Figure 02: Variation of Lateral Earth Pressure Coefficients. The coefficient of lateral earth pressure, K, is defined as the ratio of the horizontal effective stress, σ’h, to the vertical effective stress, σ’v. All Rights Reserved. No files available for this topic. The equations for active and passive lateral earth pressure coefficients are given below. Lateral earth pressure is the pressure that soil exerts in the horizontal direction. The shear strength parameters of the soil being retained, The inclination of the surface of the backfill, The height and inclination of the retaining wall at the wall– backfill interface, The nature of wall movement under lateral pressure, The adhesion and friction angle at the wall–backfill interface. Lateral Earth Pressure There are 3 states of lateral earth pressure 1. Ka = Active Earth Pressure 3. It is the maximum lateral resistance that a given soil mass can offer to a retaining wall that is being pushed towards the soil mass. Depending on the lateral movement of the soil and the structure, they are categorized into three types. Generally instead of Ka, the horizontal part Kah is tabulated. Example 1: Rankine's lateral earth pressure with horizontal backfill (English units) Given: Height of earth at heel, H = 12 ft. Rankine considered soil in a state of plastic equilibrium and used essentially the same assumptions as Coulomb, except that he assumed no wall friction or soil cohesion. Fully Submerged Cohesionless Backfill: Figure 15.10(a) shows a retaining wall with a fully submerged backfill, with the groundwater table at the surface of the backfill. Eap acts at the same angle, but at one half the height. As these are rather expensive tests, empirical relations have been created in order to predict at rest pressure with less involved soil testing, and relate to the angle of shearing resistance. The actual earth pressure force Ea is the sum of a part Eag due to the weight of the earth, a part Eap due to extra loads such as traffic, minus a part Eac due to any cohesion present. You can This is mainly done considering the rotation of the structure with respect to the existing ground profile. Passive lateral earth pressures represent a limit state condition when in theory the retained soil has reached a failure limit. Kp = Passive Earth Pressure (Passive is more like a resistance) 10. These equations represent the total lateral earth pressure. Efferent literature can be found for calculating the earth pressure coefficients. OCR is the overconsolidation ratio and is the effective stress friction angle. pressure) to the lateral earth pressure. Friction angle of soil: 30 degree. That is, the soil is at the point of incipient failure by shearing due to unloading in the lateral direction. An illustration of differences between at-rest, active and passive states is given in At-Rest State article. Unit weight of backfill soil: g = 115 lb/ft 3. Eag acts on the wall’s surface at one third of its height from the bottom and at an angle δ relative to a right angle at the wall. That is, the soil is at the point of incipient failure by shearing, but this time due to loading in the lateral direction. This is mainly done considering the rotation of the structure with respect to the existing ground profile. Both the publications indicate methods of finding the earth pressure coefficients. Lateral Earth Pressure Coefficient Guide. Figure 01: Variation of Lateral Earth Pressure Coefficients. Lateral earth pressure coefficient are considered when earth retaining structures are designed. At rest lateral earth pressure, represented as K 0, is the in situ lateral pressure. The first term represents the non-cohesive contribution and the second term the cohesive contribution. Note that φ’ is the angle of shearing resistance of the soil and the backfill is inclined at angle β to the horizontal, For the case where β is 0, the above equations simplify to. Horizontal backfill. Coefficient of active earth pressure at rest, Source: 1. https://en.wikipedia.org/wiki/Lateral_earth_pressure, An example of lateral earth pressure overturning a, Soil Lateral Active Pressure and Passive Resistance. Earth pressure is the force per unit area exerted by soil. Earth pressure forces can be at-rest (Fig a), active (b) or passive (c). As indicated in figure 01 and figure 02, there should be a rotation to mobilize the pressure. In 1948, Albert Caquot (1881–1976) and Jean Kerisel (1908–2005) developed an advanced theory that modified Muller-Breslau’s equations to account for a non-planar rupture surface. Coulomb (1776)[5] first studied the problem of lateral earth pressures on retaining structures. The passive state occurs when a soil mass is externally forced laterally and inward (towards the soil mass) to the point of mobilizing its available full shear resistance in trying to resist further lateral deformation. According to the type of soil (sand and clay), we can find each coefficient from either the Coulomb method or the Rankine method. It should be noted that the design engineer should make sure the fully mobilization of passive pressure. Structural loads, structural analysis and structural design are simply explained with the worked example for easiness of understanding. Also, construction materials, shoring system design, water retaining structures, crack width calculations, etc. If you continue to use this site we will assume that you are happy with it. Requirement: Using Rankine's lateral earth pressure . For example, if the groundwater level is at a distance hwfrom the base of the wall as shown in Fig. For soils with cohesion, Bell (1915) developed an analytical solution that uses the square root of the pressure coefficient to predict the cohesion's contribution to the overall resulting pressure. The first term represents the non-cohesive contribution and the second term the cohesive contribution. At rest pressure. Geotechnical Engineering Group, UTM | Unsaturated Soil Mechanics (Malaysia). The method of calculating earth pressure coefficients for the Rankine method is elaborate here. The magnitude and distribution of lateral earth pressure This passive pressure failure limit is usually justifiable for design because the lateral displacements required to mobilize the passive conditions are very small. We use cookies to ensure that we give you the best experience on our website. Structural Guide © 2020. That is, the soil is at the point of incipient failure by shearing, but this time due to loading in the lateral direction. The first equation is for an active situation and the second for passive situations. To estimate K0 due to compaction pressures, refer Ingold (1979)[3]. Typical range of lateral earth pressure coefficients As these are rather expensive tests, empirical relations have been created in order to predict at rest pressure with less involved soil testing, and relate to the angle of shearing resistance. There are two commonly uses lateral earth pressure theories: Coulomb (1776) and Rankine (1857). Eac is generally assumed to be zero unless a value of cohesion can be maintained permanently. The active state occurs when a retained soil mass is allowed to relax or deform laterally and outward (away from the soil mass) to the point of mobilizing its available full shear resistance (or engaging its shear strength) in trying to resist lateral deformation.