Analytical theory for one‐dimensional consolidation of clayey soils exhibiting rheological characteristics under time‐dependent loading

Abstract

SUMMARYThis paper presents analytical solutions to the one-dimensional consolidation problem taking into consideration the rheological properties of clayey soil under variable loadings. A four-element rheological model is introduced, and different loading types are involved, i.e. constant loading, one-step loading, triangular loading, rectangular loading, and isosceles-trapezoidal cyclic loading. The differential equations governing consolidation are solved by the Laplace transform. Based on the solutions obtained, the influences of the rheological parameters and loading conditions on the consolidation process are investigated. It has been shown that the consolidation behavior is mainly governed by four dimensionless parameters, a 1 , a 2 , b, and T v0 . Load shape has a great influence on the rate of consolidation. A decrease either in the modulus of the spring in the Kelvin body or in the viscosity coefficient of independent dashpot will slow down the rate of consolidation. An increase in the viscosity coefficient of the dashpot in the Kelvin body will make the rate of consolidation increase at an early stage but decrease at a later stage. For isosceles-trapezoidal cyclic loading, the consolidation rate in each cycle reaches a maximum at the end of the constant loading phase and the minimum at the end of this cycle.

Consolidation of viscoelastic soil by vertical drains incorporating fractional‐derivative model and time‐dependent loading

“…In these theories, the external loading was usually assumed to be applied instantaneously and kept constant throughout the consolidation process, but the time-dependent loadings (eg, multi-step and cyclic loadings) are more commonly encountered in practical engineering. 6 Schiffman 7 originally studied the consolidation problem involving the time-dependent loading. Subsequently, Olson,8 Leo, 4 and Zhu and Yin 9 dealt with the consolidation by vertical drains under ramp loading.…”

Analytical Solution for One-Dimensional Consolidation of Soil with Exponentially Time-Growing Drainage Boundary under a Ramp Load

“…Since Terzaghi [1] published his consolidation theory in 1925, noteworthy process has been achieved in consolidation theory. In order to accurately describe the soil properties, a considerable amount of scholars has made a great effort to build the governing equation of consolidation problem for soil according to different soil constitutive models, such as Terzaghi-Rendulic diffusion equation [2], three-dimensional Biot's consolidation equation [3], Maxwell model [4], Kelvin model [5,6], and Merchant model [7]. Considering the significant influence of initial condition on the consolidation process of soil, a large number of investigators have also proposed various solutions for onedimensional consolidation problem of soil under different loads, such as linear load [8], rectangular load [9], random load [10], cyclic loading [11][12][13], and ramp loading [13][14][15].…”

Modeling Effects of Clay Structure on Consolidation Behavior

“…The small strain governing equation for consolidation with Gibson-Lo model incorporated results in a set of set of governing equations (Gibson and Lo (1961) and Xie et al (2008)):…”