Chapter 4. Introduction to Deep Foundation Design 1. A 20-m long concrete pile is driven into cohesionless soil of two strata. The topsoil stratum has unit weight of 18.5 kN/m 3 , internal friction angle of 30, and thickness of 12 m. The second stratum has unit weight of 19.0 kN/m 3 , internal friction angle of 35, and thickness of 50 m. The groundwater table is found to be at 42 m below the ground surface. The concrete pile is circular in cross section with a diameter of 40 cm. Determine the ultimate bearing load of the pile. Solution: The pile and the subsoil condition are show in the figure below. The pile length is 20 m, and GWT is 42 m below ground surface, so GWT is 22 m below the tip of the pile and has no effect on bearing capacity. Use the Nordlund method for cohesionless soils. For uniform pile diameter (no tapering), = 0, use Equation (4.9). The ultimate bearing capacity of the driven pile is:
Transcript
Chapter 4. Introduction to Deep Foundation Design
1. A 20-m long concrete pile is driven into cohesionless soil of two strata. The topsoil stratum has unit weight of 18.5 kN/m3, internal friction angle of 30, and thickness of 12 m. The second stratum has unit weight of 19.0 kN/m3, internal friction angle of 35, and thickness of 50 m. The groundwater table is found to be at 42 m below the ground surface. The concrete pile is circular in cross section with a diameter of 40 cm. Determine the ultimate bearing load of the pile.
Solution:The pile and the subsoil condition are show in the figure below. The pile length is 20 m, and GWT is 42 m below ground surface, so GWT is 22 m below the tip of the pile and has no effect on bearing capacity.
Use the Nordlund method for cohesionless soils.
For uniform pile diameter (no tapering), = 0, use Equation (4.9). The ultimate bearing capacity of the driven pile is:
Since the pile penetrates two soil layers, the above equation can be written as:
The perimeter of the pile is:
The cross-sectional area at the pile toe is:
The effective stress at the pile toe:
Since the limiting value of t is 150 kPa, choose t = 150 kPa
The following table is developed to obtain the parameters in the ultimate bearing capacity equation.
Parameters in the ultimate bearing capacity equationSoil
strataGiven parameters
Figures/Tables used
Derived parameters
Layer 1
ϕ1 = 30°Displaced soil volume: V = 0.1256 m3/m
Figure 4.5, Table 4.1
Kz(1) = 0.300logV + 1.459 = 1.189
Displaced soil volume: V = 0.1256 m3/m, ϕ1 = 30°, and precast concrete pile
Figure 4.6, curve (c)
1/1 = 0.84, so 1 = 25.2°,
ϕ1 = 30°, 1/1 = 0.84Figure 4.7 (use / = 0.8 in the chart)
The total ultimate bearing capacity of the driven concrete pile is: Qu = Qs + Qt =3241.3 + 628 = 3869.3 kN
2. A concrete pile is driven into a homogeneous cohesionless soil. The soil’s unit weight is 18.5 kN/m3, and its internal friction angle is 35. The groundwater table is not found during the subsoil exploration. The pile is subjected to a load of 800 kN. Using a factor of safety of 3 and pile diameter of 30 cm, determine the required pile length.
Solution:The pile and the subsoil condition are illustrated in the figure below. The pile length is L.
Use the Nordlund method for cohesionless soils.
For uniform pile diameter (no tapering), = 0, use Equation (4.9). The ultimate bearing capacity of the driven pile is:
The perimeter of the pile is:
The cross-sectional area at the pile toe is: The effective stress at the pile toe:
Note the limiting value of t is 150 kPa.
Given: ϕ = 35°, displaced soil volume: V = 0.071 m3/m, find Kz from Table 4.1:Kz = 0.600logV + 2.369=1.680
From Figure 4.6, curve “c”, find / = 0.7, so = 24.5°.From Figure 4.7, using / = 0.7 and ϕ = 35°, find CK 0.85
Average z= 18.5 L/2 =9.25L (kN/m2)
t depends on pile length L and can be determined from Figure 4.8.
