Analytical solutions of one-dimensional large strain consolidation of saturated and homogeneous clays K.H. Xie a , C.J. Leo b, * a Department of Civil Engineering, Zhejiang University, PR China b School of Engineering and Industrial Design, University of Western Sydney, Locked Bag 1797, Penrith South DC, NSW 1797, Australia Received 24 September 2003; received in revised form 17 February 2004; accepted 23 February 2004 Available online 7 May 2004 Abstract Fully explicit analytical solutions are developed for one-dimensional large strain consolidation in both thick and thin soil layers. Numerical examples are given and comparisons are made with the classical small strain theory. It is shown that, unlike the results in classical small strain theory, the average degree of consolidation defined by stress (i.e. U p Þ and that defined by strain (i.e. U s Þ in large strain theory are different. The magnitude of settlement predicted by large strain theory is found to be smaller while both the development of settlement and the dissipation of excess pore water pressure (as shown by U s and U p Þ are found to be faster than in small strain consolidation in the cases studied. Another interesting observation is that the discrepancy between large and small strain theories diminishes with reducing compressibility (i.e. increasing stiffness) of soil and decreasing magnitude of applied load. Ó 2004 Elsevier Ltd. All rights reserved. Keywords: Large strain; Consolidation; Clays; Saturated; One-dimensional; Soft soils 1. Introduction Over the last 30 years or more, a number of investi- gators (e.g. [1–3,5–7,9,11]) have advanced the theoretical development of one-dimensional large strain consoli- dation of soft soils. While analytical solutions have been developed for the classical one-dimensional small strain consolidation [4,8,10,13–16], it appears that none has been found for large strain consolidation. The aim of this paper is to present the development of fully explicit analytical solutions of one-dimensional consolidation in which the mechanics of large strain are explicitly taken into consideration. The organization of this paper is as follows. The un- derlying theory and equations governing one-dimen- sional large strain consolidation of saturated and homogeneous clays are introduced and presented in La- grangian and convective coordinates, these formulations have their origins in the work of Gibson et al. [5–7]. The general relationships in one-dimensional large strain consolidation of such variables as the effective vertical stress, static pore water pressure, total vertical stress are established, and the equation governing excess pore water pressure is deduced. Then fully explicit analytical solu- tions are developed for one-dimensional large strain consolidation. By way of numerical examples, the large strain consolidation behavior and its departure from conventional small strain theory are examined. 2. The theory for one-dimensional large strain consolida- tion 2.1. Coordinate systems Fig. 1 shows a saturated clay layer of initial thickness H with the bottom fixed and referenced to both the Lagrangian and the convective coordinate systems. The Lagrangian coordinate a and the convective coordinate n are measured downwards in the direction of gravity. The convective coordinate n has its origin at the initial * Corresponding author. Fax: +61-2-98525741. E-mail address: c.leo@uws.edu.au (C.J. Leo). 0266-352X/$ - see front matter Ó 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.compgeo.2004.02.006 Computers and Geotechnics 31 (2004) 301–314 www.elsevier.com/locate/compgeo