MSE Wall Design Calculation.pdf
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This document summarizes the design calculations for section 1 of a mechanically stabilized earth (MSE) wall. It analyzes the external stability including sliding resistance, overturning, and bearing capacity. It also evaluates the internal stability, checking the pullout and tensile resistance of the soil reinforcements. The calculations show the wall design satisfies factors of safety for different load cases, indicating the section 1 panel arrangement and reinforcement design is adequate.
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MSE Wall Design Calculation.pdf
- 1. PROJECT : PREPARED BY : DATE : T.Z.S.K 4/11/2022 T . Z COMPANY : REV NO : - DATE : DESIGN CALCULATION REPORT Section (1) Panels Arrangement PREPARED BY : 11-Apr-22
- 2. PROJECT : PREPARED BY : DATE : T.Z.S.K 4/11/2022 Design Calculation Results (SECTION 1) SUMMARY EXTERNAL STABILITY Sliding Case I F.S = 3.17 > 1.50 OK Case II F.S = 3.82 > 1.50 OK Case III F.S = 4.24 > 1.50 OK Case IV F.S = 3.01 > 1.50 OK Case V F.S = 3.82 > 1.50 OK Overturning Case I F.S = 7.01 > 2.00 OK Case II F.S = 7.53 > 2.00 OK Case III F.S = 8.48 > 2.00 OK Case IV F.S = 3.82 > 2.00 OK Case V F.S = 7.53 > 2.00 OK Bearing Capacity Case I q = 110.71 kN/m2 Case II q = 173.98 kN/m2 Control Case III q = 118.19 kN/m2 Case IV q = 128.60 kN/m2 Case V q = 173.98 kN/m2 INTERNAL STABILITY Pullout Resistance Layer 1 Tmax = 9.77 kN per strip < 16.20 kN OK Layer 2 Tmax = 13.05 kN per strip < 21.75 kN OK Layer 3 Tmax = 16.77 kN per strip < 28.28 kN OK Layer 4 Tmax = 18.73 kN per strip < 33.97 kN OK Tensile Resistance Layer 1 Tmax = 18.82 kN per strip < 33.51 kN OK Layer 2 Tmax = 22.99 kN per strip < 33.51 kN OK Layer 3 Tmax = 26.68 kN per strip < 33.51 kN OK Layer 4 Tmax = 30.20 kN per strip < 33.51 kN OK Pullout Resistance Layer 1 Tmax = 14.56 kN per strip < 18.00 kN OK Layer 2 Tmax = 18.17 kN per strip < 24.17 kN OK Layer 3 Tmax = 22.58 kN per strip < 31.42 kN OK Layer 4 Tmax = 25.22 kN per strip < 37.74 kN OK Tensile Resistance Layer 1 Tmax = 23.61 kN per strip < 44.67 kN OK Layer 2 Tmax = 28.11 kN per strip < 44.67 kN OK Layer 3 Tmax = 32.49 kN per strip < 44.67 kN OK Layer 4 Tmax = 36.70 kN per strip < 44.67 kN OK Pullout Resistance Layer 1 Tmax = 12.13 kN per strip < 18.00 kN OK Layer 2 Tmax = 16.59 kN per strip < 24.17 kN OK Layer 3 Tmax = 20.31 kN per strip < 31.42 kN OK Layer 4 Tmax = 22.27 kN per strip < 37.74 kN OK Tensile Resistance Layer 1 Tmax = 22.97 kN per strip < 44.67 kN OK Layer 2 Tmax = 29.21 kN per strip < 44.67 kN OK Layer 3 Tmax = 32.90 kN per strip < 44.67 kN OK Layer 4 Tmax = 36.42 kN per strip < 44.67 kN OK Seismic Impact Seismic Impact Static Seismic Impact Static Static Seismic Impact Static
