Viscoelastic–plastic constitutive model with damage of frozen soil under impact loading and freeze–thaw loading

doi:10.1016/j.ijmecsci.2021.106890

International Journal of Mechanical Sciences

Volume 214, 15 January 2022, 106890

https://doi.org/10.1016/j.ijmecsci.2021.106890 Get rights and content

Highlights

•
Experiments on frozen soil under impact and freeze-thaw loading were conducted.
•
The influence and mechanism of freeze-thaw loading on frozen soil was discussed.
•
The damage of frozen soil under freeze-thaw loading was analyzed.
•
A viscoelastic-plastic constitutive model with damage was established for frozen soil.

Abstract

This study aims to provide an understanding of the damage evolution and dynamic mechanical behavior of frozen soil under freeze–thaw (F-T) loading and impact loading. We used the split Hopkinson pressure bar (SHPB) device to evaluate the dynamic mechanical properties of frozen soil at different numbers and temperatures of F-T cycles. Our results indicate that the F-T process has a strong influence on the dynamic mechanical behavior of frozen soil. The peak stress of the frozen soil gradually weakens with an increase in the number of F-T cycles until the cycle number reaches the critical value for the steady state of the soil specimen (approximately 3–7 cycles). We observed a decrease in the peak stress of the frozen soil with a decrease in freezing temperature. We defined the F-T damage using wave impedance, which characterizes the microstructural properties of frozen soil, coupled it with the impact damage that satisfies the two–parameter Weibull distribution, and obtained the total damage of the frozen soil under F-T loading and impact loading. By combining the discretized Zhu–Wang–Tang (ZWT) model with the plastic theory that satisfies the Drucker–Prager (D-P) yield criterion, which is based on the improved hardening criterion with strain rate terms, we constructed a viscoelastic–plastic constitutive model with damage in frozen soil under F-T loading and impact loading. The results predicted by this model agree with the experimental data, validating its feasibility.

Abstract

This study aims to provide an understanding of the damage evolution and dynamic mechanical behavior of frozen soil under freezethaw (F-T) loading and impact loading.We used the split Hopkinson pressure bar (SHPB) device to evaluate the dynamic mechanical properties of frozen soil at different numbers and temperatures of F-T cycles. Our results indicate that the F-T process has a strong influence on the dynamic mechanical behavior of frozen soil. The peak stress of the frozen soil gradually weakens with an increase in the number of F-T cycles until the cycle number reaches the critical value for the steady state of the soil specimen (approximately 37 cycles). We observed a decrease in the peak stress of the frozen soil with a decrease in freezing temperature. We defined the F-T damage using wave impedance, which characterizes the microstructural properties of frozen soil, coupled it with the impact damage that satisfies the twoparameter Weibull distribution, and obtained the total damage of the frozen soil under F-T loading and impact loading. By combining the discretized ZhuWangTang (ZWT) model with the plastic theory that satisfies the DruckerPrager (D-P) yield criterion, which is based on the improved hardening criterion with strain rate terms, we constructed a viscoelasticplastic constitutive model with damage in frozen soil under F-T loading and impact loading. The results predicted by this model agree with the experimental data, validating its feasibility.

Graphical abstract

Introduction

The distribution of permafrost regions accounts for approximately 24% of the total land area of the world [1]. Frozen soil is a heterogeneous four–phase composite material composed mainly of soil particles, liquid water, ice particles, and gas [2]. Because of the existence of ice, the connection characteristics between each phase in the frozen soil change, resulting in very different mechanical properties compared to those of conventional soil. Moreover, as temperature easily affects the properties and states of ice or liquid water, the mechanical properties of frozen soil exhibit strong temperature sensitivity.

