094488 in L= 24 ft k0f= 0.440807097 t= 0.3 t= 50 yrs tan 0.5 P-EV = 1.35 St= 1.0 ft zi= 86 m H= 5.294118 ft V2= 18 k/ft Sl= 0.5 ft CRz0-z2= 8.6 m/yr H1= 35.29412 ft F*min= 0.311666667 Tranverse W11 0.374 in diameter CRz2+= 8.6 m/yr La= 10.58824 ft F*max= 0.623333333 CRsteel= 28 m/yr r= 125 pcf Kab = 0.537 Longitudinal W20 0.505 in diameter b= 125 pcf Fy= 65 ksi P-EH = 1.5 Level Z Zp-ave H Tmax F* Le pPr tTn Np Nt Ng Sh (ft) (ft) ksf k/ 5 ft wide panel dim (ft) k/ft k/wire - - - - 1 1.25 9.90 0.47 5.86 0.604 13.41 18.03 2.66 1.7 2.2 3 3W20 + W11 x 1.0' 2 3.75 12.40 0.65 8.07 0.565 13.41 21.13 2.66 1.8 3.0 4 4W20 + W11 x 1.0' 3 6.25 14.90 0.82 10.21 0.526 13.41 23.64 2.66 1.9 3.8 4 4W20 + W11 x 1.0' 4 8.75 17.40 0.98 12.26 0.487 13.41 25.57 2.66 2.0 4.6 5 5W20 + W11 x 1.0' 5 11.25 19.90 1.14 14.24 0.448 13.41 26.90 2.66 2.1 5.4 6 6W20 + W11 x 1.0' 6 13.75 22.19 1.29 16.13 0.409 14.25 29.10 2.66 2.1 6.1 7 7W20 + W11 x 1.0' 7 16.25 24.31 1.44 17.94 0.370 15.75 31.89 2.66 2.1 6.7 7 7W20 + W11 x 1.0' 8 18.75 26.44 1.57 19.65 0.331 17.25 33.98 2.66 2.2 7.4 8 8W20 + W11 x 1.0' 9 21.25 28.56 1.77 22.10 0.312 18.75 37.56 2.66 2.2 8.3 9 9W20 + W11 x 1.0' 10 23.75 30.69 2.04 25.51 0.312 20.25 43.58 2.66 2.2 9.6 10 10W20 + W11 x 1.0' 11 26.25 32.81 2.35 29.36 0.312 21.75 50.05 2.66 2.2 11.0 12 12W20 + W11 x 1.0' 12 28.75 34.94 2.70 33.73 0.312 23.25 56.96 2.66 2.2 12.7 13 13W20 + W11 x 1.0' Asum = 17.63 GALVANIZED GRIDS AND MARGINAL QUALITY FILL (1,000 -cm< min < 3,000 -cm) COHERENT GRAVITY METHOD

