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**Unformatted text preview: **Lateral Earth Pressures
Foundation Design
CE 482 Earth Pressures
• Geostatic Stress
caused by gravity (weight of
subsurface materials) • Induced Stress
caused by external loads
(applied loads) Vertical Geostatic Stress Effective stress Brown, pg. 218 Horizontal Geostatic Stress Brown, pg. 218 Coefficient of Lateral Earth Pressure K= σh’
σv’ K = coefficient of lateral earth pressure
σh’ = horizontal effective stress
σv’ = vertical effective stress At-Rest Condition
K0 = (1 - sin φ’) OCRsin φ’
(for level ground surface), where:
K0 = coefficient of lateral earth pressure at rest
φ’ = effective friction angle of soil
OCR = overconsolidation ratio of soil Typical K0 Values
Cohesionless Soils (Sand): 0.4 to 0.6
Cohesive Soils (Silt/Clay): 0.4 to 0.8
*Overconsolidated Soils and Compacted Fill may exceed 1 At-Rest Condition σh’ = Ko*σv’ Active Earth Pressure Lamb & Whitman, p. 164 Active Earth Pressure Coduto, p. 754 Active Earth Pressure • Wall moves away from soil
• Soil mass stretches (relaxes)
horizontally
• Shear strength fully mobilized
• Plastic equilibrium State of
Stress
Active Earth
Condition p. 753 Coduto Required
Displacement Active Earth
Pressure p. 754 Coduto Active Earth Pressure p. 755 Coduto Passive Earth Pressure Coduto, p. 755 Lateral Earth Pressures
Passive Earth Condition p. 756 Coduto Lateral Earth Pressures
Passive Earth Condition p. 757 Coduto Presumptive
Lateral Earth
Pressures
from Building
Codes
p. 776 Coduto Terzaghi & Peck’s
Equivalent Fluid Pressure Method Pa/b = GhH2
2 Va/b = GvH2
2 Pa/b = normal force between soil and wall per unit length of wall
Va/b = shear force between soil and wall per unit length of wall
b = unit length of wall (usually 1 ft)
Gh, Gv = horizontal and vertical equivalent fluid densities
H = height of wall Terzaghi and Peck’s
Presumptive Lateral Earth Pressures p. 773 Coduto Presumptive Lateral Earth Pressures
T&P - for retaining wall with infinite slope p. 774 Coduto Presumptive Lateral Earth Pressures
Terzaghi and Peck - for retaining wall with partial slope p. 775 Coduto Presumptive Lateral Earth Pressures
Terzaghi and Peck - for retaining wall with partial slope p. 775 Coduto Classical Earth Pressure Theories Rankine (c = 0 and φ ≥ 0)
Coulomb (c = 0 and φ ≥ 0) Rankine Theory
Assumptions p.758 Coduto Rankine Earth Pressure Theory
(c = 0 and φ ≥ 0)
Active Condition - Free Body Diagram p.759 Coduto Rankine Earth Pressure Theory
(c = 0 and φ ≥ 0) Active Condition p.758, 760 Coduto Rankine Earth Pressure Theory
(c = 0 and φ ≥ 0) Active Condition p. 760 Coduto Rankine Earth Pressure Theory
(c = 0 and φ ≥ 0) Passive Condition - Free Body Diagram p.759 Coduto Rankine Earth Pressure Theory
(c = 0 and φ ≥ 0) Passive Condition p. 762 Coduto Coulomb Earth Pressure Theory
(c = 0 and φ ≥ 0) Active Condition Only p. 764, Coduto Coulomb Earth Pressure Theory
(c = 0 and φ ≥ 0) Active Condition Only p. 764-5 equations, Coduto Coulomb Earth Pressure Theory
(c = 0 and φ ≥ 0) Active Condition Only p. 764-5 equations, Coduto Lateral Earth Pressures
for soils with c ≥ 0 and φ ≥ 0) Critical Height, Hc
p. 767-8 Coduto Lateral Earth Pressures
Theoretical Active Lateral Earth Pressure for soils with
c ≥ 0 and φ ≥ 0; modified Rankine theory p. 768 Coduto Lateral Earth Pressures
Theoretical Passive Lateral Earth Pressure for soils with c ≥ 0 and φ ≥ 0) p. 768 Coduto Computation of
Simple Active and
Passive Pressures NAVFAC 7.02, p.62 Summary of
Simple Active
and Passive
Pressures NAVFAC 7.02, p.60 Restrained/Braced Walls
Measured Pressure Distribution Restrained/Braced Walls
MACTEC Design Pressure Distribution 0.2H H=HEIGHT OF 0.6H BASEMENT WALL IN FT. O.2H
22 H
(P.S.F.) Surcharge Pressures σ = Kq p. 777 Coduto Lateral Earth Pressures from Surcharge Loads
from Spangler & Handy, Soil Engineering, 1982 concentrated load on surface of backfill Lateral Earth Pressures from Surcharge Loads
