9.12Frictional Resistance (Q) in SandAccording to Eq. (9.14), the frictional resistance0, = Ep ALfThe unit frictional resistance, f, is hard to estimate. In making an estimation of f, severalimportant factors must be kept in mind:1. The nature of the pile installation. For driven piles in sand, the vibration caused dur-ing pile driving helps densify the soil around the pile. The zone of sand densificationmay be as much as 2.5 times the pile diameter, in the sand surrounding the pile.2 It has been observed that the nature of variation of fin the field is approximately asshown in Figure 9.16. The unit skin friction increases with depth more or less lin-early to a depth of L' and remains constant thereafter. The magnitude of the criticaldepth L' may be 15 to 20 pile diameters. A conservative estimate would beL' 15D(9.40)3. At similar depths, the unit skin friction in loose sand is higher for a high-displacement pile, compared with a low-displacement pile.4. At similar depths, bored, or jetted, piles will have a lower unit skin frictioncompared with driven piles.Taking into account the preceding factors, we can give the following approximaterelationship for f (see Figure 9.16):For z = 0 to L',f = Ko, tan 8(9.41)and for z = L' to L,f = f=r(9.42)In these equations,K= effective earth pressure coefficiento, = effective vertical stress at the depth under consideration8' = soil-pile friction angleIn reality, the magnitude of K varies with depth; it is approximately equal to theRankine passive earth pressure coefficient, K,, at the top of the pile and may be lessthan the at-rest pressure coefficient, K,, at a greater depth. Based on presently availableresults, the following average values of K are recommended for use in Eq. (9.41):9.8 Meyerhof's Method for Estimating Q,SandThe point bearing capacity, q,, of a pile in sand generally increases with the depth ofembedment in the bearing stratum and reaches a maximum value at an embedment ratioL/D = (L/D),r. Note that in a homogeneous soil L, is equal to the actual embedmentlength of the pile, L. However, where a pile has penetrated into a bearing stratum, L, A driven closed-ended pile, circular in cross section, is shown in Figure P9.4.Calculate the following.a. The ultimate point load using Meyerhof's procedure.d. The ultimate frictional resistance Q,. [Use Eqs. (9.40) through (9.42), and takeK = 1.4 and 8' = 0.64'.]e. The allowable load of the pile (use FS = 4).Y - 15.7 kN/m= 32GroundwatertableYu - 18.2 kN/m³d= 32Yu - 19.2 kN/m³= 4015 m381 mmFigure P9.4

Ultimate point load is calculated by the following formula: Qb=σv'NqAbwhere Ab=area of pile =…

A driven closed-ended pile, circular in cross section, is shown in Figure P9.4. Calculate the following. a. The ultimate point load using Meyerhof's procedure. d. The ultimate frictional resistance Q,- [Use Eqs. (9.40) through (9.42), and take K = 1.4 and 8' = 0.64'.] e. The allowable load of the pile (use FS = 4). Y -15.7 KN/m = 32 Groundwater Yu - 18.2 AN/m = 32 Yu- 19.2 KN/m - 40 15 m

A driven closed-ended pile, circular in cross section, is shown in Figure P9.4. Calculate the following. a. The ultimate point load using Meyerhof's procedure. d. The ultimate frictional resistance Q,- [Use Eqs. (9.40) through (9.42), and take K = 1.4 and 8' = 0.64'.] e. The allowable load of the pile (use FS = 4). Y -15.7 KN/m = 32 Groundwater Yu - 18.2 AN/m = 32 Yu- 19.2 KN/m - 40 15 m

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Braced cuts

The braced cut is a method of providing lateral support to the soil in foundation trenches, to prevent the trenches from deformation by the caving in of soil and resisting it from moving laterally. During shallow excavation in firm soil, generally, slopes are provided to resist the caving in of soil. During shallow excavation in soft soil and deep excavation, the chances of caving in of soil increase. Hence, it becomes necessary to make a provision to resist the deformation of trenches due to caving in of soil. The braced cut is the method used for such conditions. The excavation using braced cuts is a bit uneconomical as compared to the traditional open-cut excavation method but provides better safety than the cut excavation method.