CASE 5(b). Model II H= 30 ft Kaf= 0.283 p= 0.9 X= 2240 m = 0.088188976 in L= 24 ft k0f= 0.440807097 t= 0.5 t= 50 yrs tan 0.5 P-EV = 1.35 St= 1.0 ft zi= 86 m H= 5.294118 ft V2= 18 k/ft Sl= 0.5 ft CRz0-z2= 8.6 m/yr H1= 35.29412 ft F*min= 0.311666667 Tranverse W11 0.374 in diameter CRz2+= 8.6 m/yr La= 10.58824 ft F*max= 0.623333333 CRsteel= 56 m/yr r= 125 pcf Kab = 0.537 Longitudinal W20 0.505 in diameter b= 125 pcf Fy= 65 ksi P-EH = 1.5 Level Z Zp-ave H Tmax F* Le pPr tTn Np Nt Ng Sh (ft) (ft) ksf k/ 5 ft wide panel dim (ft) k/ft k/wire - - - - 1 1.25 9.90 0.47 5.86 0.604 13.41 18.03 2.76 1.7 2.1 3 3W20 + W11 x 1.0' 2 3.75 12.40 0.65 8.07 0.565 13.41 21.13 2.76 1.8 2.9 3 3W20 + W11 x 1.0' 3 6.25 14.90 0.82 10.21 0.526 13.41 23.64 2.76 1.9 3.7 4 4W20 + W11 x 1.0' 4 8.75 17.40 0.98 12.26 0.487 13.41 25.57 2.76 2.0 4.4 5 5W20 + W11 x 1.0' 5 11.25 19.90 1.14 14.24 0.448 13.41 26.90 2.76 2.1 5.2 6 6W20 + W11 x 1.0' 6 13.75 22.19 1.29 16.13 0.409 14.25 29.10 2.76 2.1 5.9 6 6W20 + W11 x 1.0' 7 16.25 24.31 1.44 17.94 0.370 15.75 31.89 2.76 2.1 6.5 7 7W20 + W11 x 1.0' 8 18.75 26.44 1.57 19.65 0.331 17.25 33.98 2.76 2.2 7.1 8 8W20 + W11 x 1.0' 9 21.25 28.56 1.77 22.10 0.312 18.75 37.56 2.76 2.2 8.0 9 9W20 + W11 x 1.0' 10 23.75 30.69 2.04 25.51 0.312 20.25 43.58 2.76 2.2 9.3 10 10W20 + W11 x 1.0' 11 26.25 32.81 2.35 29.36 0.312 21.75 50.05 2.76 2.2 10.7 11 11W20 + W11 x 1.0' 12 28.75 34.94 2.70 33.73 0.312 23.25 56.96 2.76 2.2 12.2 13 13W20 + W11 x 1.0' Asum = 17.03 GALVANIZED GRIDS AND MARGINAL QUALITY FILL (1,000 -cm< min < 3,000 -cm) COHERENT GRAVITY METHOD

CASE 6 H= 30 ft Kaf= 0.283 p= 0.9 X= 975 m = 0.038386 in L= 24 ft k0f= 0.440807097 t= 0.45 t= 75 yrs tan 0.5 P-EV = 1.35 b= 0.164 ft H= 5.294118 ft V2= 18 k/ft H1= 35.29412 ft min=tan( r)= 0.674502089 La= 10.58824 ft F*max= 2 r= 125 pcf Kab = 0.537 s= 6 mm = 0.23622 in Cu= 7 b= 125 pcf Fy= 65 ksi P-EH = 1.5 Level Z Zp-ave H Tmax F* Le pPr tTn Np Nt Ng Sh (ft) (ft) ksf k/ 5 ft wide panel dim (ft) k/strip k/strip - - - (ft) 1 1.25 9.90 0.47 5.86 1.917 13.41 9.39 9.18 0.6 0.6 2 2.50 2 3.75 12.40 0.65 8.07 1.751 13.41 10.75 9.18 0.8 0.9 2 2.50 3 6.25 14.90 0.82 10.21 1.586 13.41 11.69 9.18 0.9 1.1 2 2.50 4 8.75 17.40 0.98 12.26 1.420 13.41 12.23 9.18 1.0 1.3 2 2.50 5 11.25 19.90 1.14 14.24 1.254 13.41 12.35 9.18 1.2 1.6 2 2.50 6 13.75 22.19 1.29 16.13 1.089 14.25 12.70 9.18 1.3 1.8 2 2.50 7 16.25 24.31 1.44 17.94 0.923 15.75 13.04 9.18 1.4 2.0 2 2.50 8 18.75 26.44 1.57 19.65 0.757 17.25 12.74 9.18 1.5 2.1 3 1.67 9 21.25 28.56 1.77 22.10 0.675 18.75 13.33 9.18 1.7 2.4 3 1.67 10 23.75 30.69 2.04 25.51 0.675 20.25 15.47 9.18 1.6 2.8 3 1.67 11 26.25 32.81 2.35 29.36 0.675 21.75 17.76 9.18 1.7 3.2 4 1.25 12 28.75 34.94 2.70 33.73 0.675 23.25 20.22 9.18 1.7 3.7 4 1.25 Asum = 14.41 PLAIN STEEL STRIPS AND HIGH QUALITY FILL ( min > 10,000 -cm) COHERENT GRAVITY METHOD

