I need a Civil Eng. soil mechanics

98 Civil & Environmental Engineering Department EGCE 324L (Soil Mechanics Laboratory) Binod Tiwari, PhD Stability Analysis of Slopes Background Evaluating the stability of slopes in soil is an important, interesting, and challenging aspect of civil engineering. Concerns with slope stability have driven some of the most important advances in our understanding of the complex behavior. Extensive engineering and research studies performed over the past 70 years provide sound set of soil mechanics principles with which to attack practical problems of slope stability. There are a number of methods ranging from very simple to highly complicated numerical calculation approach, available for the stability analysis of slopes and a number of computer software are available for the solution. However, very simple methods that can be accomplished through a simple spreadsheet programming are still popular. In this class, we will conduct stability analysis for a V O R S H I R U V W H D G \ V H H S D J H F R Q G L W L R Q X V L Q J 2 U G L Q D U \ 0 H W K R G R I 6 O L F H D Q G % L V K R S V simplified method and compare the results. Simple theory involved in the analysis Ordinary Method of slice For the slope shown in the figure 1, ¦ ¦ ' p n nn n p n nn n n s WCos W L c F 1 1 sin) ' tan '. ( D I D (1) 6 L P S O L I L H G % L V K R S · V 0 H W K R G Based on the analysis made on the slope element shown in figure 2, ¦ ¦ ' p n nn n p n n n n n s Wm W L c F 1 1 ) ( sin1 ) ' tan '. ( D I D , where (2) sn n nF m D I D D sin '. tan cos ) ( b n = width of the slice (We need to perform iteration for this analysis) 99 Civil & Environmental Engineering Department EGCE 324L (Soil Mechanics Laboratory) Binod Tiwari, PhD Figure 1 Stability analysis by ordinary method of slices ) L J X U H 6 W D E L O L W \ D Q D O \ V L V E \ % L V K R S V V L P S O L I L H G P H W K R G 100 Civil & Environmental Engineering Department EGCE 324L (Soil Mechanics Laboratory) Binod Tiwari, PhD Stability Analysis for Steady-state Seepage For steady-state seepage, we need to modify equations 1 and 2 to cover the influence of water.

Equation (1) is modified as, ¦ ¦ ' ' p n nn n p n nn n n n n s WL u Cos W L c F 1 1 sin) ' tan ) ( '. ( D I D (3) Equation (2) is modified as ¦ ¦ ' ' p n nn n p n n n n n n n s Wm L u W L c F 1 1 ) ( sin1 ) ' tan ) ( '. ( D I D (4) Information needed Cross-section of slope Engineering scale Scientific calculator or computer Procedure 1. Divide the entire slope into a number of equally spaced (or based on slopes) slices.

2. Measure the required parameters and populate the excel spreadsheet (shown in the table below).

3. Calculate factor of safety using the above equations. Compare with two methods. Figure 3 101 Civil & Environmental Engineering Department EGCE 324L (Soil Mechanics Laboratory) Binod Tiwari, PhD Jc I J Z slice X ys yw yg b hs hw hsave hwave W DuWcos DWsin D LUWcos D U 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 FS 102 Civil & Environmental Engineering Department EGCE 324L (Soil Mechanics Laboratory) Binod Tiwari, PhD Jc I J Z slice X ys yw yg b hs hw hsave hwave W DuWsin D LUW Um D Num 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 FS FS 103 Civil & Environmental Engineering Department EGCE 324L (Soil Mechanics Laboratory) Binod Tiwari, PhD Slope A Task: 1. Please calculate the factor of safety of slope A. Consider unit weight of soil as 18 kN/m 3, cohesion as 2 kPa, and friction angle as 10 0. 2. Please also calculate the friction angle to give FS of 1 (Ignore cohesion).

