Equivalent-time-line Model of One-dimensional Shear Rheology for Clay

HU Ya-yuan1 XIE Jia-qi1

(1.Research Center of Coastal and Urban Geotechnical Engineering, Zhejiang University, Hangzhou, Zhejiang, China 310058)

【Abstract】In order to reveal the rheological characteristics for clay under variable shear stress, an elastic viscoplastic model of one-dimensional shear rheology was established. The shear strain rate was divided into elastic shear strain rate and viscoplastic shear strain rate by dint of the modeling ideas of equivalent time rheological model proposed by Yin and Graham. The elastic shear strain rate had no relation with loading path and was simulated by a non-linear function. As to the viscoplastic shear strain rate, the fundamental formula of viscoplastic shear strain, equivalent time and shear stress was deduced on the basis of Singh-Mitchell empirical formula of the creep rate under the action of constant shear stress. In terms of equivalent time method proposed by Yin et al., the relational expression was put into the empirical formula of the creep rate. Subsequently, the viscoplastic shear strain rate was obtained, taking shear stress and shear strain as variables. The sum of elastic shear strain rate and viscoplastic shear strain rate formulated the equivalent-time-line constitutive relation of one-dimensional shear rheology. The comparison was drawn among the multi-stage loading test of silt clay, the loading-unloading test of loess and the shear strain expressions of this constitutive relationship correspondingly to verify the applicability of this model under variable shear stress. The research results show that the prediction curves obtained by this model are in good agreement with the test curves of the multi-stage loading test and loading-unloading test, which indicates that the model has good applicability under variable shear stress loading. The good predictability of the model also shows that the equivalent time method used in this model is not only suitable for one-dimensional compressional rheology, but also applicable to one-dimensional shear rheology, which expands applied range of the equivalent time method.

【Keywords】 road engineering; shear rheological model; equivalent time method; shear rheology; Singh-Mitchell empirical model;


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    [1] SUN Jun. Rheology of Rock and Soil Materials and Engineering Application [M]. Beijing: China Architecture & Building Press, 1999 (in Chinese).

    [2] HU Ya-yuan, YANG Ping, YU Qi-zhi. Time Effect of Secondary Consolidation Coefficient of Over-consolidated Soil [J]. China Journal of Highway and Transport, 2016, 29 (9): 29–37 (in Chinese).

    [3] ZHU Yan-bo, YU Hong-ming. Empirical Unsaturated Creep Models for Weak Intercalated Soils of Badong Formation [J]. China Journal of Highway and Transport, 2016, 29 (4): 22–29 (in Chinese).

    [4] YIN Zong-ze. Geotechnical Principles [M]. Beijing: China Water & Power Press, 2007 (in Chinese).

    [5] VYALOV C C. Rheological Principle of Soil Mechanics [M]. Translated by DU Yu-pei. Beijing: Science Press, 1987 (in Chinese).

    [6] TANG Hai-ming, CAO Hui, ZHU Jin-sheng, et al. Cause Analysis and Thinking of Instability of a Deep Excavation in Tianjin Area [J]. Geotechnical Investigation & Surveying, 2010 (S1): 299–302 (in Chinese).

    [7] WANG Chang-ming, WANG Qing, ZHANG Shuhua. Creep Characteristics and Creep Model of Marine Soft Soils [J]. Chinese Journal of Rock Mechanics and Engineering, 2004, 23 (2): 227–230 (in Chinese).

    [8] XU Jin, ZHANG Jia-sheng, ZHAO Tong-shun, et al. Creep Triaxial Tests and Constitutive Model of Embankment Foundation Soil [J]. Journal of Central South University: Science and Technology, 2011, 42 (10): 3136–3142 (in Chinese).

    [9] KONG Ling-wei, ZHANG Xian-wei, GUO Ai-guo, et al. Creep Behaviour of Zhanjiang Strong Structured Clay by Drained Triaxial Test [J]. Chinese Journal of Rock Mechanics and Engineering, 2011, 30 (2): 365–372(in Chinese).

    [10] XIE Xin-yu, LI Jin-zhu, WANG Wen-jun, et al. Rheological Test and Empirical Model of Ningbo Soft Soil [J]. Journal of Zhejiang University: Engineering Science, 2012, 46 (1): 64–71 (in Chinese).

    [11] SINGH A, MITCHELL J K. General Stress-strain time Function for Soils [J]. Journal of the Soil Mechanics and Foundations Division, 1968, 94: 21–46.