from Spangler & Handy, Soil Engineering, 1982 The pressures given by this
method are approximately
twice as great as those
given by classical
Boussinesq theory due to
assumption of a rigid and
unyielding wall. Lateral Earth Pressures from Surcharge Loads
from Spangler & Handy, Soil Engineering, 1982 line load of infinite length perpendicular to wall Lateral Earth Pressures from Surcharge Loads
from Spangler & Handy, Soil Engineering, 1982 parallel line load of infinite length Lateral Earth Pressures from Surcharge Loads
from Spangler & Handy, Soil Engineering, 1982 area load of infinite length Lateral Earth Pressures
from Surcharge Loads
from Spangler & Handy, Soil
Engineering, 1982 area load of finite length Lateral Earth
Pressures from
Surcharge
Loads
from Spangler & Handy,
Soil Engineering, 1982
area load of finite length Groundwater Effects
• The effective stress in the soil below the
groundwater will decrease, which decreases the
active, passive, and at-rest pressures
• Horizontal hydrostatic pressures develop against
the wall
• The effective stress between the bottom of the
footing and the soil becomes smaller => less
sliding friction Groundwater Effects p. 780 Coduto Cantilever Retaining Walls
External and Internal Stability p. 787-8 Coduto Cantilever Retaining Walls
External Stability p. 788-9 Coduto Lateral Earth Pressures
Cantilever Retaining Walls
External Stability p. 788-9 Coduto External Stability: Sliding Forces acting between a
cantilevered wall and the
ground.
The wall, footing, and
backfill soil immediately
above the footing form the
wall-soil unit, which is used
to perform external stability
analyses.
p. 787-8 Coduto External Stability:
Sliding
Sliding stability is evaluated using a limit
equilibrium approach by considering
forces acting on the wall-soil unit if it
were about to fail.
The factor of safety is the ratio of forces
required to cause failure to actual forces. External Stability:
Sliding Forces causing sliding (known as
driving forces) may include:
• Horizontal component of lateral earth
pressure (active),
• Hydrostatic forces, and
• Seismic forces. External Stability:
Sliding Forces resisting sliding
(known as resisting forces)
include:
• Lateral earth pressures
(passive),
• Sliding friction, and
• Hydrostatic forces. External Stability:
Sliding
Ultimate Friction and
Adhesion Factors for
Dissimilar Materials NAVFAC 7.02, p.63 External Stability:
Sliding The factor of safety is defined as the ratio
of resisting forces to driving forces.
IBC 1610.2 requires a factor of safety against
sliding of at least 1.5.
A higher factor of safety, perhaps 2.0, may be
justified for clay backfill. External Stability:
Sliding The factor of safety may be increased
by the following:
•
•
•
•
• Enlarge heel,
Add a key beneath footing,
Use better backfill materials,
Install tie-down anchors, and
Install tie-back anchors. External Stability:
Overturning
Overturning stability is also evaluated using
a limit equilibrium approach.
A rigorous approach would compute the
factor of safety at various points to search
for the lowest factor.
The typical approach only considers one
point: at the toe. External Stability:
Eccentricity For service conditions, the normal force
along the base of footing must be located
within the middle third of the footing to
maintain a compressive stress along the
entire base of the footing. External Stability:
Overturning and Eccentricity The factor of safety may be increased
by the following:
•
•
•
•
• Extend the toe of the footing,
Extend the heel of the footing,
Use better backfill materials,
Install tie-down anchors, and
Install tie-back anchors. External Stability:
Bearing Capacity and Settlement Allowable bearing capacity value provided
by geotechnical engineer has built-in factor
of safety of at least 2.0 and more
commonly 3.0.
