Spencer_forSARA2003 ′ F DumEq 0.105 1.287 1.287 #VALUE! ### Ω H R 27 5 1.73 10 15 61.518 0.2 4.91 7.95 13.40 -5.89 17.467 # x c φ W u l P T E λ 0 17.47 3.27 ### 15 0.000 1 16.58 1.37 ### ### ### 30 ### 1.136 ### 2.10 ### ### #VALUE! 0.012 ### 12.12 2 15.70 0.00 ### ### ### 30 ### 0.997 ### 1.63 ### ### #VALUE! 0.025 ### 11.24 3 14.72 -1.18 ### ### ### 0 ### 0.879 ### 1.54 ### ### #VALUE! 0.038 ### 10.30 4 13.74 -2.14 ### ### ### 0 ### 0.770 ### 1.37 ### ### #VALUE! 0.050 ### 9.32 5 12.76 -2.92 ### ### ### 0 ### 0.673 ### 1.25 ### ### #VALUE! 0.062 ### 8.34 6 11.78 -3.56 ### ### ### 0 ### 0.582 ### 1.17 ### ### #VALUE! 0.072 ### 7.36 7 10.79 -4.10 ### ### ### 0 ### 0.496 ### 1.12 ### ### #VALUE! 0.082 ### 6.38 8 9.81 -4.53 ### ### ### 0 ### 0.415 ### 1.07 ### ### #VALUE! 0.090 ### 5.40 9 8.83 -4.87 ### ### ### 0 ### 0.336 ### 1.04 ### ### #VALUE! 0.096 ### 4.42 10 7.85 -5.13 ### ### ### 0 ### 0.259 ### 1.02 ### ### #VALUE! 0.101 ### 3.43 11 6.87 -5.31 ### ### ### 0 ### 0.184 ### 1.00 ### ### #VALUE! 0.103 ### 2.45 12 5.89 -5.42 ### ### ### 0 ### 0.110 ### 0.99 ### ### #VALUE! 0.105 ### 1.47 13 4.91 -5.46 ### ### ### 0 ### 0.037 ### 0.98 ### ### #VALUE! 0.104 ### 0.49 14 3.93 -5.42 ### ### ### 0 ### -0.037 ### 0.98 ### ### #VALUE! 0.101 ### -0.49 15 2.94 -5.31 ### ### ### 0 ### -0.110 ### 0.99 ### ### #VALUE! 0.097 ### -1.47 16 1.96 -5.13 ### ### ### 0 ### -0.184 ### 1.00 ### ### #VALUE! 0.091 ### -2.45 17 0.98 -4.87 ### ### ### 0 ### -0.259 ### 1.02 ### ### #VALUE! 0.083 ### -3.43 18 0.00 -4.53 ### ### ### 0 ### -0.336 ### 1.04 ### ### #VALUE! 0.074 ### -4.42 19 -0.98 -4.10 ### ### ### 0 ### -0.415 ### 1.07 ### ### #VALUE! 0.064 ### -5.40 20 -1.96 -3.56 ### ### ### 0 ### -0.496 ### 1.12 ### ### #VALUE! 0.053 ### -6.38 21 -2.94 -2.92 ### ### ### 0 ### -0.582 ### 1.17 ### ### #VALUE! 0.040 ### -7.36 22 -3.93 -2.14 ### ### ### 0 ### -0.673 ### 1.25 ### ### #VALUE! 0.027 ### -8.34 23 -4.91 -1.18 ### ### ### 0 ### -0.770 ### 1.37 ### ### #VALUE! 0.014 ### -9.32 24 -5.89 0.00 ### ### ### 0 ### -0.879 ### 1.54 ### ### #VALUE! 0.000 ### -10.30 Undrained shear strength r "i e " s "t $ a% E&'an( deth 0 1.5 3 5 7 10 )&* $+ 40 28 20 20 26 37 )(,a* 10 30 )(,a* 16 M Forces Var h c γ w P w M w r u x c y c &in &a y bot y top γ ave α rad σ ' L x c m φ m ) * γ clay )( /& 3 * framed cells contain equations framed cells contain equations -10.00-5.00 0.00 5.00 10.0015.0020.00 -10.00 -5.00 0.00 5.00 10.00 Units: m, !"m , !"m 2 , !, or oth$r co%& &t$%t &$t o( u% t&. )rray (ormula& &lop$ a%*l$ "t $ a% E&'an(&ent λ = λ ' sin [ ( x i − x 0 ) ( x n − x 0 ) π ] λ x % enter " R tati n x % x 0 0 25 50 0 2 + D e p t h SP!"# method Varying side$force angle E i λ i E i λ i-1 E i-1 E i-1 T i P i W i α i l %' t %t Ω A B C D E F G H I J K L M N O P Q 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Practical Probabilistic Slope Stability Analysis
