EXAMPLE 1 DESIGN OF CANTILEVERED WALL, GRANULAR SOIL

Transcription

1 EXAMPLE DESIGN OF CANTILEVERED WALL, GRANULAR SOIL A sheet pile wall is required to support a 2 excavation. The soil is uniform as shown in the figure. To take into account the friction between the wall and the soil, we use friction angle δ = φ/2. Please note this value is applied only for passive pressure. Use factor of safety =.5 for passive pressure. Question: What is the embedment and maximum bending moment in the pile? Active pressure above cut: φ = 35, Ka = 2, P = Kaγ(2 ) = (0.27)(25)(2) = Ksf Active pressure below cut: Below the cut, use pressure slope input. The pressure slope Pa = Kaγ = (0.027)(25) = Kcf Passive pressure below cut: Soil friction φ = 35, wall friction δ = φ/2, Kp = 6.74 (NAVFAC or Epres program) The pressure slope Pp = Kpγ/F.S. = (6.74)(25)/.50 = 0.56 Kcf A short result for input and output is presented. NOTE: spacing for the sheet pile The program shows that the minimum embedment is 9.3 and the pile length is 2.3. The maximum moment in the pile is 7 Kip-ft /ft. The maximum moment is at 5.9 from the ground surface. EXAMPLE X γ = 25 pcf φ = 35 o δ = φ/2 (only for passive) H = 2 Dredge Line P = ksf kcf Y 0.56 kcf CivilTech Software SHORING EXAMPLES

2 EXAMPLE 2 Alternative Input for Example The conditions are the same as example. In example 2, we use an alternative input to check the versatility of the program. Instead of inputting both active and passive pressures below the cut, we input the net passive pressure below the cut. The net passive pressure is equal to Pp- Pa. Question: What is the embedment and maximum bending moment in pile? Active pressure above cut: Same as Example. Net pressure below cut: Active pressure slope is Pa = Kaγ = (0.27)(25) = Kcf Passive pressure slope is Pp = Kpγ/F.S. = (6.74)(25) /.5 = 0.56 Kcf Net passive pressure slope is Pn = Pp - Pa = = Kcf The point of zero pressure is e = P/ Pn = 0.405/0.526 = 0.77 Input two active pressures in driving pressure input: One is from x = 0 to x = 2. Another is from x = 2 to x = There is no active pressure input below dredge line. The passive pressure starts Y = 0.77, with a net slope = Kcf The same as example. Alternative: Another alternative input is also presented in attached file, example 2A. In this input, the net passive pressure slope, Kcf is directly inputted from Y = 0 with starting pressure of Ksf. In this way, the calculation of zero pressure point, e, can be omitted. CivilTech Software SHORING EXAMPLES 2

3 EXAMPLE 2 X γ = 25 pcf φ = 35 o δ = φ/2 (only for passive) H = 2 e Y = 0.77 P = ksf Y kcf EXAMPLE 3 SURCHARGE, Ps = H = 2 P = P4 =.2 P2 = P5 =.752 P3 = SOIL γ = 25 pcf φ = 30 o δ = φ/2 SOIL 2 γ2 = 30 pcf φ2 = 35 o δ = φ/2 CivilTech Software SHORING EXAMPLES 3

4 EXAMPLE 3 DESIGN OF SHEET PILE WALL WITH TWO SOIL AND SURCHARGE LOAD A sheet pile wall is required to support 2 excavation. F.S. =.5 is required for passive pressure. Soil conditions are shown in the figure. The surcharge load will be in a separate diagram. Question: What is the embedment and maximum bending moment in pile? Active pressure above cut: <soil > φ=30, Ka =0.33, P = Kaγ(2 ) = (0.33)(25)(2) = Ksf Active pressure below cut: <soil > pressure slope, Pa = Kaγ = (0.33)(25) = 0.04 Kcf P2 = Kaγ(5 ) = (0.33)(25)(5) = 0.68 Ksf <soil 2> φ2= 35, Ka = 0.27, pressure slope Pa = Kaγ = (0.27)(30) = Kcf P3 = Kaγ (5 ) = (0.27)(30)(5) = Ksf Passive pressure below cut: <soil > φ = 30, δ= φ/2, Kp = 4.8 (NAVFAC or Epres program) pressure slope, Pp = Kpγ/F.S. = (4.8)(25) /.5 = 0.4 Kcf P4 = Pp(3 ) = 0.4(3) =.2 Ksf <soil 2> φ2 = 35, δ= φ2/2, Kp = 6.74 (NAVFAC or Epres program) pressure slope, Pp = Kpγ/F.S.= (6.74)(30) /.5 = (6.74)(30) /.5 = Kcf P5 = Pp(3 ) = 0.584(3 ) =.752 Ksf Use spacing for the sheet pile and 0.24 Ksf for surcharge load. The program shows that the minimum embedment is 3.3 and the pile length is 25. The maximum moment in the pile is 53.3 K-ft/ft at 7.7 from the ground surface. CivilTech Software SHORING EXAMPLES 4