From Figure 4.9 and use ϕ = 35°, find Nq 75
So:
To satisfy FS = 3:
Use trial-and-error:
Assume L/B = 30, i.e., L = 9 m, find = 0.65, calculate Qu = 4894 kN
Assume L/B = 20, i.e., L = 6 m, find = 0.66, calculate Qu = 3188kN
Assume L/B = 15, i.e., L = 4.5 m, find 0.66, calculate Qu = 2269 kN
Assume L/B = 16, i.e., L = 4.8 m, find 0.66, calculate Qu = 2435 kN
So, L = 4.8 m to satisfy FS = 3.0
3. A 15-m closed-end steel pipe pile is driven into layered undrained clay. The top layer has unit weight of 18.5 kN/m3, undrained cohesion of 90 kN/m2, and a thickness of 10 m. The second layer has unit weight of 19.5 kN/m3, undrained cohesion of 120 kN/m2, and it extends to a great depth. The groundwater table is at the ground surface. The pile diameter is 40 cm. Determine the ultimate bearing load of the pile.
Solution:
Solution using allowable stress design:
The pile and subsoil condition are shown in the following figure.
Since the subsoil is undrained clay, use the -method. Since = 0, the undrained shear strength su= cu.
The unit skin resistance is:
Three methods are used to determine and compare , as shown in the following table.
Soil
StrataMethods Input values
Figure or
equation used
Layer 1
Tomlinson
(1979)
L/B = 10/0.4=25,su= 90kPa.
Smooth steel pile.
Figure 4.120.75 (use
interpolation)
Terzaghi et
al. (1996)su= 90 kPa Figure 4.12 0.50
Sladen
(1992)
su= 90 kPa;C1 = 0.5;
=(18.5-9.81)10/2=43.4kPa
0.36
Layer 2 Tomlinson
(1979)
L/B = 5/0.4=12.5, su= 120 kPa.Smooth steel pile.
Figure 4.12 0.47
Terzaghi et
al. (1996)
su= 120 kPaFigure 4.12 0.42
Sladen (1992)
su= 120 kPa;C1 = 0.5;
=(18.5-9.81)10 + (19-9.81) 5/2=109.9kPa
0.48
The values determined usingTergazhi’s method are used.
The perimeter of the pile is: l = B = 1.25 m
The cross-sectional area at the pile toe:
Layer 1:
Layer 2:
The total skin resistance is:
The unit toe resistance is:
The total toe resistance is:
The total ultimate bearing capacity of the driven concrete pile is:
Qu = Qs+ Qt = 877.5 + 135 = 1012.5kN
Solution using limit state design:
The cross-sectional area at the pile toe: At=14
π B2=0.126m2
The characteristic value of the bearing resistance is the minimum value of:
Rc ;k=( R toe ;cal+Rskin ;cal )average
ξ3
=cu N c A t+α su πBl
ξ3
and
Rc ;k=( R toe ;cal+Rskin ;cal )minimum
ξ4
=cu N c A t+α su πBl
ξ4
Assuming the geotechnical parameters are the result of only one ground test per clay layer,ξ3 and ξ4 are assumed both equal to 1.4 as suggested in EN-1997-1:2004 (Design approach 2). Hence, using Terzaghi´s method for and assuming also that the material properties are design values (as if they were already multiplied by their corresponding partial factor of safety):
and assuming that toe = skin = 1.1 (Note that these might change locally and according to the chosen design approach)
Rc ;d=R toe ;k
γtoe
+R skin;k
γ skin
=136.081.1
+ 893.471.1
=935.95 kN
4. A subsoil profile is shown in Figure 4.23. The concrete pile’s diameter is 50 cm.Determine the total length of the concrete pile to take a load of 250 kN with a factor of safety of 3.
Figure 4.23 Subsoil profile for Problem 4
Solution:
Solution using allowable stress design:
The scour zone is not considered in bearing capacity calculation.
Since the subsoil is clay and is beneath the groundwater table, use the -method. Since = 0, the undrained shear strength su= cu.
Also given: concrete pile diameter B = 0.5 m. Total load Q = 250 kN
Assume the length of the pile in the second layer is L.
The unit skin resistance is:
To avoid using trial-and-error, use the Sladen method (1992) to directly calculate L.
The cross-sectional area at the pile toe: The total skin resistance is:
The unit toe resistance is:
The total toe resistance is:
The total ultimate bearing capacity of the driven concrete pile is:
Qu = Qs + Qt= 300 + 150L + 212 = 512 + 150L(kN)
Solve the above equation and find L = 3.75 m
L = 4.0 m can be chosen.