Module1lFDumEq0.1051.2871.287SMSForcesVarying l0.000.00For plotting tension crack17.475.00WHhcgwPwMwruxcycRxminxmax17.473.272751.73101561.51795998730.24.917.9513.40-5.8917.467Kahc0.33333333331.7320508076#xybotytopgavecfWaradulPTEls 'LxLy017.473.275.00150.000116.581.375.0020.0010.003047.41.13610.732.1049.7228.5048.10.01212.9812.125.63215.700.005.0020.0010.003076.30.99717.271.6380.9636.3696.30.02532.4911.247.26314.72-1.185.0019.5835.260107.40.87921.891.54112.0142.14155.70.03850.9410.308.54413.74-2.145.0019.0027.150124.20.77025.311.37137.1228.84230.50.05074.979.329.61512.76-2.925.0018.6622.520137.80.67328.091.25149.2621.95306.30.06290.908.3410.47611.78-3.565.0018.4320.000149.00.58230.371.17156.3618.25377.00.072102.757.3611.19710.79-4.105.0018.2720.000158.30.49632.251.12160.9017.34438.40.082111.926.3811.7889.81-4.535.0018.1520.000165.80.41533.801.07165.0616.66489.60.090120.145.4012.2698.83-4.874.5018.0120.000167.00.33634.041.04164.0316.15528.50.096123.774.4212.64107.85-5.134.0017.8420.000161.90.25933.001.02158.1615.78553.80.101122.793.4312.95116.87-5.313.5017.6720.660155.60.18431.711.00152.3716.03565.90.103120.932.4513.17125.89-5.423.0017.5121.100148.10.11030.180.99146.5416.19565.90.105118.261.4713.31134.91-5.462.5017.3421.320139.40.03728.410.98140.4416.27554.80.104114.610.4913.39143.93-5.422.0017.1721.320129.6-0.03726.410.98133.8016.27533.70.101109.85-0.4913.39152.94-5.311.5016.9821.100118.6-0.11024.180.99126.3616.19503.70.097103.81-1.4713.31161.96-5.131.0016.7720.660106.5-0.18421.711.00117.8616.03466.30.09196.36-2.4513.17170.98-4.870.5016.5220.00093.2-0.25919.001.02107.9915.78423.40.08387.37-3.4312.95180.00-4.530.0016.2020.00078.7-0.33616.041.0496.7416.15376.30.07477.03-4.4212.6419-0.98-4.100.0016.0020.00067.7-0.41513.801.0789.1216.66325.10.06469.32-5.4012.2620-1.96-3.560.0016.0020.00060.1-0.49612.251.1285.3417.34269.20.05364.22-6.3811.7821-2.94-2.920.0016.0020.00050.9-0.58210.371.1779.7418.25210.10.04057.52-7.3611.1922-3.93-2.140.0016.0022.52039.7-0.6738.091.2573.9221.95146.90.02750.84-8.3410.4723-4.91-1.180.0016.0027.15026.1-0.7705.311.3768.3928.8478.60.01444.70-9.329.6124-5.890.000.0016.0035.2609.3-0.8791.891.5467.1242.14-0.00.00041.75-10.308.54Undrained shear strength profile of soft clayEmbankmentdepth01.535710(m)cmfmgmcu402820202637(kPa)103020(kPa)(o)(kN/m3)gclay16(kN/m3)
&APage &P&C&"Times New Roman,Regular"&8Spencer_forSARA2003framed cells contain equations
Module1
&APage &P
SpencerCircularlFDumEq0.1031.2531.253Ka0.33SForcesSMVarying l0.0000.000hc1.7320508076WHhcgwPwMwruxcycxminxmax2751.73101562.32137410110.28.008.00-18.1215.37-2.94417.028xcycR-15.180-1.661-2818.00Lever arms#xybytgavecfWaradulPTEls 