- 3. PROJECT : PREPARED BY : DATE : T.Z.S.K 4/11/2022 Wall Information Section name = SECTION 1 Wall Height H = 4.52 m Reinforcing fill length L = 4.50 m B = 4.64 m Reinforced Soil Unit Weight ϒsoil = 21.00 kN/m3 Reinforcement fill φ = 34.00 Degree Retained Soil Unit Weight ϒsoil = 21.00 kN/m3 Retained fill φ = 34.00 Degree Foundation Soil Unit Weight ϒfoundation = 19.00 kN/m3 Foundation internal friction angle φ = 30.00 Degree Foundation cohesion c = 0.00 kN/m2 Nr = 22.40 Traffic surcharge q = 13.00 kN/m2 Panel First strip location = 1.88 m Location of slab bottom = 1.10 m Vertical sapcing of strip Sv = 0.75 m Panel width b = 1.50 m Panel height h = 1.50 m Panel thickness t = 0.14 m Strip width b = 50.00 mm Stritp thickness t = 4.00 mm Horizontal spacing of strip (1st Layer) Sh = 0.50 m Horizontal spacing of strip Sh = 0.75 m Steel reinforcement strength fy = 448.00 Mpa Load Factor, ϒ (LRFD 11.5.5) Typical application Bearing Resistance Vertical ϒEV = 1.35 Horizontal ϒEH = 1.5 Sliding and Eccentricity Vertical ϒEV = 1 Horizontal ϒEH = 1.5 Live Load Surcharge on MSE Wall Bearing and reinforcement tensile Resistance ϒLS = 1.75 Sliding, eccentricity and reinforcement pullout resistance ϒLS = 1.75 Resistance Factor, φ (LRFD Table 11.5.6-1) Mechanically Stabilized Earth Walls Pullout resistance of tensile reinforcement Static loading = 0.9 MSE WALL DESIGN CALCULATION REPORT
- 4. PROJECT : PREPARED BY : DATE : T.Z.S.K 4/11/2022 Load Cases Vertical Load Horizontal Load Live Load Load Factor ϒ (LRFD 11.5.5) ϒEV ϒEH ϒLS Case I Strength I 1.00 1.50 - Case II Strength II 1.35 1.50 1.75 Case III Service I 1.00 1.00 1.00 Resistance Factor φP φT Case IV Static loading 0.90 0.75 Case V Combined static and impact loading 1.00 1.00 I. External Stability Static Mass Stability Vertical loads Reinforced Soil V1 = ϒsoil H L = 21.00 x 4.52 x 4.50 = 427.14 kN/m Case I V1 = 427.14 x 1 V1 = 427.14 kN/m Case II V1 = 427.14 x 1.35 V1 = 576.64 kN/m Case III V1 = 427.14 x 1 V1 = 427.14 kN/m Forces acting on the MSE Wall Forces : V1 = ϒsoil H L V2 = qs L F1 = 0.5 ϒ H2 Ka F2 = qs H Kaf