5 EXAMPLE 4 DESIGN OF SHEET PILE WALL WITH COHESIVE SOIL AND SURCHARGE LOAD Introduction : In this example, the surcharge load is merged with the active pressure. It also can be separated as example 3. Soil 2 below cut line is a cohesive material with cohesion = 500 pcf (F.S. included). Question: What is the embedment and maximum bending moment in the pile? Active pressure above cut: <soil > φ=30, Ka = 0, P = Ka q = (0.33)(300) = 0. Ksf. P2 = Ka (q + γh) = 0.33 ( x 2) = Ksf Passive pressure below cut: <soil 2> φ2 = 0, Ka = 2, P3 = 4c - σv = 4(500) - (q + γh) = [ (2)] = 0.23 Ksf For passive pressure input, use Top Pres.= 0.23 and Pres. Slope = 0 The program shows that the minimum embedment is 4.58 and the pile length is The maximum moment in the pile is 43.2 Kip-ft/ft at 27.3 from the ground surface. EXAMPLE 4 q = 300psf P = 0. H = 2 P3 = 0.23 P2 = SOIL (LOOSE SAND) γ = 22.5 pcf φ = 30 o δ = 0 Cu = 0 SOIL 2 (MED. CLAY) γ2 = 0 pcf φ2 = 0 Cu = 500 psf CivilTech Software SHORING EXAMPLES 5

6 EXAMPLE 5 DESIGN OF SHEET PILE WALL WITH DIFFERENTIAL WATER LEVELS The water level is higher outside of the excavation base. Seepage is allowed to flow through the bottom of the pile. The water pressures of both sides are equal, therefore, the net pressure is zero at the bottom of the pile. Question: What is the embedment and maximum bending moment in the pile? Active pressure above cut: φ = 35, Ka = 5, P = Kaγ(5 ) = (0.27)(25)(5 ) = 0.7 2, P2 = (0.27)( )(2-5 ) + P = Ksf Active pressure below cut: Pa = Kaγ = (0.27)( ) = 0.07 Ksf Passive pressure below cut: φ= 35, Kp = δ = φ /2, P =0 Pp = Kpγ /F.S. = (6.74)(62.6) /.5 = 0.28 Ksf Due to seepage, the net water pressure = 0 at the embedment bottom. Because the embedment depth is unknown, the value can be set 999 to let the program find embedment. (See Chapter 5). The program shows that the minimum embedment is 6.8 and the pile length is The maximum moment in the pile is 38.9 Kip-ft/ft at 20 from the ground surface. EXAMPLE 5 5 H = 2 5 bottom F. S. =.5 P = 0.7 γ = 25 pcf φ = 35 o δ = φ/2 (Only for passive) 2 H = 2 P2 = Pw = The depth is unknown, input 999 in program CivilTech Software SHORING EXAMPLES 6

7 EXAMPLE 6 DESIGN OF ANCHORED SHEET PILE WALL WITH THE SAME WATER LEVEL This example has a 36 deep excavation to which tieback anchors are applied. The water levels are the same inside and outside of the excavation. Two layers of soil are presented in the example. Question: What is the embedment, anchor force, and maximum bending moment in the pile? Active pressure above cut: <soil > φ = 34, Ka = 0, P = Kaγ (0 ) = , P2 = P + Kaγ (36-0) = P + (0.28)(60)(26) = Ksf Active pressure below cut: <soil 2> φ2 = 34.5, Ka = 36, P3 = Ka[γ(0) + γ (26)] =.26 [0(0) + 60(26)] = Ksf Passive pressure below cut: φ2= 34.5, Kp = 6.63, Pp = Kpγ Pn = Pp - Pa = ( )(65) = 0.44 Ksf Try input anchor level at 9 from the ground surface. The program shows that the minimum embedment is 7.5 and the pile length is The maximum moment in the pile is 68.7 Kip-ft/ft at 26 from the ground surface. The brace force = 8.8 K/ft. EXAMPLE T P=0.308 H = 36 P2=0.745 SAND BACK FILL γ = 0 γ = 60 pcf φ = 34 o δ = 0 Ka = 0.28 P3= MEDIUM SAND γ = 65 pcf Kp = 6.63 φ = 34.5 o δ/φ = 0.4 Ka = 0.26 Kp - Ka = 6.37 CivilTech Software SHORING EXAMPLES 7