The total pile length is:2m(scour zone) + 8m +4m = 14 m.
Solution using limit state design:
In limit state design approaches using partial factors of safety as demonstrated in this book, the concept of the global factor of safety suggested in this problem is not applicable. Hence, an alternative solution in which the pile length required to satisfy that Rc;d ≥ Fc;d (where Rc;d is the design resistance and Fc;d is the design value of all forces imposed on the pile) is proposed.
The cross-sectional area at the pile toe:
The forces imposed on the pile should include both the forces and the self-weight of the pile. In the calculation below it is assumed that both of these forces are permanent and unfavorable, as well as included in the load of 250 kN. Hence the partial factor of safety G =1.35. Assuming that the pile will have to penetrate into the third soil layer by a length L, and noting that the scour zone is neglected in the calculation, then
Fc;d = V G × γG
F c; d=250 × 1.35
Fc;d = 337.50 kN
Noting that partial factors of safety for geotechnical parameters are all equal to 1.00 for the design approach used here. Also assuming the geotechnical parameters are the result of only one ground test per layer,it can be found that the characteristic value of the bearing capacity of the pile is the minimum of:
Rc ;k=( R toe ;cal+Rskin ;cal )average
ξ3
and Rc ;k=( R toe ;cal+Rskin ;cal )minimum
ξ4
But because ξ3 and ξ4 are assumed both equal to 1.4 when only one test is available, as suggested in EN-1997-1:2004 then,
Rc ;k=(Rtoe ;cal+R skin;cal)
1.4
The skin resistance for each layer can then be calculated. The aim is to leave the total skin resistance as a function of the penetration of the pile into layer 3 (L)
In layer 2 (clay):
su= 100 kPa; C1 = 0.5; =(18-9.81)8/2=33 kPa
=0.30f s (2 )=α su=0.30 ×100=30 kPa
In layer 3 (clay):
R skin;cal (3)=α su πBl= 0.42×120×π×0.5×L = 79.17L[kN]su= 120 kPa; C1 = 0.5;
=(18-9.81)8 + (19-9.81) L/2=65.5 + 4.6L(kPa)
f s (3 )=α su=120 α
The perimeter of the pile is: l = B = 1.25 m
The characteristic skin resistance is:
Qs ; k=Rskin ;cal (2 )+R skin ;cal(3)
Qs ; k=30 ×1.25 ×8+120α ×1.25 × L
Qs ; k=300+150 αL
The toe bearing capacity:
Rtoe ;cal=cu N c At=120 ×9 × 0.196=211.68kN
Hence
Rc ;k=( R toe ;cal+Rskin ;cal )
1.4=
(211.68+300+150 αL)1.4
=511.68+150 αL1.4
Rc ;k=365.49+107αL
and assuming that toe = skin = 1.1 (Note that these might change locally and according to the chosen design approach)
Rc ;d=R toe ;k
γtoe
+R skin;k
γ skin
=211.681.1
+ 300+150 αL1.1
=192.44+136.36 αL
Finally, it must be satisfied that Rc;d ≥ Fc;d
Rc;d ≥ Fc;d
192.44+136.36 αL≥ 337.50
And solving the equation with
192.44+136.36(0.5 (65.5+4.6 L120 )
0.45)L ≥ 337.50
192.44+136.36 (0.56+0.17 L ) L≥ 337.50
192.44+76.36 L+23.18 L2 ≥337.50
L ≥1.34 m
This means that the length of the pile should be at least 2 m + 8 m + 1.34m ≅11.5 m in length.
5. A concrete pile is designed to support a load of 4600 kN. The pile is driven into a homogeneous drained clayey sand with c = 50 kN/m2 and = 32. The unit weight of the subsoil is 19 kN/m3. The concrete pile is square in cross section with a width of 30 cm. Use FS = 3. Determine the minimum length of the pile.
Solution:Since the subsoil is drained clay, the -method is used.Assume the minimum length of the pile is L in meter.
The unit skin resistance is:
= 19(L/2) = 9.5L (kN/m2)Use Table 4.4, and given clay soil with = 32, select upper limit of = 0.4.
