Example 1: Rankine's lateral earth pressure with horizontal backfill (English units) Given: Height of earth at heel, H = 12 ft. For example, if the groundwater level is at a distance hwfrom the base of the wall as shown in Fig. The ratio of horizontal to vertical stress is called coefficient of lateral earth pressure (K). Two of the more commonly used are presented below. have discussed in addition to other aspects. Depending on the rotation of the wall, the pressure coefficient varies. In addition, if the structure is not capable of moving(rotating) due to some obstruction (due to a floor, due to props or any other reason), we should consider the at-rest condition for the design. 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. Lateral Earth Pressure 0γ 2 0 1 2 0 2 1 P =P +P =qK H + H K At Rest q H z σh γ c φ K0 q K0 (q+γH) 1 2 P1 P2 P0 H/3 H/2 z' K0: coefficient of at-rest earth pressure The total force: σh =K σv′ +u 0 where K0=1−sinφ for normally consolidated soil 0 1 2 2 3 P H P P z + ′ = σv If the water table is located at depth z

Unit weight of backfill soil: g = 115 lb/ft 3. The limiting horizontal pressures at failure in extension or compression are used to determine the Ka and Kprespectively. At rest lateral earth pressure, represented as K0, is the in situ lateral pressure. 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. Earth Pressure At Rest At rest earth pressure occur when there is no wall rotation such as in a braced wall. You can In the case of a uniform pressure loading on a terrace above a retaining wall, Eap equates to this pressure times Ka times the height of the wall. Suggest one!

At rest lateral earth pressure, represented as K 0, is the in situ lateral pressure. Otherwise, Eap must be multiplied by cosθ cosβ / cos(θ − β). Terzaghi and Peck, in 1948, developed empirical charts for predicting lateral pressures. Figure 02: Variation of Lateral Earth Pressure Coefficients. Friction angle of soil: = 30 degree. Coefficient of active earth pressure3. Instead of evaluating the above equations or using commercial software applications for this, books of tables for the most common cases can be used. For the active pressure coefficient, the logarithmic spiral rupture surface provides a negligible difference compared to Muller-Breslau. These equations represent the total lateral earth pressure (not effective). Figure 01 and Figure 02 are extracted from different publications. 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. Passive lateral earth pressures represent a limit state condition when in theory the retained soil has reached a failure limit. There are many theories for predicting lateral earth pressure; some are empirically based, and some are analytically derived. The Rankine method is simple compared with the Coulomb method.

Retaining and sheet-pile walls, both braced and unbraced excavations, grain in silo walls and bins, and earth or rock contacting tunnel walls and other underground structures require a quantitative estimate of the lateral pressure on a structural member for either a design or stability analysis. Both the publications indicate methods of finding the earth pressure coefficients.

Friction angle of soil: 30 degree. Collapse of a building due to unsafe excavation, Unit weight of backfill soil:g = 115 lb/ft3, 1. determine Rankine total active force, Pa, at heel per foot width of wall, 2. determine Rankine's total passive force, Pp at toe per foot width of wall, Pa = gH2Ka/2 = 2760 lb/ft               (per one ft width of wall), Pp = gH2Kp/2 = 690 lb/ft               (per one ft width of wall). Element designs with notes and discussions have added to get comprehensive knowledge. H z γ c φ q γsat c φ GWT H1 Lateral earth pressure coefficient are considered when earth retaining structures are designed.

K for a particular soil deposit is a function of the soil properties and the stress history. As indicated in figure 01 and figure 02, there should be a rotation to mobilize the pressure. https://en.wikipedia.org/wiki/Lateral_earth_pressure, Geotropika – Ichitra 2019 Appreciation lucheon, Tips on Leadership, Teamworking and Communication- Survey Camp. Horizontal backfill, Unit weight of backfill soil: g = 115 lb/ft 3. If you continue to use this site we will assume that you are happy with it.