Lateral earth pressure
It is important because it affects the consolidation behavior and strength of the soil and because it is considered in the design of geotechnical engineering structures such as retaining walls, basements, tunnels, deep foundations and braced excavations.
The earth pressure problem dates from the beginning of the 18th century, when Gautier[1] listed five areas requiring research, one of which was the dimensions of gravity-retaining walls needed to hold back soil.
However, the first major contribution to the field of earth pressures was made several decades later by Coulomb,[2] who considered a rigid mass of soil sliding upon a shear surface.
Rankine[3] extended earth pressure theory by deriving a solution for a complete soil mass in a state of failure, as compared with Coulomb's solution which had considered a soil mass bounded by a single failure surface.
For loosely deposited sands at rest, Jaky[6][7] showed analytically that K0 deviates from unity with downward trend as the sinusoidal term of the internal friction angle of material increases, i.e.
Some researchers state, however, that slightly modified forms of Jaky's equation show better fit to their data.
For overconsolidated soils, Mayne & Kulhawy[15] suggested the following expression: The latter requires the OCR profile with depth to be determined.
To estimate K0 due to compaction pressures, refer to Ingold (1979)[16] Pantelidis[14] offered an analytical expression for the coefficient of earth pressure at rest, applicable to cohesive-frictional soils and both horizontal and vertical pseudo-static conditions, which is part of a unified continuum mechanics approach (the expression in question is given in the section below).
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.
That is, the soil mass is at the point of incipient failure by shearing due to loading in the lateral direction.
That is, the soil is at the point of incipient failure by shearing, but this time due to loading in the lateral direction.
Müller-Breslau (1906)[19] further generalized Mayniel's equations for a non-horizontal backfill and a non-vertical soil-wall interface (represented by an angle
Instead of evaluating the above equations or using commercial software applications for this, books of tables for the most common cases can be used.
Rankine's theory, developed in 1857,[3] is a stress field solution that predicts active and passive earth pressure.
It assumes that the soil is cohesionless, the wall is non-battered and frictionless whilst the backfill is horizontal.
In 1948, Albert Caquot (1881–1976) and Jean Kerisel (1908–2005)[5] developed an advanced theory that modified Muller-Breslau's equations to account for a non-planar rupture surface.
For the active pressure coefficient, the logarithmic spiral rupture surface provides a negligible difference compared to Muller-Breslau.
Mononobe-Okabe's[20][21] and Kapilla's[22] earth pressure coefficients for dynamic active and passive conditions respectively have been obtained on the same basis as Coulomb's solution.
The above coefficients are included in numerous seismic design codes worldwide (e.g., EN1998-5,[23] AASHTO[24]), since being suggested as standard methods by Seed and Whitman.
The various design codes recognize the problem with these coefficients and they either attempt an interpretation, dictate a modification of these equations, or propose alternatives.
made by AASHTO[24] and the Building Seismic Safety Council[27] return coefficients of earth pressure very close to those derived by the analytical solution proposed by Pantelidis[14] (see below).
Mazindrani and Ganjale[29] presented an analytical solution to the problem of earth pressures exerted on a frictionless, non-battered wall by a cohesive-frictional soil with inclined surface.
[29] Based on a similar analytical procedure, Gnanapragasam[30] gave a different expression for ka.
It is noted, however, that both Mazindrani and Ganjale's and Gnanapragasam's expressions lead to identical active earth pressure values.
Following either approach for the active earth pressure, the depth of tension crack appears to be the same as in the case of zero backfill inclination (see Bell's extension of Rankine's theory).
Pantelidis[14] offered a unified fully analytical continuum mechanics approach (based on Cauchy's first law of motion) for deriving earth pressure coefficients for all soil states, applicable to cohesive-frictional soils and both horizontal and vertical pseudo-static conditions.
are the effective elastic constants of soil (i.e. the Young modulus and Poisson's ratio respectively)
According to this Engineer Manual, an appropriate SMF value allows calculation of greater-than-active earth pressures using Coulomb's active force equation.
An exhaustive comparison of the earth pressure methods included in EN1998-5:2004 (use of Mononobe-Okabe method, M-O), prEN1998-5:2021 and AASHTO (M-O with half peak ground acceleration) standards, against contemporary centrifuge tests, finite elements, and the Generalized Coefficients of Earth Pressure[14] has been carried out by Pantelidis and Christodoulou.
[32] The latter include, among others, results from 157 numerical cases with two finite element programs (Rocscience’s RS2 and mrearth2d) and two different contemporary centrifuge test studies[33][34]