    [12] MESRI G, FEBRES-CORDERO E, SHIELDS D R, et al. Shear Stress-strain-time Behavior of Clays [J]. Géotechnique, 1981, 31 (4): 537–552.

    [13] KONDNER R L. Hyperbolic Stress-strain Response: Cohesive Soils [J]. Journal of Soil Mechanics and Foundation Division, 1964, 89 (SM1): 126–127.

    [14] ZHU Hong-hu, CHEN Xiao-ping, CHENG Xiao-jun, et al. Study on Creep Characteristics and Model of Soft Soil Considering Drainage Condition [J]. Rock and Soil Mechanics, 2006, 27 (5): 694–698 (in Chinese).

    [15] LI Jun-shi, LIN Yong-mei. Singh-Mitchell Creep Model of Shanghai Very Soft Silt Clay [J]. Rock and Soil Mechanics, 2000, 21 (4): 363–366 (in Chinese).

    [16] WANG Chen, ZHANG Yong-li, LIU Hao-wu. A Modified Singh-Mitchell’s Creep Function of Sliding Zone Soils of Xietan Landslide in Three Gorges [J]. Rock and Soil Mechanics, 2005, 26 (3): 415–418 (in Chinese).

    [17] LU Ping-zhen, ZENG Jing, SHENG Qian. Creep Tests on Soft Clay and Its Empirical Models [J]. Rock and Soil Mechanics, 2008, 29 (4): 1041–1044, 1052 (in Chinese).

    [18] LIU Ye-ke, DENG Zhi-bin, CAO Ping, et al. Triaxial Creep Test and Modified Singh-Mitchell Creep Model of Soft Clay [J]. Journal of Central South University: Science and Technology, 2012, 43 (4): 1440–1446 (in Chinese).

    [19] WANG Peng-cheng, LUO Ya-sheng, HU Lian-xin, et al. Research on Triaxial Creep Characteristics and Models of Remolded Loess [J]. Rock and Soil Mechanics, 2015, 36 (6): 1627–1632 (in Chinese).

    [20] WANG Peng-cheng, LUO Ya-sheng, ZHANG Xidong, et al. Research on the Triaxial Creep Characteristics of Q3 Loess Under Loading and Unloading by Steps [J]. Chinese Journal of Underground Space and Engineering, 2014, 10 (6): 1273–1242 (in Chinese).

    [21] YIN J H, GRAHAM J. Viscous-elastic-plastic Modelling of One-dimensional Time-dependent Behavior of Clays [J]. Canadian Geotechnical Journal, 1989, 26 (2): 199–209.

    [22] YIN J H, GRAHAM J. Equivalent Times and One-dimensional Elastic Viscoplastic Modelling of Time-dependent Stress-strain Behavior of Clays [J]. Canadian Geotechnique Journal, 1993, 31 (1): 42–52.

    [23] YIN Jian-hua, ZHU Jun-gao. Elastic Visco-plastic Consolidation Modelling of Soft Clay [J]. Chinese Journal of Geotechnical Engineering, 1999, 21 (3): 360–365 (in Chinese).

    [24] ZHU Hong-hu, CHEN Xiao-ping, YIN Jian-hua. Creep-consolidation Coupled Finite Element Analysis of a Highway Embankment on Soft Ground [J]. Geotechnical Investigation and Surveying, 2009 (11): 23–27 (in Chinese).

    [25] ZHU G F, YIN J H. Elastic Visco-plastic Consolidation Modelling of Clay Foundation at Berthierville Test Embankment [J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2000, 24 (5): 491–508.

    [26] HU Ya-yuan. A 1-D Nonparallel Equivalent-time-lines Rheological Model for Clay [J]. Journal of Civil, Architectural & Environmental Engineering, 2012, 34 (2): 32–38 (in Chinese).

    [27] ZHOU Qiu-juan, CHEN Xiao-ping. Experimental Study on Creep Characteristics of Soft Soils [J]. Chinese Journal of Geotechnical Engineering, 2006, 28 (5): 626–630 (in Chinese).

This Article


CN: 61-1313/U

Vol 31, No. 02, Pages 289-297+318

February 2018


Article Outline


  • 0 Introduction
  • 1 Singh-Mitchell empirical formula
  • 2 Equivalent-time-line model of one-dimensional shear rheology
  • 3 Solutions of the model under single-stage and multi-stage loading conditions
  • 4 Parameters determination and model verification
  • 5 Conclusions
  • References