Engineers often use frozen soil as the base of a building and subject it to various mechanical loads. Many studies on the basic physical and mechanical properties of frozen soil under static or quasi–static loading and impact loading have been reported [3], [4], [5], [6]. The strain rate and temperature effects of frozen soil under impact loading have also been widely studied [7]. Several studies on the dynamic mechanical properties of frozen soil under impact loading have focused on the changes in frozen soil specimens and the differences in loading methods. The changes in frozen soil specimens include differences in the particle ratio, moisture content, and prefabrication defects [8], [9], [10]. The different loading methods mainly include uniaxial loading, confining pressure, dynamic and static combination of loading modes, and cyclic impact [11, 12]. Numerical simulations and constitutive modes of frozen soil under different loading methods have also been reported [13, 14].

Previous studies on frozen soil have mainly focused on the mechanical loading. However, the mechanical properties of frozen soil are also greatly affected by environmental loading, such as freeze–thaw (F-T) loading, there are few related studies. F-T loading, caused by the periodic phase change of moisture inside porous material, is a typical form of environmental loading for materials in cold regions [15], [16], [17]. Previous studies have reported that F-T loading resulting from changes in temperature has an important role in the performance deterioration of materials by damaging the material and aggravating the damage caused by mechanical loading [18, 19]. At present, the basic mechanical properties of some materials, such as concrete and asphalt mixture, under F-T loading have been explored. In addition, a series of constitutive models based on the basic theories of composite materials, damage mechanics, and thermodynamics and that reflect the mechanical behavior of materials under F-T loading have been established [20, 21].

Soil–based research has gradually recognized the importance of F-T loading. In many studies, it was found that repeated F-T loading resulted in changes in basic soil properties, including strength, stiffness, wave speed, permeability, and thermal conductivity [22], [23], [24], [25]. Konrad et al. [26] studied the microscopic structure and pore characteristics of soil under F-T loading and inferred that soil properties changed mainly because F-T loading changed the soil structure, destroying the bonding force between the soil particles and rearranging them, which ultimately led to changes in the basic physical properties of the soil. Wang et al. [27] argued that F-T loading does not affect the shape of the stress–strain behavior curves of soil. However, the number of F-T cycles greatly influenced the modulus of elasticity and failure strength, and the minimal values for both the modulus of elasticity and failure strength were frequently reached after the specimen was exposed to approximately 3–7 F-T cycles. Liu et al. [28] conducted a series of F-T loading experiments on the Qinghai–Tibet plateau silt and reported that the F-T loading greatly affected the internal friction angle and cohesion of silt. Some investigators have examined the effects of fiber-reinforced material on soil under F-T loading and noted that such materials have a significant enhancement effect on the mechanical properties of soil [29, 30].

Recently, several attempts have been made to study the mechanical properties of frozen soil under F-T loading. Zhou et al. [31] considered the mechanical property degradation of frozen soil under F-T loading and proposed a modified constitutive model for simulating the triaxial stress–strain characteristics of F-T loess. Fan et al. [32] comprehensively studied the coupled influence of the F-T procedure and stress conditions on the cyclic mechanical properties of frozen clay and presented an empirical formula to quantitatively characterize their effect on the permanent deformation of frozen clay. Previous studies on F-T loading have mostly focused on conventional soils and static conditions. However, in practical engineering, frozen soil in cold regions is often influenced by F-T loading and impact loading. Addressing the safety problems of frozen soil under the influence of F-T loading and impact loading is an urgent need, but largely underexplored.

Therefore, in this study, we tested the dynamic mechanical properties of frozen soil at different numbers of F-T cycles and temperatures. Initially, during the F-T cycle, we set the freezing temperatures at −15 °C, −20 °C, and −25 °C, and the thawing temperature at 5 °C; the number of F-T cycles was 0, 1, 3, 5, and 7. Then, we maintained the soil specimen at −25 °C for 12 h. Finally, we used a split Hopkinson pressure bar (SHPB) device to conduct an impact–loading experiment to obtain the dynamic stress–strain curve under the corresponding loading conditions. We defined the F-T damage using the wave impedance that can characterize the microstructural properties of the frozen soil; we then coupled it with the impact damage that satisfies the two–parameter Weibull distribution, and obtained the total damage of the frozen soil under the F-T loading and impact loading. We propose a viscoelastic–plastic constitutive model with damage in frozen soil based on the Zhu–Wang–Tang (ZWT) model and the plastic theory that satisfies the Drucker–Prager (D-P) yield criterion. This model can effectively reveal the damage mechanism of frozen soil under F-T loading and impact loading.

