Lateral Earth Pressures

Lateral Earth Pressures - Lateral Earth Pressures...

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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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