- 5. PROJECT : PREPARED BY : DATE : T.Z.S.K 4/11/2022 Moment arm of V1 = 2.25 m MV1 = 427.14 x 2.25 MV1 = 961.065 kN-m/m Case I MV1 = 961.065 KN-m/m Case II MV1 = 1297.44 KN-m/m Case III MV1 = 961.07 KN-m/m Traffic surcharge V2 = q L V2 = 13.00 x 4.5 V2 = 58.50 kN/m Factored V2 = 58.50 x 1.75 Factored V2 = 102.38 kN/m Moment arm of V2 = 2.25 m MV2 = 58.50 x 2.25 MV2 = 131.63 kN-m/m Factored MV2 = 102.38 x 2.25 Factored MV2 = 230.34 kN-m/m Case I ∑V = 427.14 kN/m Case II ∑V = 679.01 kN/m Case III ∑V = 485.64 kN/m Case I ∑Mv = 961.07 kN-m/m Case II ∑Mv = 1527.78 kN-m/m Case III ∑Mv = 1092.69 kN-m/m Horizontal loads ka = tan(45 - φ/2)2 For retained ka = 0.28 For surcharge kaf = 0.28 Retained Soil F1 = 0.5 ϒsoil H2 Ka = 60.65 kN/m Case I F1 = 90.97 kN/m Case II F1 = 90.97 kN/m Case III F1 = 60.65 kN/m Moment arm of F1 = 1.51 m Case I MF1 = 137.07 kN-m/m Case II MF1 = 137.07 kN-m/m Case III MF1 = 91.38 kN-m/m
- 6. PROJECT : PREPARED BY : DATE : T.Z.S.K 4/11/2022 Traffic surcharge F2 = q H Kaf F2 = 16.61 kN/m Factored F2 = 29.07 kN/m Moment arm of F2 = 2.26 m MF2 = 37.54 kN-m/m Factored MF2 = 65.70 kN-m/m Case I ∑F = 90.97 kN/m Case II ∑F = 120.04 kN/m Case III ∑F = 77.26 kN/m Case I ∑MF = 137.07 kN-m/m Case II ∑MF = 202.77 kN-m/m Case III ∑MF = 128.92 kN-m/m Sliding (LRFD 11.10.5.3) Sliding F.S = ∑V x tanφ ∑F Case I F.S = 3.17 > 1.5 OK Case II F.S = 3.82 > 1.5 OK Case III F.S = 4.24 > 1.5 OK Overturning (LRFD 11.10.5.3) Overturning F.S = ∑Mv ∑MF Case I = 7.01 ≥ 2 OK Case II = 7.53 ≥ 2 OK Case III = 8.48 ≥ 2 OK Bearing Capacity at Base Eccentricity e = L - ∑Mv-∑Mf 2 ∑V Case I e = 0.32 m ≤ 0.77 m OK Case II e = 0.30 m ≤ 0.75 m OK Case III e = 0.27 m ≤ 0.75 m OK
- 7. PROJECT : PREPARED BY : DATE : T.Z.S.K 4/11/2022 σv = ∑V L-2e Case I σv = 110.71 kN/m2 Case II σv = 173.98 kN/m2 Case III σv = 118.19 kN/m2 11.4.2 (f) qult = cf Nc + 0.5 (L-2e) ϒf Nr qult = 844.62 kN/m2 F.S = qult σv = 7.63 > 1.5 OK Sliding at base of first grid F1 at first grid F1 = 0.5 ϒb d2 Ka = 50.12 kN/m F2 = q d ka = 15.88 kN/m ∑F = 66.00 kN/m F.S = ϒb d L tanφ C ∑F = 4.17 > 1.5 OK
- 8. PROJECT : PREPARED BY : DATE : T.Z.S.K 4/11/2022 II. Internal Stability Distance from Top Steel Strip Tributary Spacing d1 = 1.88 m V1 = 1.18 m d2 = 2.63 m V2 = 0.75 m d3 = 3.38 m V3 = 0.75 m d4 = 4.13 m V4 = 0.77 m Force developed in the reinforcement Static Load Compute Kr (LRFD Figure 11.10.6.2.1-3) At Z = 0 Kr = 0.48 Under Z = 6 m Kr = 0.34 MSE Wall Panel Arrangement for Section 1 LRFD 11.4.3.Fig 29 Variation of stress ratio with depth in MSE Wall Friction