'LxLyxiybiyti018.073.275.0015.000.000EquilCheck15.373.275.00116.881.685.0020.0010.003059.70.93110.101.9855.6532.2140.40.01618.029.475.530.0000.00014.751.405.00215.700.005.0020.0010.003098.40.95816.642.06100.2746.8395.50.03132.168.297.160.0000.00014.120.005.00314.72-0.955.0019.6536.220105.60.76721.511.36104.3239.37139.50.04455.057.218.470.0000.00012.66-2.455.00413.74-1.845.0019.1328.870120.00.73824.451.33127.4430.54202.60.05571.666.239.390.0000.00011.19-4.255.00512.76-2.635.0018.7624.080133.20.68227.151.26143.0524.28273.90.06686.005.2510.240.0000.0009.73-5.664.96611.78-3.375.0018.5020.000145.20.64129.601.22155.9919.53351.50.07697.834.2711.000.0000.0008.26-6.794.21710.79-4.015.0018.3020.000156.10.58331.811.18163.5518.76425.90.084107.343.2911.690.0000.0006.80-7.703.4689.81-4.635.0018.1520.000166.00.56233.831.16172.7418.50502.20.091115.172.3012.320.0000.0005.33-8.442.7298.83-5.154.5017.9720.000170.00.48434.641.11172.6017.69566.90.097121.021.3212.890.0000.0003.86-9.021.97107.85-5.524.0017.7720.990167.10.36034.061.05165.1317.56608.60.100123.440.3413.330.0000.0002.40-9.451.22116.87-5.783.5017.6021.940162.30.26133.071.02159.2717.78632.50.103123.74-0.6413.650.0000.0000.93-9.760.47125.89-5.943.0017.4322.580155.80.16831.751.00153.8217.93640.50.103122.80-1.6213.860.0000.000-0.53-9.940.00134.91-6.022.5017.2622.940147.90.07630.140.98148.4018.01633.80.102120.65-2.6013.980.0000.000-2.00-10.000.00143.93-6.002.0017.0923.030138.5-0.01928.230.98142.7618.03613.00.099117.23-3.5814.010.0000.000-3.47-9.940.00152.94-5.881.5016.9122.820127.6-0.12126.010.99136.8018.00578.60.094112.38-4.5713.940.0000.000-4.93-9.760.00161.96-5.651.0016.7122.290115.0-0.23323.441.01130.4217.94531.00.088105.87-5.5513.760.0000.000-6.40-9.450.00170.98-5.280.5016.4821.390100.5-0.36020.481.05123.6117.89470.70.08197.39-6.5313.460.0000.000-7.86-9.020.00180.00-4.730.0016.1920.01083.5-0.50717.011.12116.1517.92398.60.07286.47-7.5113.000.0000.000-9.33-8.440.0019-0.98-4.080.0016.0020.00069.2-0.58714.101.18105.9218.80324.30.06275.79-8.4912.410.0000.000-10.80-7.700.0020-1.96-3.390.0016.0020.00058.6-0.61511.951.2094.0219.16254.50.05166.33-9.4711.730.0000.000-12.26-6.790.0021-2.94-2.610.0016.0020.00047.1-0.6689.601.2582.9319.95187.40.03956.74-10.4511.000.0000.000-13.73-5.660.0022-3.93-1.810.0016.0024.20034.7-0.6847.081.2769.9624.45124.30.02648.16-11.4310.210.0000.000-15.19-4.250.0023-4.91-0.930.0016.0029.04021.5-0.7344.381.3259.8630.6161.40.01340.92-12.429.370.0000.000-16.66-2.450.0024-5.89-0.000.0016.0036.2907.3-0.7571.481.3548.0839.09-0.00.00034.13-13.408.460.0000.000-18.12-0.000.00Undrained shear strength profile of soft clayEmbankmentdepth01.535710(m)cmfmgmcu402820202637(kPa)103020(kPa)(o)(kN/m3)gclay16(kN/m3)
Units: m, kN/m3, kN/m2, kN, or other consistent set of units.Array formulasslope angleSoft clayEmbankmentlx0xnCenter of Rotationxnx0cu (kPa)Depth40282020263701.535710SPENCER methodVarying side-force angle lFormulas: hc = 2*cm/(lmKa), Pw = 0.5*gw*hc^2, Mw = Pw*(yc-H+0.6667*hc)xmin = -(abs(R^2-yc^2))+xc, xmax = (abs(R^2-(yc-H+hc)^2))+xcx(0) = xmax, x(2) = xc+(abs(R^2-yc^2)), x(1) = (B16+B18)/2 x(3) = B18-($B$18-xmin)/22, drag downwards to