Instability Conditions of Loose Sand in Plane Strain J. Chu 1 and D. Wanatowski, A.M.ASCE 2 Abstract: When a loose sand specimen is loaded under an undrained condition, it may become unstable. The instability conditions may be specified by an instability line determined using undrained tests. However, the instability behavior of sand has seldom been studied under plane-strain conditions. Experimental data obtained under both triaxial and plane-strain conditions are presented in this paper to define the instability conditions of loose sand under plane-strain conditions. Using the state parameter, a unified relationship can be established between the normalized slope of instability line and the state parameters for both axisymmetric and plane-strain conditions. Using this relationship, the instability conditions established under axisymmetric conditions can also be used for plane-strain conditions. DOI: 10.1061/ASCE1090-02412008134:1136 CE Database subject headings: Laboratory tests; Liquefaction; Sand; Stress strain relations. Introduction It is well known that loose granular soil exhibits liquefaction behavior even under static load. It is also observed experimentally that sand can become unstable even before the stress state reaches the failure state. This type of instability has been observed to occur for saturated loose sand under undrained conditions Lade and Pradel 1990; Han and Vardoulakis 1991; Lade 1992; Leong et al. 2000 and for saturated medium to dense sand under strain path controlled conditions Chu 1991; Chu et al. 1993; Chu and Leong 2001. The term instability as used here refers to a be- havior in which large plastic strains are generated rapidly due to the inability of a soil element to sustain a given load or stress. In recent years, instability has been considered as one of the failure mechanisms that leads to flow slide or collapse of granular soil slopes in a number of case studies, e.g., Kraft et al. 1992, Lade 1992, 1993, Hight et al. 1999, Olson et al. 2000, and Sento et al. 2004. Although Hill’s postulate Bishop and Hill 1951; Hill 1958 has been used as a stability condition in plasticity, the violation of it does not always imply that a soil element is in an unstable condition, as experimentally demonstrated by Lade and Pradel 1990. Therefore, Hill’s postulate is only a necessary, but not sufficient condition for stability. It has been established by Lade 1992 that instability occurs when the stress ratio at the onset of instability is above the instability line. The instability line is defined as the line that separates potentially unstable stress states from stable stress states. Lade 1992 explains that the stress state at which instability would occur corresponds to the top of the current yield surface which is slightly before, but very close to, the top of the undrained effective stress path, as shown in Fig. 1. Therefore the instability line can be determined experimentally by a line connecting the peak of a series of effective stress paths obtained from undrained tests. For the sand studied in this paper, the instability line as determined using the undrained tests on loose sand is shown in Fig. 2. The critical state line CSL, which is also the failure line for loose sand as determined by drained tests, is also shown in Fig. 2. The region between the instability line and the failure line has been called the zone of potential instability Lade 1992. Other definitions similar to the instability line have also been given to specify the instability condition, such as the collapse surface by Sladen et al. 1985 and the state boundary surface by Sasitharan et al. 1993. However, the differences among the dif- ferent definitions are small, as pointed out by Lade 1993. The physical meanings behind the different interpretations are also essentially the same, i.e., to specify a yielding point where large plastic strains can develop Chu et al. 2003. It should be pointed out that the instability line is not unique, but varies with the void ratio of sand and the applied effective stresses. Fig. 3 shows the effective stress paths obtained from a series of isotropically consolidated undrained compression CIUC tests conducted on specimens with different consolidation void ratios, e c , under the same mean effective stress. It can be seen from Fig. 3 that the smaller the e c , the higher the instability 1 Associate Professor, School of Civil and Environmental Engineering, Nanyang Technological Univ., Blk N1, 50 Nanyang Ave., Singapore 639798 corresponding author. E-mail: cjchu@ntu.edu.sg 2 Lecturer, Nottingham Centre for Geomechanics, School of Civil Engineering, Univ. of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom. E-mail: dariusz.wanatowski@nottingham.ac.uk Note. Discussion open until June 1, 2008. Separate discussions must be submitted for individual papers. To extend the closing date by one month, a written request must be filed with the ASCE Managing Editor. The manuscript for this paper was submitted for review and possible publication on September 25, 2006; approved on May 11, 2007. This paper is part of the Journal of Geotechnical and Geoenvironmental Engineering, Vol. 134, No. 1, January 1, 2008. ©ASCE, ISSN 1090- 0241/2008/1-136–142/$25.00. Fig. 1. Location of instability line for loose sand Reprinted with permission from Lade 1992 136 / JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING © ASCE / JANUARY 2008