For yielding walls, lateral earth pressures can be computed assuming active conditions and wedge theory, using a planar surface of sliding defined by the Rankine theory. Table 8.1 provides soil properties for computing active earth pressures for five types of soil. Table 8.2 provides friction factors and adhesion for dissimilar materials. See Figs. 8.10 and 8.11 for the magnitude and location of resultant forces on retaining walls considering various types of soil backfill and backslide geometries. The pressures presented in these figures assume mobilization of the soil shear strength along the entire Rankine active failure plane, extending uninterrupted from the ground surface at the base of the wall or to the location on the wall at which the total earth load is being computed. Figure 8.11 shows the failure surface geometry and associated earth pressure distributions for various design conditions. If the soil behind the wall consists of more than one soil type, the design earth pressure should be determined using the weighted average of the properties of the soil types within and along the theoretical failure plane.
AASHTO provides that, for yielding walls, lateral earth pressures should be computed assuming active stress conditions and wedge theory using a planar surface of sliding defined by Coulomb theory. The computational procedures for active pressures are
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FIGURE 8.9 Relationship between wall movement and earth pressures. (a) Ideal cases where the backfill begins from at-rest pressures; (b) case for a sand backfill compacted to a medium-dense condition with no wall movement. (From Clough, G. W. and Duncan, J. M., “Earth Pressures,” Chap. 6 in Foundation Engineering Handbook, Fang, H. Y., Van Nostrand Reinhold, New York, 1991, with permission) |
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Soil type number |
Soil description |
uses symbol" |
Unit horizontal soil pressure^7 kh, lb/ft2/ft (kN/m3) |
Rankine active earth pressure coefficient^ К a |
Total soil unit weight 7, lb/ft3 (kN/m2/m) |
Effective angle of friction ф;, 0 |
|
1 |
Sands and gravels with little or no fines |
GW, GP, SW, SP (AASHTO A7) |
30" (4.7) |
0.25 |
120 (18.8) |
37 |
|
2 |
Sands and gravels with some silt |
GM-GP, GM-GW, SM-SP, SM-SW |
35 (5.5) |
0.29 |
120 (18.8) |
33 |
|
3 |
Silty and clayey sands and gravels |
GM, GC, SM, SC |
45 (7.1) |
0.45 |
100 (15.7) |
22 |
|
4 |
NOCrf to LOC’ silts and clays |
ML, MH, CL, CH |
100 (15.7) |
0.80 |
125 (19.6) |
0« |
|
5 |
HOC/ clays which can become saturated |
CL, CH |
120 (18.8) |
1.00 |
120 (18.8) |
0« |
|
675 |
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"Unified Soil Classification System (see Fig. 8.14). bAt (3 = 0°, representing a horizontal backslope behind the wall. For a sloping backfill ((3 > 0), refer to Figs. 8.10 and 8.11. kh = Kgy. cThe minimum value of kh for design should be 35 lb/ft3. ^Normally overconsolidated (OCR =1). ^Lightly overconsolidated (OCR = 1 to 2). ^Heavily overconsolidated (OCR >2). ^Undrained shear strength. Source: From Design Manual, Part 4, Pennsylvania Department of Transportation, Harrisburg, Pa., with permission. |
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Interface materials |
Friction factor, tan 8 |
Friction angle 8, ° |
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Mass concrete on the following foundation materials: |
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Clean sound rock |
0.70 |
35 |
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Clean gravel, gravel-sand mixtures, coarse sand |
0.55-0.60 |
29-31 |
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Clean fine to medium sand, silty medium to coarse |
0.45-0.55 |
24-29 |
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sand, silty or clayey gravel |
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Clean fine sand, silty or clayey fine to medium sand |
0.35-0.45 |
19-24 |
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Fine sandy silt, nonplastic silt |
0.30-0.35 |
17-19 |
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Very stiff and hard residual or preconsolidated clay |
0.40-0.50 |
22-26 |
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Medium stiff and stiff clay and silty clay |
0.30-0.35 |
17-19 |
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(Masonry on foundation materials has same friction factors.) Steel sheet piles against the following soils: |
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Clean gravel, gravel-sand mixtures, well-graded rock fill |
0.40 |
22 |
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with spalls |
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Clean sand, silty sand-gravel mixture, single-size hard |
0.30 |
17 |
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rock fill |