autofill. ybot(0 )= -(abs(R^2-(B16-xc)^2))+yc, autofill. (Columns ytop, gave and c invoke the user-defined functions shown in Fig. 2.)f(1) = IF(0.5*(C16+C17)>0, $Q$45,0), autofill (also for the formulas below.)W(1) = (B16-B17)*0.5*((D16-C16)+(D17-C17))*E17, arad(1) =ATAN((C16-C17)/(B16-B17))u(1) =ru*E17*0.5*(D16-C16+D17-C17), l(1) =(B16-B17)/COS(I17)Formulas for P and T as shown in text.E(0) = Pw, E(1) = N16+L17*SIN(I17)-M17*COS(I17)l(0)=0, l(1)=IF($R$5,$N$2*SIN(($B$16-B17)/($B$16-$B$40)*PI()),$N$2)s = (P/l - u), Lx(1) = 0.5*(B16+B17)-xc, Ly(1) =yc-0.5*(C16+C17), DumEq = F*1SM =SUM((M17:M40*SIN(I17:I40)+L17:L40*COS(I17:I40)-H17:H40)*Q17:Q40+ (M17:M40*COS(I17:I40)-L17:L40*SIN(I17:I40))*R17:R40)-F11, (Ctrl & Shift, then Enter) SForces =SUM(M17:M40*COS(I17:I40)-L17:L40*SIN(I17:I40))-E11, (Ctrl & Shift, then Enter)EiliEili-1Ei-1Ei-1TiPiWiailybotytopWRead the Low (2003) paper "Practical Probabilistic Slope Stability Analysis", downloadable from http://alum.mit.edu/www/bklow.For hands-on:(1) Initialize l (Cell N2) to zero and F (Cell O2) to 1.0.(2) Initialize (xc, yc, R) to arbitrary initial circle (6, 8, 12).(3) Invoke Solver (Menu bar: Tools/Solver);click Solve. Then click OK to accept the solution found.- This file contains VBA codes, as shown in Tools\Macro\Visual Basic Editor\ Modules\Module 1, and explained in the paper.- Need to set Tools\Macro\Security to medium, then close and re-open file with macros enabled. VBA codes will function only when Macro Security is set to medium.- If never use Excel's built-in Solver before, will need to activate it once via Tools\Add-Ins\Solver Add-in.&C&"Times New Roman,Regular"&8from Spencer_forSARA2003framed cells contain equationsUnits: m, kN/m3, kN/m2, kN, or other consistent set of units.Array formulasslope angleCenter of RotationEiliEili-1Ei-1Ei-1TiPiWiail
SpencerCircular000000000000000000000000000000000000000000000000000000000000000000000000000000000
&APage &P
SpencerNoncircularlFDumEqKahc0.0981.0001.0000.321.7815148835meanStDevvnCorrelation matrix, "crmat"SForcesSMVarying lDistNamevimismNsN(v-mN)/sNcmfmgmcu1cu2cu3cu4cu5cu60.0000.000lognormalcm10.4721071455101.509.8731.5620.3841-0.30.5000000lognormalfm30.9485048337303.0029.8313.0870.362-0.310.5000000lognormalgm20.7576088869201.0019.9601.0370.7690.50.51000000lognormalcu134.0729809574406.0039.1585.083-1.00100010.60653065970.36787944120.18887560280.09697196790.03567399330lognormalcu222.7355057338284.2027.2183.391-1.3220000.606530659710.60653065970.31140322390.15987974610.05881647161.5WHhcgwPwMwruxcyclognormalcu315.9068070156203.0019.3722.373-1.4610000.36787944120.606530659710.5134171190.26359713810.096971967932751.781015.868976399966.45508332120.28.008.00lognormalcu415.8520032655203.0019.3602.365-1.4840000.18887560280.31140322390.51341711910.5134171190.18887560285lognormalcu522.4631074225263.9025.4983.351-0.9060000.09697196790.15987974610.26359713810.51341711910.36787944127lognormalcu634.8174096798375.5536.5475.194-0.3330000.03567399330.05881647160.09697196790.18887560280.3678794412110Lever