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TABLE 11.8
Value of Stiffness Factor (µL) for Piers of Various Embedment Lengths and Diameters Drilled in Cohesionless Soils of Various Relative Densities
Pier Diameter (in.)
18 24 30 36 42
18 24 30 36 42
18 24 30 36
42
State nh (tons/ft3) nh (lbs./in.3)
Pier Length (in.)
120 120 120 120 120
240 240 240 240 240
360 360 360 360
360
Very Loose 7
8.10
1.73 1.33 1.10 0.96 0.85
(3.46) (2.66) (2.20) 1.92 1.60
5.19* (3.99) (3.30) (2.88)
(2.55)
Loose Medium 21 56 24.30 64.81
2.16 (2.52) 1.60 1.98 1.37 1.68 1.19 1.44 1.05 1.27
4.32* 5.04* (3.20) (3.96) (2.74) (3.36) (2.38) (2.88) (2.10) (2.54)
6.48* 7.56* 4.95* 5.94* 4.11* 5.04* (3.57) 4.32*
(3.15) (3.81)
Dense Very Dense 74 92 85.65 106.48
(2.70) (2.82) (2.11) (2.22) 1.77 1.86 1.52 1.60 1.35 1.41
5.40* 5.64* 4.22* 4.44* (3.54) (3.72) (3.04) (3.22) (2.70) (2.82)
8.10* 8.46* 6.33* 6.66* 5.31* 5.58* 4.56* 4.80*
4.05* 4.23*
1.73 indicates short pier (µL less than 2.0) 5.19* indicates long pier (µL larger than 4.0) (3.46) indicates µL between 2.0 and 4.0
in the stiffness EL of the pier section decreases the lateral deflection of long piers, but does not affect the lateral deflections of short piers.
For long piers, the lateral deflection y at the ground surface can be calculated directly from
y =[2.40 p] nh3 5 EL 5
For short piers, the lateral defection y at the ground surface for a free-headed condition can be calculated from
18 p Ê1+1.33 e y= L nh ,
For e = 0, y = 18 p h
©2000 CRC Press LLC
FIGURE 11.11 Lateral deflection related to stiffness factor for piers drilled in cohesionless soils.
The above equations can be plotted as shown in Figure 11.11. Table 11.9 is prepared on the basis of Figure 11.11, considering the cases of both long and short piers.
©2000 CRC Press LLC
TABLE 11.9
Maximum Working Load (tons) for Free-Headed Piers of Various Diameters and Lengths Drilled in Cohesionless Soils of Various Relative Densities with Lateral Deflection of 0.5 in.
Pier Diameter (in.)
18
24
30 36 42
18
24
30
36
42
18
24
30
36
42
State nh (tons/ft3)
Relative Density (%) Pier
Length (in.)
120
120
120 120 120
240
240
240
240
240
360
360
360
360
360
Very Loose 7
20
1.62
1.62
1.62 1.62 1.62
6.48 (4.26) 6.48 (6.81) 6.48 (9.81) 6.48
6.48
14.59 (4.26) 14.59 (6.81) 14.59 (9.84) 14.59
(13.11) 14.59
(16.82)
Loose 21 30
4.86
4.86
4.86 4.86 4.86
(8.28)
19.44 (13.24) 19.44 (19.12) 19.44 (25.50) 19.44 (32.72)
(8.28)
(13.24)
(19.12)
43.78 (25.50) 43.78
(32.72)
Medium 56 50
12.96 (17.43) 12.96
12.96 12.96 12.96
(14.86)
51.84 (23.75) 51.84 (34.29) 51.84 (45.72) 51.84 (58.67)
(14.86)
(23.75)
(34.29)
(45.72)
116.76
(58.67)
Dense 74 70
17.12 (17.30) 17.12
17.12 17.12 17.12
(17.30)
(27.65)
68.48 (39.92) 68.48 (53.23) 68.48 (68.01)
(17.30)
(27.65)
(39.92)
(53.23)
(68.01)
Very Dense 92 80
21.29 (20.10) 21.29 (32.14) 21.29 21.29 21.29
(20.10)
(32.12)
85.16 (46.38) 85.16 (61.84) 85.16 (79.36)
(20.10)
(32.12)
(46.38)
(61.84)
(79.36)
1.62 indicates lateral pressure on the basis of short pier (4.26) indicates lateral pressure on the basis of long pier
11.7 PRESSUREMETER TEST
The value of horizontal subgrade reaction kh can also be determined experimentally by using the Menard pressuremeter. The pressuremeter probe is inserted in the test
©2000 CRC Press LLC
hole at the desired depth. The radial expansion of the hole is expressed as a function of increasing radial pressures applied to its wall, similar to a common load test. Thus, the deformation modulus Es can be determined at any depth. The following formula is used in the determination of the coefficient of horizontal subgrade reaction:
1 1+m ÈR 2 ùC C D kh 3 Es ∈ R 2û 4.5 Es 3 2
In which
k = Coefficient of horizontal subgrade reaction (kg/cm3) µ = Poisson’s ratio (0.3 for most soils)
Ro = Radius of pressuremeter probe D = Pier diameter (cm)
C1 = Structural coefficient of soil (0.33 for sand, 0.66 for claystone)
C2 = Shape factor in shear deformation zone (2.65 where L/D less than 20) C3 = Shape factor in consolidation zone (1.50 where L/D less than 20)
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