- 9. PROJECT : PREPARED BY : DATE : T.Z.S.K 4/11/2022 Layer 1 Vertical Stress 1 Reinforced Soil Kr = 0.44 σv = ϒsoil H = 39.48 kN/m2 Case I σv = 39.48 kN/m2 Case II σv = 53.30 kN/m2 Case III σv = 39.48 kN/m2 = 2 Traffic Surcharge σv = 13.00 kN/m2 σv = 22.75 kN/m2 Case I ∑σv = 39.48 kN/m2 Case II ∑σv = 76.05 kN/m2 Case III ∑σv = 52.48 kN/m2 Horizontal Stress σh = ϒp (σv kr + Δσh) σh = σv kr Case I σh = 26.06 kN/m2 Case II σh = 50.19 kN/m2 Case III σh = 23.09 kN/m2 At per strip At = 0.38 m2 Traffic Load are NEGLECTED in pullout calculation as per AASHTO LRFD 11.10.6.3.2. Tmax = σh Sv For Pullout Tmax = 9.77 kN per strip < 16.20 kN OK For Tensile Tmax = 18.82 kN per strip < 33.51 kN OK Layer 2 Vertical Stress 1 Reinforced Soil Kr = 0.42 σv = ϒsoil H = 55.23 kN/m2 Case I σv = 55.23 kN/m2 Case II σv = 74.56 kN/m2 Case III σv = 55.23 kN/m2 2 Traffic Surcharge σv = 13.00 kN/m2 σv = 22.75 kN/m2 BP 5
- 10. PROJECT : PREPARED BY : DATE : T.Z.S.K 4/11/2022 Case I ∑σv = 55.23 kN/m2 Case II ∑σv = 97.31 kN/m2 Case III ∑σv = 68.23 kN/m2 Horizontal Stress σh = ϒp (σv kr + Δσh) σh = σv kr Case I σh = 23.20 kN/m2 Case II σh = 40.87 kN/m2 Case III σh = 28.66 kN/m2 At per strip At = 0.56 m2 Traffic Load are NEGLECTED in pullout calculation as per AASHTO LRFD 11.10.6.3.2. Tmax = σh Sv For Pullout Tmax = 13.05 kN per strip < 21.75 kN OK For Tensile Tmax = 22.99 kN per strip < 33.51 kN OK Layer 3 Vertical Stress 1 Reinforced Soil Kr = 0.40 σv = ϒsoil H = 70.98 kN/m2 Case I σv = 70.98 kN/m2 Case II σv = 95.82 kN/m2 Case III σv = 70.98 kN/m2 2 Traffic Surcharge σv = 13.00 kN/m2 σv = 22.75 kN/m2 Case I ∑σv = 70.98 kN/m2 Case II ∑σv = 118.57 kN/m2 Case III ∑σv = 83.98 kN/m2 Horizontal Stress σh = ϒp (σv kr + Δσh) σh = σv kr Case I σh = 29.81 kN/m2 Case II σh = 47.43 kN/m2 Case III σh = 33.59 kN/m2 At per strip At = 0.56 m2 BP 5
- 11. PROJECT : PREPARED BY : DATE : T.Z.S.K 4/11/2022 Traffic Load are NEGLECTED in pullout calculation as per AASHTO LRFD 11.10.6.3.2. Tmax = σh Sv For Pullout Tmax = 16.77 kN per strip < 28.28 kN OK For Tensile Tmax = 26.68 kN per strip < 33.51 kN OK Layer 4 Vertical Stress 1 Reinforced Soil Kr = 0.38 σv = ϒsoil H = 86.73 kN/m2 Case I = 86.73 kN/m2 Case II = 117.09 kN/m2 Case III = 86.73 kN/m2 2 Traffic Surcharge σv = 13.00 kN/m2 σv = 22.75 kN/m2 Case I ∑σv = 86.73 kN/m2 Case II ∑σv = 139.84 kN/m2 Case III ∑σv = 99.73 kN/m2 Horizontal Stress σh = ϒp (σv kr + Δσh) σh = σv kr Case I σh = 33.30 kN/m2 Case II σh = 53.70 kN/m2 Case III σh = 38.30 kN/m2 At per strip At = 0.56 m2 Traffic Load are NEGLECTED in pullout calculation as per AASHTO LRFD 11.10.6.3.2. Tmax = σh Sv For Pullout Tmax = 18.73 kN per strip < 33.97 kN OK For Tensile Tmax = 30.20 kN per strip < 33.51 kN OK