arms01.535710dv#xybytgavecfWaradulPTEls 'LxLybPrFail017.223.225.0015.870.000EquilCheckArray formula: Ctrl+Shift, then Enter1.9620.0249116.191.665.0020.7610.4730.948504833754.60.99010.641.8745.4334.8934.70.01513.658.715.560.0000.000215.170.005.0020.7610.4730.948504833788.91.01617.321.9583.9050.4879.40.02925.767.687.170.0000.000314.28-0.865.0020.3830.81098.80.76922.141.2496.8938.26119.30.04155.876.728.430.0000.000413.38-1.695.0019.7924.440110.80.74424.841.21117.4629.64177.00.05272.015.839.270.0000.000512.49-2.435.0019.3720.190122.00.69727.341.16131.6823.50243.50.06285.824.9410.060.0000.000DeterministicCriticalNormals, reliability-based critical611.60-3.115.0019.0616.950132.20.64829.621.12142.2818.98314.30.07197.454.0410.770.0000.000xybytxybyt710.71-3.725.0018.8315.900141.40.60031.681.08149.6817.19384.60.079106.743.1511.410.0000.00018.073.275.0017.25433.21445.000089.81-4.305.0018.6415.880149.90.57833.591.07157.4516.92456.50.086114.142.2612.010.0000.00016.881.685.0016.23951.64805.0000LogNormals, reliability-based critical98.92-4.794.5518.4415.860153.40.50534.371.02157.0516.18518.30.091119.651.3712.550.0000.00015.700.005.0015.22460.00005.000017.22046405883.21849098235108.03-5.144.0918.2115.850150.90.37033.820.96149.8115.18558.40.095122.660.4712.970.0000.00014.72-0.955.0014.3227-0.87585.000016.1940518791.65516702865117.14-5.373.6418.0216.700146.60.25632.860.92144.1115.41580.00.097123.34-0.4213.260.0000.00013.74-1.845.0013.4208-1.70925.000015.167639699305126.24-5.533.1817.8317.350141.00.17431.600.91139.2115.72588.70.098122.04-1.3113.450.0000.00012.76-2.635.0012.5188-2.46035.000014.2752101133-0.86367877515135.35-5.622.7317.6517.750134.30.09730.100.90134.3215.92585.80.097119.70-2.2013.570.0000.00011.78-3.375.0011.6169-3.14085.000013.3827805274-1.68508980515144.46-5.632.2717.4617.920126.60.01628.380.89129.2715.99571.80.094116.45-3.1013.630.0000.00010.79-4.015.0010.7150-3.75265.000012.4903509414-2.43183810645153.57-5.571.8217.2717.840117.9-0.06926.410.89123.8815.96547.40.090112.07-3.9913.600.0000.0009.81-4.635.009.8131-4.33595.000011.5979213555-3.10804718435162.67-5.431.3617.0717.500108.0-0.16224.190.90118.1115.82512.80.084106.43-4.8813.500.0000.0008.83-5.154.508.9111-4.82704.540410.7054917696-3.71860954565171.78-5.180.9116.8416.85096.7-0.26821.680.93111.9715.60468.10.07799.32-5.7713.300.0000.0007.85-5.524.008.0092-5.16994.08099.8130621836-4.30123170795180.89-4.780.4516.5715.85083.7-0.42418.760.98107.5815.52409.70.06991.11-6.6612.980.0000.0006.87-5.783.507.1073-5.39903.62138.9206325977-4.79450450284.545284861519-0.00-4.170.0016.2315.87068.1-0.60015.251.08104.1617.15336.70.05981.09-7.5612.470.0000.0005.89-5.943.006.2054-5.55243.16188.0282030117-5.14094993344.09056972320-0.90-3.410.0016.0015.89054.1-0.70312.131