Question

9.12
Frictional Resistance (Q) in Sand
According to Eq. (9.14), the frictional resistance
0, = Ep ALf
The unit frictional resistance, f, is hard to estimate. In making an estimation of f, several
important factors must be kept in mind:
1. The nature of the pile installation. For driven piles in sand, the vibration caused dur-
ing pile driving helps densify the soil around the pile. The zone of sand densification
may be as much as 2.5 times the pile diameter, in the sand surrounding the pile.
2 It has been observed that the nature of variation of fin the field is approximately as
shown in Figure 9.16. The unit skin friction increases with depth more or less lin-
early to a depth of L' and remains constant thereafter. The magnitude of the critical
depth L' may be 15 to 20 pile diameters. A conservative estimate would be
L' 15D
(9.40)
3. At similar depths, the unit skin friction in loose sand is higher for a high-
displacement pile, compared with a low-displacement pile.
4. At similar depths, bored, or jetted, piles will have a lower unit skin friction
compared with driven piles.
Taking into account the preceding factors, we can give the following approximate
relationship for f (see Figure 9.16):
For z = 0 to L',
f = Ko, tan 8
(9.41)
and for z = L' to L,
f = f=r
(9.42)
In these equations,
K= effective earth pressure coefficient
o, = effective vertical stress at the depth under consideration
8' = soil-pile friction angle
In reality, the magnitude of K varies with depth; it is approximately equal to the
Rankine passive earth pressure coefficient, K,, at the top of the pile and may be less
than the at-rest pressure coefficient, K,, at a greater depth. Based on presently available
results, the following average values of K are recommended for use in Eq. (9.41):
9.8 Meyerhof's Method for Estimating Q,
Sand
The point bearing capacity, q,, of a pile in sand generally increases with the depth of
embedment in the bearing stratum and reaches a maximum value at an embedment ratio
L/D = (L/D),r. Note that in a homogeneous soil L, is equal to the actual embedment
length of the pile, L. However, where a pile has penetrated into a bearing stratum, L, <L
Beyond the critical embedment ratio, (L/D)., the value of q, remains constant (q, = q).
That is, as shown in Figure 9.12 for the case of a homogeneous soil, L = L,.
For piles in sand, c' = 0, and Eq. (9.13) simpifies to
0, = A,4, = A,q'N
(9.15)
The variation of N* with soil friction angle o' is shown in Figure 9.13. The interpolated
values of N for various friction angles are also given in Table 9.5. However, Q, should
not exceed the limiting value Agi; that is,
(9.16)
Table 9.5 Interpolated Values of
N; Based on Meyerhof's Theory
Soll friction
angle, (deg)
N
20
12.4
21
13.8
22
15.5
23
17.9
24
21.4
25
26.0
26
29.5
27
34.0
28
39.7
29
46.5
30
56.7
31
.
68.2
32
81.0
33
96.0
34
115.0
35
143.0
36
168.0
37
194.0
38
231.0
39
276.0
40
346.0
41
420.0
525.0
42
43
650.0
44
780.0
45
930.0
The limiting point resistance is
4 = 0.5 p,N tan d'
(9.17)
where
P. = atmospheric pressure (=100 kN/m? or 2000 Ib/n)
4' = effective soil friction angle of the bearing stratum

A driven closed-ended pile, circular in cross section, is shown in Figure P9.4.
Calculate the following.
a. The ultimate point load using Meyerhof's procedure.
d. The ultimate frictional resistance Q,. [Use Eqs. (9.40) through (9.42), and take
K = 1.4 and 8' = 0.64'.]
e. The allowable load of the pile (use FS = 4).
Y - 15.7 kN/m
= 32
Groundwater
table
Yu - 18.2 kN/m³
d= 32
Yu - 19.2 kN/m³
= 40
15 m
381 mm
Figure P9.4

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