Typically, settlement is the controlling
factor. External Stability: Deep-seated Failure May be a controlling factor in the following
cases:
• Soft clay backfill and foundation material,
• Adverse bedding planes in bedrock, and
• Liquefaction. Internal Stability
Structural Design Coduto, p. 805 Key Design Issues:
Drainage and Waterproofing Drainage is provided for backfill to prevent
buildup of hydrostatic pressures.
Waterproofing is provided to control
migration of moisture through the wall Key Design Issue:
Drainage Coduto, p. 819 Key Design Issue:
Drainage Coduto, p. 819 Key Design
Issue:
Waterproofing Coduto, p. 819 Key Design Issue:
Clay Backfill • Active pressures for clays are not as
reliable.
• Clay may creep and re-establish at-rest
conditions.
• Expansive clays may impose swell
pressures that sometimes exceed at-rest
pressures. Key Design Issue:
Clay Backfill • Clay backfill should be avoided.
• Clay is difficult to compact and performs
poorly as backfill.
• Where clay exists behind walls (shored),
drainage and moisture control measures
may be implemented to maintain stable
moisture contents. Key Design Issue:
Seismic Loading The California Building Code states that the
seismic increment of active earth pressure
be applied to buildings with walls that
retain earth having exterior grades on
opposite sides differing by more than 6
feet. Key Design Issue:
Seismic Loading Revised version of Chapter 16, Chapter 16A of the 2001 California
Building Code, which is based on the 1997 UBC for DSA and OSHPD
reviewed projects (Section 1630A.1.1 Item 5) Key Design Issue:
Seismic Loading PA + PA ΔPAE Key Design Issue:
Seismic Loading
Chapter 16A of the 2001
California Building Code,
Section 1611.A.6 addresses
retaining walls. Key Design Issue:
Seismic Loading for Yielding Walls
The dynamic incremental component
(DPAE) may be evaluated using the
equation proposed by Seed and
Whitman (1970):
DPAE ~ (3/8)khγH2
where kh is the “horizontal ground
acceleration divided by gravitational
acceleration.” Key Design Issue:
Seismic Loading: Non-Yielding Walls
The dynamic thrust, DPE, is approximately:
DPE = khγH2
As for yielding walls, the point of application of
the dynamic thrust is typically taken at a height
of 0.6H above the base of the wall. Key Design Issue:
Seismic Loading
The seismic coefficient kh is not equal to
the peak ground acceleration.
The value should be significantly lower,
generally below 0.15, to account for:
The effective ground acceleration
(repeatable ground motion), and
The averaging of the lateral forces on
the retaining wall over the height of
the wall. Key Design Issue:
Seismic Loading • kh should be taken as 1/3 to 2/3
of the peak ground
acceleration.
•Without detailed analyses, a kh
equal to 1/2 of the peak ground
acceleration may be considered
reasonable. Key Design Issue:
Design Seismic Active Pressure Distribution H=
HEIGHT OF WALL OR
DIFFERENCE IN
BUILDING WALL
HEIGHT
IN FEET 16H
(P.S.F.) Mechanically Stabilized Earth Walls Mechanically Stabilized Earth Walls Bibliography
*Brown, R.W., 1990: Foundation Behavior and Repair, 2nd Edition, McGrawHill, Inc., New York, NY.
*Coduto, D.P., 2001: Foundation Design, 2nd Edition, Prentice-Hall, Inc.,
Upper Saddle River, N.J.
*Lambe, T. W. and R.V. Whitman, 1969: Soil Mechanics, John Wiley &
Sons, Inc., New York, NY.
*Naval Facilities Engineering Command (NAVFAC), 1986: Foundations and
Earth Structures, Design Manual 7.02.
*Maljian, P.A. and J.L. VanBeveren, 1974: Tied-Back Deep Excavations in
Los Angeles Area, ASCE Journal of the Construction Division, September Vol.
100, No. CO3, pp. 337-356.
*Spangler, M.G. and R.L. Handy, 1982: Soil Engineering, 4th Edition, Harper
and Row, New York, NY. ...

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