8 EXAMPLE 7 DESIGN OF ANCHORED SOLDIER PILE WALL WITH LAGGING A soldier pile wall is used in this example with one tieback anchor applied for each pile. Question: What is the embedment, anchor force, and maximum bending moment in the pile? Active pressure above cut: φ = 30, Ka = 2, P = Kaγ(2 ) = Ksf Passive pressure below cut: C = 700 psf, φ = 0, Ka = 2, P2 = 4c - σv = 4(700) - (22.5)(2 ) =.33 Ksf Try an anchor level = 5 from the pile top. The program shows that the minimum embedment is.3 and the pile length is 3.3. The maximum moment in the pile is 3.2 Kip-ft/ft at 9.3 from the ground surface. Horizontal tieback force is 0.6 Kips per pile. EXAMPLE 7 T 5 Lagging spacing = 6 H = 2 P2 =.33 P = LOOSE SAND γ = 22.5 pcf φ = 30 o δ=0 Cu = 0 Ka = 0.33 MED. CLAY γ2 = 0 pcf φ2 = 0 Cu = 700 psf Pile Dia. = 2 CivilTech Software SHORING EXAMPLES 8

9 EXAMPLE 8 DESIGN OF SHEET PILE WALL WITH TIEBACK ANCHOR This example has a limited surcharge load. The surcharge pressure from the Lpres program is 0.42 Ksf as shown in the figure. The water pressure is similar to the condition in example 5. Question: What is the embedment, anchor force, and maximum bending moment in the pile? Surcharge: Ps = 0.42 Ksf Water pressure: Pw = γw (6-8 ) = (62.4)(8) = Ksf Active pressure: P = Kaγ(8 ) = (0.27)(25)(8) = 0.27 Ksf P2 = P +Kaγ= P + (0.27)( )(7) = Ksf Pa = Kpγ = (0.27)( ) = 0.07 Kcf Passive pressure: starting 2 below dredge line P3 = Kp[γ() + γ w ()] = 8.95 [ ] =.26 Ksf Pp = Kpγ = (8.95)( ) = 0.56 Kcf Use 999 for the unknown depth. (See Example 5) The program shows that the minimum embedment is 5 and the pile length is 20. The maximum moment in the pile is 7.3 Kip-ft/ft at 2.5 from the ground surface. T = 8.2 Kips. EXAMPLE 8 q Ps = T P = H = 5 P2 = P3 = γ = 62.6 pcf γ = 25 pcf φ = 35 o δ = φ/2 6 Pw = The depth is unknown, input 999 in program CivilTech Software SHORING EXAMPLES 9

10 EXAMPLE 9 DESIGN OF COFFERDAM WITH TWO BRACES Introduction : A cofferdam is designed for a bridge pier excavation. Two braces are used herein. Question: What is the embedment, brace force, and maximum bending moment in the pile? Surcharge: Ps = 0.42 Ksf Water pressure: Pw = γw (6-8 ) = (62.4)(8) = Ksf Active pressure: P = Kaγ(8 ) = (0.27)(25)(8) = 0.27 Ksf P2 = P +Kaγ = P + (0.27)( )(7) = Ksf Pa= Kpγ = (0.27)( ) = 0.07 Kcf Passive pressure: starting 2 below dredge line P3 = Kp[γ() + γ w ()] =8.95 [ ] =.26 Ksf Pp = Kpγ = (8.95)( ) = 0.56 Kcf The condition is the same as in example 8. The maximum movement is significantly reduced due to two levels of bracing. The program shows that the minimum embedment is 4.2 and the pile length is 9.2. The maximum moment in the pile is 7.8 Kip-ft/ft at 4. from the ground surface. T = 5.3 Kips/ ft and T2=2.9 Kips/ ft. EXAMPLE 9 q Ps = T T2 P = γ = 62.6 pcf γ = 25 pcf φ = 35 o δ = φ/2 H = P3 =.26 P2 = Pw = 0 6 Pw = The depth is unknown, input 999 in program CivilTech Software SHORING EXAMPLES 0

