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The Coefficient of Passive Lateral Earth Pressure

written by: David Jr • edited by: Lamar Stonecypher • updated: 2/14/2011

Lateral earth pressure refers to lateral forces acting on a retaining structures or soil mass. The three conditions of lateral earth pressure are active earth pressure, passive earth pressure, and earth pressure at rest.

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    Lateral Earth Pressure

    Lateral earth pressure can be defined as the pressure exerted by the soil against a retaining structure on a surface of a surrounding soil mass. It can be classified as earth pressure at rest, active earth pressure, and passive earth pressure. When a soil mass pushes against a retaining structure, the pressure is known as active pressure. On the other hand, if the retaining structure pushes against the soil mass, the resulting pressure is known as passive pressure. Earth pressure at rest is where the retaining structure does not have any lateral movement.

    The shear strength of a soil mass is the resistance per area that the soil mass can offer to resist soil failure. Soil failure is where the shear stress exceeds the shear strength of soil and usually can cause a landslide. Shearing strength of soil is important in order to analyze soil stability problems such as bearing capacity, slope stability, and lateral earth pressure.

    Bearing capacity is the ability of soil to safely withstand loads placed on the soil from any engineered structure without undergoing a soil failure and settlements.

    Cohesive soil is a fine grained soil or simply known as clay soil. It can be sticky when moist and when it’s dry, it will become solid and is hard to break. Cohesive soil consists of clayey silt, sandy clay, silty clay, clay, and organic clay.

    Coefficient of passive lateral earth pressure on cohesive soil can be explained in a one single formula, which is

    Kp = 1 + sin φ / 1 – sin φ

    BW-SG-Coulomb 

    Image source = Bertbau

    Where φ is the angle of shearing resistance which can be acquired from the Mohr - Coulomb Failure Envelope.

    The passive earth pressure, pp at depth, H is given by

    pp = Kp.γ. H + 2.c.(Kp)0.5

    where “γ” is the saturated unit weight and “c” is the cohesion of clay. When the soil parameters (Kp, c and γ) are obtained and its value is put into the formula above, the passive earth pressure on cohesive soil can be acquired.

    Based on BS 8004:1986 Code of Practice for Foundations, for preliminary design purposes, the bearing capacity of cohesive soil consists of “very stiff bolder clays & hard clays” with bearing capacities ranging from 300 to 600 kN/m² (6266 psf to 12531 psf) , “Stiff clays” from 150 to 300 kN/m² (3133 psf to 6266 psf), “Firm clay” from 75 to 150 kN/m² (1567 psf to 3133 psf) and “Soft clays and silts” with less than 75 kN/m² (1567 psf) .

    Shear strength in cohesive soil can be expressed by the Mohr-Coulomb Strength Criterion

    S = c + σ. Tan φ

    Where S is the shear strength, “c” is the cohesion of clay, “φ” is the friction angle (or angle of shearing resistance) and σ is the normal stress. The values for these soil parameters, notably c, σ and φ can be determined from Mohr’s circle which is created using the data obtained from doing the following laboratory tests

    1. Direct Shear Stress

    2. Triaxial Compression Test

    3. Unconfined Compression Test

    When the values of these soil parameters are acquired and put into the formula mentioned above, the shear strength of clay can be obtained.

    One common disadvantage of cohesive soil or clay soil is that it is susceptible to water logging where the clay soil will retain water after rainy days and the soil tends to stay wet even when the water is drained out. When the soil finally dries out, usually on a hot day, it will become solid and is hard to break. Due to this inconsistency, clay soil is not suitable for almost any engineering purposes.

    Reference

    1. C. Venkatramaiah. Geotechnical Engineering (Revised Third Edition). NEW AGE INTERNATIONAL PUBLISHERS. 2006
    2. Rajapakse, Ruwan. Geotechical Engineering Calculations and Rules of Thumb. Elsevier Inc. 2008
    3. BS 8004:1996 Code of Practice for Foundation by British Standard Instittution
    4. Braja M. Das . Principles of Geotechnical Engineering (3th Edition.). Chris Carson.
    5. Wikipedia / Lateral earth pressure


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