- 12. PROJECT : PREPARED BY : DATE : T.Z.S.K 4/11/2022 Resistance in friction of one strip against soil (LRFD Equation 11.10.6.3.2-1) At Z = 0 F* = 1.80 Under Z = 6 m F* = 0.67 LRFD Figure 11.10.6.3.2-1 Default Values for the Pullout Friction Factor, F* α = 1 C = 2.00 for strip Rc = 0.10 For 3 strip per panel Rc = 0.07 For 2 strip per panel Pullout calculation at each reinforcement level Le ≥ Tmax ≥ 1 m φ F* α σv C Rc Layer 1 F* = 1.45 Le = 1.83 m ≥ 1 m Take Le = 1.83 m Layer 2 F* = 1.3 Le = 2.67 m ≥ 1 m Take Le = 2.67 m Layer 3 F* = 1.16 Le = 2.70 m ≥ 1 m Take Le = 2.70 m Layer 4 F* = 1.02 Le = 2.85 m ≥ 1 m Take Le = 2.85 m
- 13. PROJECT : PREPARED BY : DATE : T.Z.S.K 4/11/2022 Calculate L A at each layer for H/2 from bottom LA = 0.6 (H1 - d) for inextensible reinforcement for H/2 from top LA = 0.3 H1 for inextensible reinforcement LA1 = 1.36 m LA2 = 1.13 m LA3 = 0.68 m LA4 = 0.23 m LRFD Figure 11.10.6.3.1-1 Location of Potential Failure Surface for Internal Stability Design of MSE Walls Calculate L T at each layer Layer 1 LT1 = 3.18 m < 4.50 m OK Layer 2 LT2 = 3.80 m < 4.50 m OK Layer 3 LT3 = 3.38 m < 4.50 m OK Layer 4 LT4 = 3.08 m < 4.50 m OK Allowable Tensile Strength Design Life = 100 years For Corrosion Losses Ec = En - Es Loss of galvanizing = 0.015 mm/yr for first 2 year = 0.004 mm/yr for subsequent years Zinc coating lift = 16.00 years Loss of carbon steel = 0.012 mm/yr after zinc depletion Ec = 1.99 mm Ac = 99.72 mm2
- 14. PROJECT : PREPARED BY : DATE : T.Z.S.K 4/11/2022 Tal = AC FY Case V φTall = 44.67 kN Case IV φTall = 33.51 kN Pullout Resistance Strength C11.10.6.3.2 P = F* α σv Le C b Layer 1 Case V φP = 18.00 kN Case IV φP = 16.20 kN Layer 2 Case V φP = 24.17 kN Case IV φP = 21.75 kN Layer 3 Case V φP = 31.42 kN Case IV φP = 28.28 kN Layer 4 Case V φP = 37.74 kN Case IV φP = 33.97 kN Connection Strength Strip width b = 60 mm Stritp thickness t = 4 mm Yield Strength Fy = 345 Mpa C11.10.6.3.2 Tac = AC FY Case V φTac = 63.48 kN > 44.67 kN OK Case IV φTac = 47.61 kN > 33.51 kN OK III. External Stability with Seismic Peak Ground Acceleration a0/g = 0.46 11.6.5.2.1 Horizontal acceleration coefficient kh = 0.5 Kho = 0.23 ζ = Arc tan(Kh) = 12.95 kae = cos2 (φ - ζ) cos ( ζ ) cos (ζ + δ) (1 + √(sin(φ + δ) sin(φ - ζ - δ)/cos (ζ + δ) cosδ))2 kae = 0.871 0.950 x 2.114 = 0.434 11.6.5.3-2 Horizontal Seismic Thrust PAE = 0.5 KAE ϒ H2 = 93.06 kN/m