11 EXAMPLE 0 DESIGN OF COFFERDAM WITH THREE BRACES A cofferdam is designed to support an excavation for a bridge pier. Due to a railroad 6 from the wall, surcharge pressure of 0.42 Ksf is applied. No seepage is allowed below the pile bottom. The water pressures at both sides are not equal. The outside pressure is higher than inside. After subtraction of the inside pressure, the net hydraulic pressure is constant below 36. Question: What is the embedment, brace force, and maximum bending moment in the pile? Active pressure above cut: φ = 35, Ka = 8, P = Kaγ(8 ) = (0.27)(25)(8) = , P2 = Kaγ (35-8) + P = (0.27)(62.6)(27) = Ksf Water 36, Pw = (36-8)(62.4) =.747 Ksf Surcharge load: (from Lpres program) from 0 to 0, Ps = 0.42 Ksf at 36, Ps = 0 Active pressure below cut: active pressure slope: Pa = Kaγ = (0.27)(62.6) = 0.07 Kcf Net water pressure: Pw =.747 Ksf constant Passive pressure below cut: φ = 35, δ = φ/2, Kp = 37, P3 = Kpγ (2 ) = 8.95(62.6)(2) = Ksf passive pressure slope: Pp = Kpγ = 8.95(62.6) = 0.56 Kcf The soil below the excavation base is disturbed. Therefore the passive pressure of the top 2 soil below the dredge line is ignored. The input pressure diagram is shown as follows. The program shows that the minimum embedment is 8.5 and the pile length is The maximum moment in the pile is 32.4 Kip-ft/ft at 25.2 from the ground surface. T = 3.6 Kips/ ft, T2 = 2.6 Kips/ ft, and T3 = 6. Kips/ ft. CivilTech Software SHORING EXAMPLES

12 EXAMPLE 0 Surcharge q H = T T2 T3 37 P3 =.26 P = 0.27 P2 = Ps = γ = 62.6 pcf γ = 25 pcf φ = 35 o δ = φ/2 36 Pw =.747 Cancel out CivilTech Software SHORING EXAMPLES 2

13 EXAMPLE DESIGN OF TIEBACK WALL The tieback wall has an 8 spacing of soldier pile supported by timber lagging (3 x 2 ). The active pressure diagram is a trapezoid. The surcharge load of 2 of soil is added to the active diagram. The soldier pile has a 2 diameter shaft. Below the dredge line, the active pressure is acting on one diameter. The passive pressure is acting on two diameters of pile due to the arching effect. Question: What is the embedment, tieback force, and maximum bending moment in the pile? The soil report of this project requires 20(H + 2 ) for active pressure and ignoring the top 2 of passive pressure. The passive resistance is 400 pcf including F.S. Above base 8 spacing Active pressure P2 = P3 = 20(H + 2) = 20(30 + 2) = 0.64 Ksf Below base Active pressure P4 = 30(Z + 2) = 30(30 + 2) = 0.96 Ksf Active pressure slope Pa = 0.03 Kcf Acting diameter of pile. Diameter of pile = 2. Passive pressure slope Pp = 0.4 Kcf Acting 2 diameter of pile. Diameter of pile = 2. Use 3 pressure programs to input the active pressure The program shows that the minimum embedment is 6.7 and the pile length is The maximum moment in the pile is 49.7 Kip-ft at 27. from the ground surface. T = 44.7Kips, T2 = 45.Kips, T3 = 42.9Kips. EXAMPLE Surcharge = 2 (Height of Soil) 5.5 P = 0.04 P2 = H = 6 Lagging Spacing = 8 4 T H = T2 P3 = 0.64 T3 0.2 H = 6 32 P4 = Y 0.03 ( X + 2 ) Acting 2 Dia. of Pile = 4 Acting Dia. Of Pile = 2 CivilTech Software SHORING EXAMPLES 3