CASE 7 H= 30 ft Kaf= 0.283 p= 0.9 X= 975 m = 0.038385827 in L= 24 ft k0f= 0.440807097 t= 0.35 t= 75 yrs tan 0.5 P-EV = 1.35 St= 1.0 ft H= 5.294118 ft V2= 18 k/ft Sl= 0.5 ft H1= 35.29412 ft F*min= 0.311666667 Tranverse W11 0.374 in diameter La= 10.58824 ft F*max= 0.623333333 r= 125 pcf Kab = 0.537 Longitudinal W20 0.505 in diameter b= 125 pcf Fy= 65 ksi P-EH = 1.5 Level Z Zp-ave H Tmax F* Le pPr tTn Np Nt Ng Sh (ft) (ft) ksf k/ 5 ft wide panel dim (ft) k/ft k/wire - - - - 1 1.25 9.90 0.47 5.86 0.604 13.41 18.03 3.28 1.7 1.8 2 2W20 + W11 x 1.0' 2 3.75 12.40 0.65 8.07 0.565 13.41 21.13 3.28 1.8 2.5 3 3W20 + W11 x 1.0' 3 6.25 14.90 0.82 10.21 0.526 13.41 23.64 3.28 1.9 3.1 4 4W20 + W11 x 1.0' 4 8.75 17.40 0.98 12.26 0.487 13.41 25.57 3.28 2.0 3.7 4 4W20 + W11 x 1.0' 5 11.25 19.90 1.14 14.24 0.448 13.41 26.90 3.28 2.1 4.3 5 5W20 + W11 x 1.0' 6 13.75 22.19 1.29 16.13 0.409 14.25 29.10 3.28 2.1 4.9 5 5W20 + W11 x 1.0' 7 16.25 24.31 1.44 17.94 0.370 15.75 31.89 3.28 2.1 5.5 6 6W20 + W11 x 1.0' 8 18.75 26.44 1.57 19.65 0.331 17.25 33.98 3.28 2.2 6.0 6 6W20 + W11 x 1.0' 9 21.25 28.56 1.77 22.10 0.312 18.75 37.56 3.28 2.2 6.7 7 7W20 + W11 x 1.0' 10 23.75 30.69 2.04 25.51 0.312 20.25 43.58 3.28 2.2 7.8 8 8W20 + W11 x 1.0' 11 26.25 32.81 2.35 29.36 0.312 21.75 50.05 3.28 2.2 9.0 9 9W20 + W11 x 1.0' 12 28.75 34.94 2.70 33.73 0.312 23.25 56.96 3.28 2.2 10.3 11 11W20 + W11 x 1.0' Asum = 14.02 PLAIN STEEL GRIDS AND HIGH QUALITY FILL ( min > 10,000 -cm) COHERENT GRAVITY METHOD

CASE 8 H= 30 ft Kaf= 0.283 p= 0.9 X= 1829.22 m = 0.072017 in L= 24 ft k0f= 0.440807097 t= 0.45 t= 50 yrs tan 0.5 P-EV = 1.35 b= 0.164 ft H= 5.294118 ft V2= 18 k/ft H1= 35.29412 ft min=tan( r)= 0.674502089 La= 10.58824 ft F*max= 2 r= 125 pcf Kab = 0.537 s= 8 mm = 0.314961 in Cu= 7 b= 125 pcf Fy= 65 ksi P-EH = 1.5 Level Z Zp-ave H Tmax F* Le pPr tTn Np Nt Ng Sh (ft) (ft) ksf k/ 5 ft wide panel dim (ft) k/strip k/strip - - - (ft) 1 1.25 9.90 0.47 5.86 1.917 13.41 9.39 9.84 0.6 0.6 2 2.50 2 3.75 12.40 0.65 8.07 1.751 13.41 10.75 9.84 0.8 0.8 2 2.50 3 6.25 14.90 0.82 10.21 1.586 13.41 11.69 9.84 0.9 1.0 2 2.50 4 8.75 17.40 0.98 12.26 1.420 13.41 12.23 9.84 1.0 1.2 2 2.50 5 11.25 19.90 1.14 14.24 1.254 13.41 12.35 9.84 1.2 1.4 2 2.50 6 13.75 22.19 1.29 16.13 1.089 14.25 12.70 9.84 1.3 1.6 2 2.50 7 16.25 24.31 1.44 17.94 0.923 15.75 13.04 9.84 1.4 1.8 2 2.50 8 18.75 26.44 1.57 19.65 0.757 17.25 12.74 9.84 1.5 2.0 2 2.50 9 21.25 28.56 1.77 22.10 0.675 18.75 13.33 9.84 1.7 2.2 3 1.67 10 23.75 30.69 2.04 25.51 0.675 20.25 15.47 9.84 1.6 2.6 3 1.67 11 26.25 32.81 2.35 29.36 0.675 21.75 17.76 9.84 1.7 3.0 3 1.67 12 28.75 34.94 2.70 33.73 0.675 23.25 20.22 9.84 1.7 3.4 4 1.25 Asum = 17.98 PLAIN STEEL STRIPS AND GOOD QUALITY FILL (3000 -cm< min < 10,000 -cm) COHERENT GRAVITY METHOD

