# A Modified Plastic Burgers Model for the Non-Decaying Creep of Frozen Soils
###### Abstract  
A modified plastic Burgers model considering cohesion decay is proposed for frozen soils. A series of triaxial compression and creep tests were conducted on a kind of frozen silty clay for obtaining the model parameters. According to typical triaxial creep strain curves with only a decaying creep stage, a deformation parameter calibration method for a plastic Burgers model is proposed, and the validity of the method was further verified. When the original plastic Burgers model was incorporated with a cohesion decay function, it was shown that the successive development process of frozen soil creep strain from the decaying to non-decaying stage could be described reasonably. The modified model is applicable to frozen ground engineering cases with non-decaying creep involved. frozen soils; creep model; parameter calibration method; non-decaying creep pacs: 04.70.  
and then sharp increase [16; 17]. The empirical model works facilitate the understanding on the creep behavior of frozen soils, while the limitation of empirical data fitting reduces their applicability in universal stress states. For creep problems under complex stress conditions, theoretical creep models of frozen soils are proposed, with the aid of a conventional soil mechanics framework. Up to now, the available frozen soil theoretical creep models can be generally categorized as microscopic thermodynamic models, viscose-elastic-plastic models, hyperplastic models, hypoplastic models and mechanical elements models [18; 19; 20; 21; 22; 23]. Among them, mechanical elements models have been intensively developed due to their simple model structure and easy of use in engineering applications. In the framework of the frozen soil element creep models, three basic mechanical elements, i.e., the Hookean spring, Newtonian dashpot and Saint-Venant's slider, are composed of certain forms to simulate different creep strain development tendencies, by considering the mechanical characteristics of frozen soils [24]. Based on CT scanning digital images of frozen silty samples, [PERSON] et al. [25] defined a damage variable and modified [PERSON]'s model to simulate the random distribution of inner flaws in the creep process. Considering the non-linear influence of confining stress on the shear strength of frozen soil, [PERSON] et al. [26] incorporated a parabolic yield function into a Bingham body composed of a Kelvin and Maxwell body in series to simulate the decay process of a frozen silty clay. To describe the creep strain as being further reasonably involved with the non-decaying process, functional multipliers based on a microscopic point of view were defined and incorporated into the elementary creep models. According to the phenomenon that cementation between frozen soil particles becomes weakened with an increase in temperature, stress and time, a breakage ratio was defined and embedded into a Burgers model [27]. It was shown that the non-decaying creep process of a frozen silty clay can be reasonably described when the long-term strength is lower than the current stress level. Based on fractional calculus theory, fractional derivative multipliers were embedded into the Nishihara model to describe the non-decaying creep development due to microscopic damage accumulation under constant overloading [23; 28]. From the above elaboration, it is indicated that with different composing forms of mechanical elements and taking the mechanical property degradation of frozen soils into account, the frozen soil creep process under different conditions can be well described. However, among the previous elementary model works, few have been able to provide a clear calibration method for obtaining the elementary model parameters. Most of the model parameters were determined by the so-called 'trial and error method' [25; 27], which reduces the models' reliability to some extent. Moreover, it has been proven that the involvement of the non-decaying creep process is due to the continuous degradation of the frozen soil strength under constant stress conditions [6; 22].