The perimeter of the pile is 0.3 4 = 1.2 m
The cross-sectional area at the pile toe is At = 0.3 0.3 = 0.09 m2
The ultimate total skin resistance is:
Qs = fs As = 3.8L 1.2L = 4.56L2
The unit toe bearing capacity is:
Using Table 4.4, and given the clay soil with = 32, select upper limit ofNt = 30.
The effective overburden stress at the toe is:
= 19L(kN/m2)
The ultimate toe bearing capacity is:
The total ultimate bearing capacity of the driven concrete pile is:
Solve L and find: L = 12.66 m
6. As shown in Figure 4.24, a concrete pile is driven into the top two layers of subsoil strata. The subsoil profile and properties are shown in the figure. The pile’s diameter is 50 cm throughout the pile. Determine the ultimate bearing load of the pile.
Figure 4.24 Subsoil profile for Problem 6
Solution:
Ultimate bearing capacity of the pile: Qu = Qs(sand) + Qs(clay) + Qt(in clay)
Since the groundwater table is not present, assume the subsoil is drained and use the -method.
The perimeter of the pile is:
The cross-sectional area at the pile toe: Determine the skin resistance in the top sand layer.
= 185/2 = 45 kN/m2.
Use Figure 4.14, and given sandy soil with = 35, select = 0.40.
Determine the skin resistance in the bottom clay layer.
= 185+ 19(10/2)= 185 kN/m2. Use Table 4.4 and given clay soil with = 25, select minimum = 0.23.
Determine the toe bearing capacity:Using Table 4.4, and given clay soil with = 25, use minimum Nt = 3.
The effective overburden stress at the toe is:
= 185 + 1910 = 280kN/m2.
The ultimate toe bearing capacity is:
The total ultimate bearing capacity of the driven concrete pile is:
7. A pile group is comprised of four circular concrete piles. The diameter of each pile is 40 cm. The spacing between two adjacent piles is 120 cm. The pile group is driven into a homogeneous sandy riverbed to support a bridge pier. It is assumed the river flows year-round. The saturated unit weight of subsoil is 19 kN/m3, the cohesion is zero, and the internal friction angle is 36. The pile length is decided to be 12 m. Determine the ultimate bearing capacity and pile group efficiency of the pile group.
Solution:
Given parameters: b = 0.4 m, s = 1.2 m, L = 12 m, sat = 19 kN/m3, c = 0, = 36.The plan view of the pile group is show in the figure below.
The subsoil is sandy (cohesionless) soil. The unit skin resistance is fs, the unit toe resistance qt.
The ultimate bearing capacity of pile group:
The ultimate bearing capacity of an individual pile in the pile group:
Use Figure 4.14 and given sandy soil with = 36, find = 0.41
Average effective stress: = (19-9.81)12/2 = 55.1 kN/m2
Use Figure 4.15, and given sandy soil with = 36, find Nt67.The effective overburden stress at the toe is:
= (19-9.81)12 = 110.2 kN/m2.
So:
The pile group efficiency: = 6.25
8. A 30-m long closed-end steel pipe pile group is driven into layered undrained clay. The pile cap is square and the nine piles are evenly spaced. The layout of the pile group is shown in Figure 4.25. The topsoil layer has a unit weight of 18 kN/m3, undrained cohesion of 100 kN/m2, and a thickness of 10 m. The second layer has unit weight of 19 kN/m3, undrained cohesion of 150 kN/m2, and it extends to great depth. The groundwater table is at the ground surface. Determine the ultimate bearing capacity and pile group efficiency of the pile group.
Figure 4.25 Layout of pile group for Problem 8.
Solution:The section view of the pile group and the subsoil condition is shown below.
Ultimate bearing of pile group:
Ultimate point bearing capacity:
Nc* = 9 for deep foundation in undrained clay
Ultimate skin resistance:
Ultimate bearing capacity of each single pile:
Use -method to calculate the friction resistance of single pile. The values are
determined usingTergazhi’s method (Figure 4.12).
The perimeter of the pile is: l = B = 1.57 m
Layer 1:
Layer 2:
The total skin resistance is:
The pile group efficiency: = 2.76
9. The subsoil profile of a riverbed is shown in Figure 4.23. It is determined that a pile group comprising four piles is needed to support the bridge pier. The four piles are evenly spaced. The center-to-center spacing is three times of the pile diameter, and each pile’s outside circumference is assumed to align with the edge of the pile cap.