CASE 9 H= 30 ft Kaf= 0.283 p= 0.9 X= 1829.22 m = 0.072016544 in L= 24 ft k0f= 0.440807097 t= 0.35 t= 50 yrs tan 0.5 P-EV = 1.35 St= 1.0 ft H= 5.294118 ft V2= 18 k/ft Sl= 0.5 ft H1= 35.29412 ft F*min= 0.311666667 Tranverse W11 0.374 in diameter La= 10.58824 ft F*max= 0.623333333 r= 125 pcf Kab = 0.537 Longitudinal W20 0.505 in diameter b= 125 pcf Fy= 65 ksi P-EH = 1.5 Level Z Zp-ave H Tmax F* Le pPr tTn Np Nt Ng Sh (ft) (ft) ksf k/ 5 ft wide panel dim (ft) k/ft k/wire - - - - 1 1.25 9.90 0.47 5.86 0.604 13.41 18.03 2.33 1.7 2.5 3 3W20 + W11 x 1.0' 2 3.75 12.40 0.65 8.07 0.565 13.41 21.13 2.33 1.8 3.5 4 4W20 + W11 x 1.0' 3 6.25 14.90 0.82 10.21 0.526 13.41 23.64 2.33 1.9 4.4 5 5W20 + W11 x 1.0' 4 8.75 17.40 0.98 12.26 0.487 13.41 25.57 2.33 2.0 5.3 6 6W20 + W11 x 1.0' 5 11.25 19.90 1.14 14.24 0.448 13.41 26.90 2.33 2.1 6.1 7 7W20 + W11 x 1.0' 6 13.75 22.19 1.29 16.13 0.409 14.25 29.10 2.33 2.1 6.9 7 7W20 + W11 x 1.0' 7 16.25 24.31 1.44 17.94 0.370 15.75 31.89 2.33 2.1 7.7 8 8W20 + W11 x 1.0' 8 18.75 26.44 1.57 19.65 0.331 17.25 33.98 2.33 2.2 8.4 9 9W20 + W11 x 1.0' 9 21.25 28.56 1.77 22.10 0.312 18.75 37.56 2.33 2.2 9.5 10 10W20 + W11 x 1.0' 10 23.75 30.69 2.04 25.51 0.312 20.25 43.58 2.33 2.2 11.0 11 11W20 + W11 x 1.0' 11 26.25 32.81 2.35 29.36 0.312 21.75 50.05 2.33 2.2 12.6 13 13W20 + W11 x 1.0' 12 28.75 34.94 2.70 33.73 0.312 23.25 56.96 2.33 2.2 14.5 15 15W20 + W11 x 1.0' Asum = 19.63 PLAIN STEEL GRIDS AND GOOD QUALITY FILL (3000 -cm< min < 10,000 -cm) COHERENT GRAVITY METHOD

Next: Appendix G - List of Symbols and Summary of Equations »
LRFD Metal Loss and Service-Life Strength Reduction Factors for Metal-Reinforced Systems Get This Book
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TRB’s National Cooperative Highway Research Program (NCHRP) Report 675: LRFD Metal Loss and Service-Life Strength Reduction Factors for Metal-Reinforced Systems explores the development of metal loss models for metal-reinforced systems that are compatible with the American Association of State Highway and Transportation Officials' Load and Resistance Factor Design Bridge Design Specifications.

NCHRP Research Results Digest 364: Validation of LRFD Metal Loss and Service-Life Strength Reduction Factors for Metal-Reinforced Systems summarizes the results of research to further validate some key results of a project that resulted in publication of NCHRP Report 675.

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