.1796.2218.59260.30.04870.11-8.4511.790.0000.0004.91-6.022.505.3034-5.63432.70227.1357734258-5.37490997533.635854584621-1.79-2.590.0016.0015.91042.8-0.7449.601.2183.5819.29189.50.03759.31-9.3411.000.0000.0003.93-6.002.004.4015-5.64522.24276.2433438398-5.53169082953.181139446122-2.68-1.790.0016.0019.60031.3-0.7327.001.2068.2923.51126.40.02549.94-10.2310.190.0000.0002.94-5.881.503.4996-5.58031.78315.3509142539-5.61819903542.726424307623-3.57-0.910.0016.0023.87019.3-0.7774.321.2559.7029.8763.30.01343.39-11.139.350.0000.0001.96-5.651.002.5976-5.43121.32364.4584846679-5.63228189882.271709169124-4.47-0.000.0016.0030.6306.5-0.7961.461.2850.3039.06-0.00.00037.99-12.028.460.0000.0000.98-5.280.501.6957-5.18210.86403.566055082-5.5708169931.8169940306-0.00-4.730.000.7938-4.77210.40452.6736254961-5.42532923931.3622788922-0.98-4.080.00-0.1081-4.15790.00001.7811959101-5.1805674790.9075637537Undrained shear strength profile of soft clayEmbankment-1.96-3.390.00-1.0101-3.40790.00000.8887663242-4.77773458110.4528486152depth01.535710(m)cmfmgm-2.94-2.610.00-1.9120-2.59210.0000-0.0036632618-4.16749505250cu34.072980957422.735505733815.906807015615.852003265522.463107422534.8174096798(kPa)10.472107145530.948504833720.7576088869-3.93-1.810.00-2.8139-1.79300.0000-0.8960928477-3.41077946280(kPa)(o)(kN/m3)-4.91-0.930.00-3.7158-0.91360.0000-1.7885224337-2.58930911510gclay-5.89-0.000.00-4.6178-0.00000.0000-2.6809520196-1.7880316888016-3.5733816056-0.91089117720(kN/m3)-4.4658111915-00
Soft clayEmbankmentxnx0ybytytinitialcriticalcu (kPa)depth000000000000SPENCER: Search for noncircular slip surfaceInitialCirclelx0xnVarying side-force angle lRead the Low (2003) paper "Practical Probabilistic Slope Stability Analysis", downloadable from http://alum.mit.edu/www/bklow.For hands-on:(1) Click the button "InitialCircle"(2) Invoke Solver (Menu bar: Tools/Solver); click Solve. Then click OK to accept the solution found. May run Solver one more time.&C&"Times New Roman,Regular"&8from Spencer_forSARA2003framed cells contain equationsUnits: m, kN/m3, kN/m2, kN, or other consistent set of units.Array formulasslope angleCenter of RotationEiliEili-1Ei-1Ei-1TiPiWiail
SpencerNoncircular000000000000000000000000000000000000000000000000000000000000000000000000000000000
&APage &P
Soft clayEmbankmentxnx0ybytytinitialcriticalcu (kPa)depth000000000000SPENCER: Search for noncircular slip surfacelx0xnVarying side-force angle l00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000=SQRT(MMULT(TRANSPOSE(vn),MMULT(MINVERSE(crmat),vn)))Equation 9 autofilledProbability of failureEqvN(, 1)EqvN(, 2)deterministic critical=normsdist(-b)Read the Low (2003) paper "Practical Probabilistic Slope Stability Analysis", downloadable from http://alum.mit.edu/www/bklow.
For hands-on: Read the section in paper related to Figure 6.
MBD001F3B7C.unknown
MBD0002AFFA.unknown
MBD001A40AB.unknown
Related Documents