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Silty sand, gravel or sand mixed with silt or clay |
0.25 |
14 |
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Fine sandy silt, nonplastic silt |
0.20 |
11 |
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Formed concrete or concrete sheet piling against the following soils: |
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Clean gravel, gravel-sand mixture, well-graded rock fill |
0.40-0.50 |
22-26 |
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with spalls |
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Clean sand, silty sand-gravel mixture, single-size hard |
0.30-0.40 |
17-22 |
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rock fill |
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Silty sand, gravel or sand mixed with silt or clay |
0.30 |
17 |
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Fine sandy silt, nonplastic silt |
0.25 |
14 |
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Various structural materials: Masonry on masonry, igneous and metamorphic rocks: |
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Dressed soft rock on dressed soft rock |
0.70 |
35 |
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Dressed hard rock on dressed soft rock |
0.65 |
33 |
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Dressed hard rock on dressed hard rock |
0.55 |
29 |
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Masonry on wood (cross grain) |
0.50 |
26 |
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Steel on steel at sheet pile interlocks |
0.30 |
17 |
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Adhesion |
Adhesion |
|
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Interface materials* |
C, lb/ft2 a’ |
Ca, kPa |
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Very soft cohesive soil (0-250 lb/ft2) (0-12 kPa) |
0-250 |
0-12 |
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Soft cohesive soil (250-500 lb/ft2) (12-24 kPa) |
250-500 |
12-24 |
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Medium stiff cohesive soil (500-1000 lb/ft2) (24-48 kPa) |
500-750 |
24-36 |
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Stiff cohesive soil (1000-2000 lb/ft2) (48-96 kPa) |
750-950 |
36-45 |
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Very stiff cohesive soil (2000-4000 lb/ft2) (96-192 kPa) |
950-1300 |
45-62 |
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*Cohesion values are shown in parentheses. Source: From Design Manual, Part 4, Pennsylvania Department of Transportation, Harrisburg, Pa., with permission. |
2k!H2H
Hi
b
Soil type 1 (see Note 3)
0 0.2 0.4 0.6 0.8 1.0 0 0.2 0.4 0.6 0.8 1.0 0 0.2 0.4 0.6 0.8 1.0
Values of Ratio — H-
FIGURE 8.10 Charts for estimating Rankine active earth pressures against retaining walls supporting sloped ground of limited height. Notes: (1) Soil types shown on curves correspond to soil types described in Table 8.1. (2) For soil type 5, computations of soil pressure may be based on a value of H 4 ft (1.2 m) less than the actual value. (3) The minimum value of kh for design should be 35 lb/ft2/lin ft (5.50 kN/m2/m). (4) Add pressures due to water and surcharge (including 2 ft minimum soil surcharge) to the active earth pressures from these charts. (From Design Manual, Part 4, Pennsylvania Department of Transportation, Harrisburg, Pa., with permission)
DESIGN FAILURE SURFACE HORIZONTAL EARTH
CONDITION GEOMETRY PRESSURE DISTRIBUTION
LEGEND
kh1 = unit horizontal soil pressure due to backfill kh2 = unit horizontal soil pressure due to in situ soil P = angle between Rankine active failure plane and horizontal ф’ = weighted average effective stress angle of internal friction along failure plane
P = tan-1 tan ф’ + 1 + tan^’———— в
s^’ cosф’
NOTES
(1) Obtain values of kh1, kh2, and vertical component of soil pressure.
(2) The earth pressure resultant for this condition can be more accurately determined by Culmann’s graphical construction.
(3) Add pressures due to water and surcharge (including 2-ft minimum soil surcharge).
FIGURE 8.11 Assumed failure surfaces and horizontal earth pressure distributions. (From Design Manual, Part 4, Pennsylvania Department of Transportation, Harrisburg, Pa., with permission)
given below. An alternative to the computation for active pressures using the Coulomb theory for yielding walls and for cohesionless soils is to define the lateral pressures utilizing the Rankine theory.
The above procedures for developing the design pressures on yielding walls are based on the following assumptions:
1. The backfill soils are compacted with lightweight hand-compaction equipment.
2. The soil within the theoretical failure zone is made up entirely of the backfill soil.
3. No point or line loads act on the backfill surface.
4. The retaining wall deflections are consistent with the deflections required to develop the design active earth pressure.
