Based on the concept of generalized plasticity, this study proposes a constitutive model for describing the time-dependent behavior and wetting deterioration of sandstone. The proposed model (1) exhibits nonlinear elasticity under hydrostatic and shear loading; (2) follows the associated flow rule for viscoplastic deformation; (3) adopts a creep modulus that varies with stress ratios; and (4) considers the primary and secondary creep behaviors of rock. This model requires 13 material parameters, comprising 3 for elasticity, 7 for plasticity, and 3 for creep. The proposed model is first validated by comparing the triaxial tests of sandstone under different hydrostatic stress and cyclic loading conditions. Then, it is versatile in simulating the time-dependent behavior through a series of multi-staged creep tests.
The theory of generalized plasticity was first introduced by Zienkiewicz and Mroz (1984) to simulate the soil behavior and later elaborated by Pastor and Zienkiewicz (1986) and Pastor et al. (1990). Compared with other plastic models, this theory does not explicitly define yield and plastic potential surfaces. Instead, this theory adopts the gradients to the above functions so that simple models within this framework can account for material behavior response under loading. The generalized plasticity allows for plastic deformation at any stress level regarding the stress increment in both loading and unloading conditions. These features offer the advantages of the generalized plasticity model to predict the stress–strain behavior of many soil types with good accuracy under various types of loading. Researchers have recently developed many constitutive relations based on this framework to describe more sophisticated features of soil behavior, including anisotropy (Pastor, 1991), unsaturated conditions (Manzanal et al., 2011a), the degradation phenomena (Fernandez Merodo et al., 2004), and the effects of stress level and densification on sand (Ling and Liu, 2003; Manzanal et al., 2011b).
Other than soils,Weng and Ling (2012) adopted the generalized plasticity concept with nonlinear elasticity for rock behavior. The proposed model produces reasonable predictions on the elasto-plastic deformation of sandstone under various stress paths, cyclic loadings, and post-peak behavior. In addition to the simulation on the immediate deformation of rock, the time-dependent deformation (i.e., creep deformation) of rock is also a major concern in engineering practice (Cristescu, 1989; Sterpi and Gioda, 2009; Weng et al., 2010). According to previous studies on the creep deformation of sandstone (Tsai et al., 2008; Weng et al., 2010), the viscoplastic flows indicate that the viscoplastic potential surface has a similar shape to the plastic potential surface, but the size of the viscoplastic potential surface changes with time. However, the plastic potential surface has a time-independent size. Meanwhile, through the calculation of irreversible work, direct evidence of orthogonality between the yield surface and the plastic flow, as well as the viscoplastic flow, is observed. Thus, it is reasonable to state that the yield surface, the plastic potential, and the viscoplastic potential all have the same geometry. Consequently, the associated flow rules are applicable to modeling the time-dependent deformational behavior of sandstone.