14 EXAMPLE 2 DESIGN OF ANCHORED AND RACKING BRACED WALL The original design using one level of tieback is not adequate to support the wall. An additional raking brace is added to help the stability of the wall. Question: What is the embedment, brace force, and maximum bending moment in the pile? Active pressure above exc. 20(H) = 20(30 ) = 0.6 Ksf Acting 8 Active below exc. 30(Y) = 30(30 ) = 0.6 Ksf Acting 2 (diameter of pile) Passive below exc. 400Y Acting 4 (2 diameter of pile) Diameter of pile = 2 Lagging spacing = 8 Surcharge as shown Ps = 0.36 The program only calculates the horizontal bracing force. The user has to calculate the vertical force and the total force based on the horizontal force calculations. The program shows that the minimum embedment is 5.8 and the pile length is The maximum moment in the pile is 28.6 Kip-ft at 24 from the ground surface. T = 6.3 Kips, T2 = 7. Kips. The force is in brace = 50 /Sin 45 = 70.7 Kips. EXAMPLE 2 Surcharge 6 T P = H = 6 Ps = Lagging Spacing = 8 7 H = 30 T2 P2 = o P3 = H = CivilTech Software SHORING EXAMPLES 4

15 EXAMPLE 3 DESIGN OF BRACED CUT WITHOUT EMBEDMENT Introduction : For trench excavation, sometimes the supporting system only uses steel plates, swale, and braces. The steel plates do not penetrate into the ground. The program also can solve these types of problems. The program also can be applied for trench box excavation for pipelines. This example uses three level of braces for a 20 cut. To check the stability problem, the heave program can be used. Question: What is the bracing force? Active pressure: φ = 30 Ka = 0.33 P = 0.65 KaγH = (0.65)(0.33)(20) 20 = 0.5 Ksf In the program output on page 2, check the bottom which will indicate the shoring wall without bracing. 3.7 T = 2.64k/ ft 0 T2 = 2.87k/ ft 6.3 T3 = 2.64k/ ft Maximum moment in plate: 2 Kip-ft/ft EXAMPLE 3 γ = 20pcf φ = 30 o P= H = 4 H = H = 4 CivilTech Software SHORING EXAMPLES 5

16 EXAMPLE 4 DESIGN OF SHEET PILE WALL, POUR SEAL AT BOTTOM Sometimes the bottom of the excavation is sealed to prevent water and heave. In this case, two ways can be used for inputting the concrete seal. ) Use a brace at the level of the seal. Note: the depth of the brace cannot be equal to the depth of the excavation. 0.5 to.0 is required above the excavation level as the input of this example. 2) In the passive pressure input, use a large value of Pres. Top and Pres. Slope. However, if the value is too large, the program cannot function. Trial and error is required. Question: What is the embedment and maximum bending moment in the pile? Active: P = 650 psf Water: P w = γ w (25-0 ) = 62.4 (5) = 936psf Passive: Pp = 300 pcf Concrete seal was poured at bottom of excavation, then dewater to excavation base. Sheet pile spacing (width) = The program shows that the minimum embedment is 3.7 and the pile length is The maximum moment in pile is.7 Kip-ft/ft at 8 from the ground surface. T=5.8 Kips/ ft, T2=5.8 Kips/ ft, and T3=4.2 Kips/ ft. T3 is the concrete seal. If the seal is 2 thick, the compression stress is 75 psi. EXAMPLE 4 P= T T2 0 CONCRETE SEAL, 2 THICK T3 Pw = Cancel out CivilTech Software SHORING EXAMPLES 6

17 EXAMPLE 5 DESIGN OF DEEP EXCAVATION USING MULTI-TIEBACK WALL This is a real project in Seattle area. The excavation is 60 below ground. The lagging spacing is 6. 7 levels of tiebacks are used. Vertical spacings of tiebacks need to be adjusted for a minimum moment in piles and smaller reaction force in tieback. The program proves easy input interface, so the user can change the depth of each tieback and run the program several times to get an optimum result. Question: What is the embedment, tieback force and maximum bending moment in the pile? Active: Above Base P = 0.65 KaγH = (0.65)(0.28)(25)(60) =.365 ksf Below Base Passive: Below Base P 2 = KaγH = (0.28)(25)(60) = 2. ksf Pa = Kaγ = (0.28)(25) = kcf Pp = Kpγ = 6.74 (30) = kcf Surcharge 0-0, Ps = 0.64 ksf; >0, Ps 2 = 0.24 ksf The output results are shown in the following: EXAMPLE P= Surcharge γ = 25 pcf φ = 34 o ka = Ps= 0.64 Lagging Spacing = H = P2 = Acting 2 Dia. of pile = 4. Acting Dia. of pile = 2 Ps2 = γ = 30 pcf φ = 35 o δ = φ/2 kp = 6.74 CivilTech Software SHORING EXAMPLES 7