Section snippets

F-T loading experiment

The dry density of the soil used in the experiment was 1.6 g/cm³, and the granule distribution was based on a previous research [7]. The specimens were cylindrical with dimensions of ϕ30 × 18 mm, and their mass and moisture content were 26.455 g and 30%, respectively. We subjected the soil specimens to F-T cycle experiments using a MIT-80 L high- and low-temperature cycle testing machine, shown in Fig. 1.

Soil specimens can be frozen in open or closed systems. In an open system, when the

Viscoelastic–plastic damage constitutive model of frozen soil

The deformation of frozen soil during the impact process is the result of deformation and rearrangement of soil and ice particles under the action of an external force. Any deformation of frozen soil that adapts to the stress under the action of an external force cannot be completed instantaneously because of the long–chain structure connected between the soil and ice particles and the gradual nature of particle movement. Deformation goes through a series of intermediate states before it can

Determination of model parameters

The viscoelastic–plastic constitutive model proposed in this study contains 10 parameters. The damaged part includes the ratio of the transmission stress to the incident stress at the initial moment γ, the strain value corresponding to the peak stress ε_f, and the material parameters m that characterize the evolution of material damage. The constitutive model includes the cohesion c, internal friction angle φ, modulus of elasticity E₀, Poisson's ratio v, elastic constant E₂, relaxation time ϕ₂

Conclusion

In this study, the influence of the freezing temperature and the number of F-T cycles on the dynamic mechanical properties of frozen soil was identified by F-T and SHPB experiments. We defined the wave impedance of frozen soil as the F-T damage and analyzed the influence of F-T loading on the mechanical properties of frozen soil during the F-T process. Coupled with the impact damage, the total damage expression of frozen soil under impact loading and F-T loading was obtained. Based on the

CRediT authorship contribution statement

Bin Li: Investigation, Data curation, Formal analysis, Methodology, Writing – original draft, Writing – review & editing. Zhiwu Zhu: Conceptualization, Supervision, Funding acquisition, Project administration, Writing – review & editing. Jianguo Ning: Supervision, Formal analysis, Writing – review & editing. Tao Li: Supervision, Resources, Writing – review & editing. Zhiwei Zhou: Supervision, Project administration, Writing – review & editing.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

This work was supported by the National Natural Science Foundation of China (grant numbers 11672253 and 11972028), the Opening Foundation of the State Key Laboratory of Frozen Soil Engineering (grant number SKLFSE201918) and the Fundamental Research Funds for the Central Universities (grant number 2682018CX44).

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Viscoelastic–plastic constitutive model with damage of frozen soil under impact loading and freeze–thaw loading

Highlights

Abstract

Graphical abstract

Introduction

Section snippets

F-T loading experiment

Viscoelastic–plastic damage constitutive model of frozen soil

Determination of model parameters

Conclusion

CRediT authorship contribution statement

Declaration of Competing Interest

Acknowledgments

Int J Plast

Int J Plast

Int J Plast

Int J Mech Sci

J Mech Phys Solids

Cold Reg Sci Technol

Mech Mater

Int J Fatigue

Constr Build Mater

Cement Concrete Res

Cement Concrete Res

Constr Build Mater

Int J Fatigue

Cement Concrete Res

Soil Dyn Earthq Eng

Catena

Constr Build Mater

Eng Geol

Cold Reg Sci Technol

Cold Reg Sci Technol

Eng Geol

Cold Reg Sci Technol

Cold Reg Sci Technol

Cold Reg Sci Technol

Int J Impact Eng

Int J Impact Eng

Int J Mech Sci

Int J Impact Eng

J Mech Phys Solids

Int J Eng Sci

Constr Build Mater

Cement Concrete Res

Cement Concrete Res

Cold Reg Sci Technol