3. Please design countermeasures to increase the factor of safety to 1.5. Examples of countermeasures are: head excavation, toe loading, lowering ground water table, piling, and drilled shaft. Civil & Environmental Engineering Department EGCE 324L (Soil Mechanics Laboratory) Spring 2009 Instructor: Binod Tiwari, PhD 104 Example Problem & D O F X O D W H W K H I D F W R U R I V D I H W \ R I W K L V V O R S H Z L W K E R W K % L V K R S V Simplified Method and Method of Slice. Civil & Environmental Engineering Department EGCE 324L (Soil Mechanics Laboratory) Spring 2009 Instructor: Binod Tiwari, PhD 105 Civil & Environmental Engineering Department EGCE 324L (Soil Mechanics Laboratory) Spring 2009 Spring 2007 Instructor: Binod Tiwari, PhD 106 Method of Slice J18c0 I43 J Z10 slice X ys yw yg b hs hw hsave hwave W DuWcos DWsin D LUWcos D U 1 0 3.67 3.67 3.67 0.00 0.00 2 1.47 2.75 3.67 3.67 1.47 0.92 0.92 0.46 0.46 12.17 -32.04 4.60 10.32 -6.46 1.73 7.98 2.34 3 2.94 2.06 3.67 3.67 1.47 1.61 1.61 1.27 1.27 33.47 -25.14 12.65 30.30 -14.22 1.62 20.54 9.76 4 4.41 1.61 3.67 3.67 1.47 2.06 2.06 1.84 1.84 48.55 -17.02 18.35 46.43 -14.21 1.54 28.21 18.22 5 5.88 1.32 4.40 4.40 1.47 3.08 3.08 2.57 2.57 68.00 -11.16 25.70 66.72 -13.16 1.50 38.51 28.21 6 7.35 1.25 5.28 5.28 1.47 4.03 4.03 3.56 3.56 94.07 -2.73 35.55 93.96 -4.47 1.47 52.32 41.64 7 8.82 1.28 6.09 6.24 1.47 4.96 4.81 4.50 4.42 118.94 1.17 44.20 118.91 2.43 1.47 64.99 53.93 8 10.29 1.47 6.97 7.16 1.47 5.69 5.50 5.33 5.16 140.90 7.36 51.55 139.74 18.06 1.48 76.41 63.33 9 11.76 1.76 7.63 8.07 1.47 6.31 5.87 6.00 5.69 158.76 11.16 56.85 155.76 30.73 1.50 85.18 70.58 10 13.23 2.28 8.15 8.95 1.47 6.67 5.87 6.49 5.87 171.73 19.48 58.70 161.89 57.27 1.56 91.53 70.37 11 14.7 2.94 8.66 9.91 1.47 6.97 5.72 6.82 5.80 180.46 24.18 57.95 164.63 73.91 1.61 93.38 71.25 12 16.17 3.89 9.03 10.79 1.47 6.90 5.14 6.94 5.43 183.50 32.87 54.30 154.12 99.60 1.75 95.04 59.08 13 17.64 5.14 9.47 11.67 1.47 6.53 4.33 6.72 4.74 177.68 40.38 47.35 135.36 115.10 1.93 91.37 43.99 14 19.11 6.79 9.69 11.52 1.47 4.73 2.90 5.63 3.62 148.97 48.30 36.15 99.10 111.23 2.21 79.89 19.21 15 20.58 9.17 9.76 11.52 1.47 2.35 0.59 3.54 1.75 93.67 58.30 17.45 49.22 79.69 2.80 48.81 0.41 16 21.31 11.52 11.52 11.52 0.73 0.00 0.00 1.18 0.30 15.44 72.74 2.95 4.58 14.74 2.46 7.26 -2.68 550.24 26.63 549.62 1234567891011121314151617 FS 0.93 Civil & Environmental Engineering Department EGCE 324L (Soil Mechanics Laboratory) Spring 2009 Instructor: Binod Tiwari, PhD 107 % L V K R S V 6 L P S O L I L H G 0 H W K R G J18c0 I43 J Z10 slice X ys yw yg b hs hw hsave hwave W DuWcos DWsin D LUW Um D Num 1 0 3.67 3.67 3.67 0.00 0.00 2 1.47 2.75 3.67 3.67 1.47 0.92 0.92 0.46 0.46 12.17 -32.04 4.60 10.32 -6.46 1.73 7.98 4.19 0.42 9.21 3 2.94 2.06 3.67 3.67 1.47 1.61 1.61 1.27 1.27 33.47 -25.14 12.65 30.30 -14.22 1.62 20.54 12.93 0.57 21.28 4 4.41 1.61 3.67 3.67 1.47 2.06 2.06 1.84 1.84 48.55 -17.02 18.35 46.43 -14.21 1.54 28.21 20.34 0.72 26.24 5 5.88 1.32 4.40 4.40 1.47 3.08 3.08 2.57 2.57 68.00 -11.16 25.70 66.72 -13.16 1.50 38.51 29.50 0.83 33.27 6 7.35 1.25 5.28 5.28 1.47 4.03 4.03 3.56 3.56 94.07 -2.73 35.55 93.96 -4.47 1.47 52.32 41.75 0.96 40.51 7 8.82 1.28 6.09 6.24 1.47 4.96 4.81 4.50 4.42 118.94 1.17 44.20 118.91 2.43 1.47 64.99 53.95 1.02 49.51 8 10.29 1.47 6.97 7.16 1.47 5.69 5.50 5.33 5.16 140.90 7.36 51.55 139.74 18.06 1.48 76.41 64.49 1.09 54.98 9 11.76 1.76 7.63 8.07 1.47 6.31 5.87 6.00 5.69 158.76 11.16 56.85 155.76 30.73 1.50 85.18 73.58 1.14 60.43 10 13.23 2.28 8.15 8.95 1.47 6.67 5.87 6.49 5.87 171.73 19.48 58.70 161.89 57.27 1.56 91.53 80.20 1.21 61.88 11 14.7 2.94 8.66 9.91 1.47 6.97 5.72 6.82 5.80 180.46 24.18 57.95 164.63 73.91 1.61 93.38 87.08 1.24 65.55 12 16.17 3.89 9.03 10.79 1.47 6.90 5.14 6.94 5.43 183.50 32.87 54.30 154.12 99.60 1.75 95.04 88.46 1.27 64.83 13 17.64 5.14 9.47 11.67 1.47 6.53 4.33 6.72 4.74 177.68 40.38 47.35 135.36 115.10 1.93 91.37 86.31 1.28 62.97 14 19.11 6.79 9.69 11.52 1.47 4.73 2.90 5.63 3.62 148.97 48.30 36.15 99.10 111.23 2.21 79.89 69.08 1.26 51.12 15 20.58 9.17 9.76 11.52 1.47 2.35 0.59 3.54 1.75 93.67 58.30 17.45 49.22 79.69 2.80 48.81 44.85 1.20 34.75 16 21.31 11.52 11.52 11.52 0.73 0.00 0.00 1.18 0.30 15.44 72.74 2.95 4.58 14.74 2.46 7.26 8.18 1.06 7.21 550.24 643.74 12345678910111213141516171819 FS, trial 1.17 FS 1.17 5.88