Each concrete pile’s diameter is 50 cm, and length is 15 m. Determine the ultimate bearing capacity and pile group efficiency of the pile group.
Solution:The subsoil condition is shown below:
The plan view of the pile group is show in the figure below. Pile length L = 15 m
The scour zone is not considered in bearing capacity calculation.
(1) Determine the ultimate bearing capacity of pile group:
For undrained clayey soil:
Unit skin resistance in layer 1:
Unit skin resistance in layer 2:
Unit toe resistance:
, use the limiting value of 9.
(2) Determine the ultimate bearing capacity of an individual pile in the pile group:
Follow the solution in Problem 4, and use the Sladen method (1992)
The cross-sectional area at the pile toe: The total skin resistance is:
The unit toe resistance is:
The total toe resistance is:
The total ultimate bearing capacity of the driven concrete pile is: Qu = Qs + Qt= 622.5 + 211.6 = 834.1 kN
The pile group efficiency: = 5.51
10. A 15-m long closed-end steel pipe pile group is driven into a homogeneous clay. The pile cap is square and the nine piles are evenly spaced. The layout of the pile group is shown in Figure 4.25. The pile group is subjected to a vertical load of 5200 kN. The soil has a unit weight of 18.5 kN/m3, cohesion of 100 kN/m2, friction angle of 10 degrees. The clay layer is 100 m deep and beneath the clay layer is dense sand. The groundwater table is at the ground surface. Preliminary laboratory testing found the clay’s void ratio is 0.45, compression index is 0.3, swell index is 0.08, and the clay is overconsolidated. The preconsolidation pressure is 200 kN/m2.Determine the primary consolidation settlement of the pile group.
Solution:
Subsoil parameters: sat = 18.5 kN/m3, c = 100 kN/m2, = 10, e0 = 0.45, cc = 0.3, cs = 0.08, c= 200 kN/m2.
The layout of pile group is shown below. AndB = 4 m, L = 12 m.
The 2:1 method is used to calculate the vertical stress increases due to the pile group
loading. The vertical stress increases are assumed to occur starting at the depth of two
thirds of the pile length.
(1) Determine the depth of the soil layer for which the consolidation settlement should
be calculated. The consolidation settlement should be considered to a depth of z
0.1 0.
Use 2:1 method:
where:
z starts from the (2/3)L = 8 m
The effective stress:
Let: z = 0.10, and solve z = 12.9 m. Use z = 13.0 m
(2) Since the vertical stress increase is nonlinear with depth, the thick soil layers should be divided into a number of thin layers, and the consolidation settlement for each thin layer is calculated, then the individual settlements are summed. Based on Figure 3.24 and for easy calculation, the second clay layer of the subsoil is divided into two layers, as shown in the figure below.
The vertical stress increases, the average vertical stress increase, and the average
effective stress in each layer are calculated and listed as follows. Note, the vertical
stress increase is calculated from a depth of 10 m, while the effective stress is
calculated from the ground surface.
The average vertical stress increase uses Equation (3.55):
z(m)
Vertical stress
increase (kN/m2)
0 325.0
1 208.0
2 144.4
4 81.2
6 52.0
9.5 28.5
13 18.0
Layer
Average
vertical stress
increase,
z(av)
(kN/m2)
Average in-situ
effective stress,
0(av) (kN/m2)
Precon-solidation pressure, c
(kN/m2)
Thickness, H (m)
#1 216.9(18.5-
9.81)9=78.2180 2
#2 86.9(18.5-
9.81)12=104.3180 4
#3 30.7(18.5-
9.81)17.5=152.1180 7
In layer #1: c=200 kN/m2 <0(av) +z(av) = 78.2+216.9=295.1 kN/m2, the soil is overconsolidated.
In layer #2: c =200 kN/m2 >0(av) +z(av) = 104.3+86.9=191.2kN/m2,the soil is overconsolidated.
In layer #3: c =200 kN/m2 >0(av) +z(av) = 152.1+30.7=182.8 kN/m2,the soil is overconsolidated.
The total consolidation settlement is: 20.4 cm.
11. The problem statement is the same as in Problem 9, and the subsoil profile is shown in Figure 4.23. The total load on the pile cap is 6000 kN. Assume both clay layers are normally consolidated. Both clay layers have the void ratio of 0.4, compression index of 0.3. Determine the total settlement of the pile cap.