- 15. PROJECT : PREPARED BY : DATE : T.Z.S.K 4/11/2022 Moment arm of PAE = 1.51 m Moment MAE = 140.22 KN-m Horizontal Inertia Force PIR = 0.5 Kh ϒ H2 = 49.34 kN/m Moment arm of PIR = 2.26 m Moment MIR = 111.51 KN-m ∑MF = 251.72 KN-m Sliding (LRFD 11.10.5.3) Sliding F.S = ∑V x tanφ ∑F Rv = 427.14 kN/m Moment arm of Pv = 2.25 m Moment Mv = 961.07 KN-m Rh = 95.87 kN/m F.S = 3.01 > 1.5 OK Overturning (LRFD 11.10.5.3) Overturning F.S = ∑Mv ∑MF = 3.82 > 2 OK Bearing Capacity at Base Eccentricity e = L - ∑Mv-∑Mf 2 ∑V = 0.59 < 0.75 OK σv = ∑V L - 2e σv = 128.60 kN/m2
- 16. PROJECT : PREPARED BY : DATE : T.Z.S.K 4/11/2022 qult = cf Nc + 0.5 (L-2e) ϒf Nr qult = 706.78 kN/m2 F.S = qult σv = 5.50 > 1.5 OK IV. Internal Stability with Seismic PI = Kh Wa = 22.20 kN/m Tmd = Pi Lei / ∑Lei Layer 1 Tmd = 4.78 kN per strip Layer 2 Tmd = 5.12 kN per strip Layer 3 Tmd = 5.81 kN per strip Layer 4 Tmd = 6.49 kN per strip Ttotal = Tmax + Tmd Layer 1 For Pullout Ttotal = 14.56 kN per strip < 18.00 kN OK For Tensile Ttotal = 23.61 kN per strip < 44.67 kN OK Layer 2 For Pullout Ttotal = 18.17 kN per strip < 24.17 kN OK For Tensile Ttotal = 28.11 kN per strip < 44.67 kN OK Layer 3 For Pullout Ttotal = 22.58 kN per strip < 31.42 kN OK For Tensile Ttotal = 32.49 kN per strip < 44.67 kN OK Layer 4 For Pullout Ttotal = 25.22 kN per strip < 37.74 kN OK For Tensile Ttotal = 36.70 kN per strip < 44.67 kN OK
- 17. PROJECT : PREPARED BY : DATE : T.Z.S.K 4/11/2022 V. Impact Load Width of slab b = 2.1 m Depth of slab h = 1.1 m Eccetricity of traffic barrier e = 0.12 m Slab Length L = 6 m 11.10.10.2 Static impact Load P = 44.48 kN Earth pressure F1 = 0.5 Ka ϒ h2 Case I F1 = 3.59 kN/m Case II F1 = 4.85 kN/m Traffic surcharge F2 = Ka q h Case I F2 = 4.04 kN/m Case II F2 = 7.08 kN/m PH1 = 7.41 kN/m Case I ∑ F 11.01 kN/m Case II ∑ F = 19.34 kN/m Horizontal pressure due to traffic barrier L1 = (cr + bf - 2e') (tan 45 + φ/2) = 3.50 m Δσhmax = 2 ∑F / L1 Case I Δσhmax = 6.29 kN/m2 Case II Δσhmax = 11.06 kN/m2
- 18. PROJECT : PREPARED BY : DATE : T.Z.S.K 4/11/2022 Tmax = σh Sv Layer 1 For Pullout Tmax = 12.13 kN per strip < 18.00 kN OK For Tensile Tmax = 22.97 kN per strip < 44.67 kN OK Layer 2 For Pullout Tmax = 16.59 kN per strip < 24.17 kN OK For Tensile Tmax = 29.21 kN per strip < 44.67 kN OK Layer 3 For Pullout Tmax = 20.31 kN per strip < 31.42 kN OK For Tensile Tmax = 32.90 kN per strip < 44.67 kN OK Layer 4 For Pullout Tmax = 22.27 kN per strip < 37.74 kN OK For Tensile Tmax = 36.42 kN per strip < 44.67 kN OK