A Quantification Model for the Structure of Clay Materials

Abstract

Background

In this paper, the quantification for clay structure is explicitly explained, and the approach and goals of quantification are also discussed. The authors consider that the purpose of the quantification for clay structure is to determine some parameters that can be used to quantitatively characterize the impact of clay structure on the macro-mechanical behaviour.

Methods

According to the system theory and the law of energy conservation, a quantification model for the structure characteristics of clay materials is established and three quantitative parameters (i.e., deformation structure potential, strength structure potential and comprehensive structure potential) are proposed. And the corresponding tests are conducted.

Results

The experimental results show that these quantitative parameters can accurately reflect the influence of clay structure on the deformation behaviour, strength behaviour and the relative magnitude of structural influence on the above two quantitative parameters, respectively.

Conclusions

These quantitative parameters have explicit mechanical meanings, and can be used to characterize the structural influences of clay on its mechanical behaviour.

Keywords

Clay materials Structure characteristics Mechanical behavior Quantification model

Introduction

Clay structure refers to the characteristics and arrangement of clay particles and pores and the interaction between these particles. The structure properties play an important role in clay materials, a concept that was first introduced by Terzaghi (1) and has served as the research core of clay mechanics in the 21^st century (2). It may ultimately be possible to predict the mechanical behavior of geotechnical materials in terms of the characteristics of the microstructure, although attaining this goal is difficult. Thus far, many scholars have made attempts to investigate the structure characteristics from the micro perspective. For example, Mitchell (3) and Osipov (4) systematically expounded upon the quantitative analysis for the microstructure of clay and rock and its controlling factors in detail; Gao (5-6-7) analyzed the microstructure of loess by scanning electron microscopy and explored the collapsibility mechanism of loess. Wang et al (8) proposed the quantitative evaluation index for the shape and orientation of microstructure units and the characteristics of pore structure elements based on SEM image processing technology. Cárdenas et al (9), Schäffer et al (10) and Taina et al (11) used many indicators to describe the pore system, such as diameter, volume, and size distribution through micro-morphological methods. Cohesive clays have complex structures; thus, it is complicated to quantitatively characterize their microstructures, and it is more complicated to use such quantitative parameters to characterize the mechanical behavior of the material. Facing this predicament, we cannot help but raise the following questions. What is the purpose of researching structure characteristics? What is the exact meaning of the quantification of clay structure characteristics? Finally, what is the aim of quantification? From the viewpoint of the authors, these are the most fundamental issues concerning structural characteristics research on clay, but regretfully, a consensus to these key problems has yet to be reached.

In this paper we explicitly explain the quantification of structural characteristics and analyze the goals and approaches of this quantification. Then, according to the system theory and by considering energy, a quantification model that can reflect both the deformation structural behavior and strength structural behavior is proposed, and experimental research is conducted to verify the model assumptions. The results illustrate that the three parameters in the model are easy to test, with clear physical meaning, and can accurately reflect the basic features of the influence of the clay structure on its mechanical properties.

New approach of quantification for clay structure

The exact meanings of quantification

The previous works that describe the quantification of clay structure characteristics were not straightforward. The limitations of the previous works can be classified into three groups. 1) The meaning of quantification was not explicit, as there were multiple objectives. For example, in some reports, the fabric of the geochemical material obtained from micro-images or the geometric features obtained from fractal dimension methods are deemed as the target of the quantification (12-13-14-15). 2) There is not much consideration on the characterization of the relation between the microstructure and the macro-mechanical behavior (16-17-18). 3) Only some specific variables are considered and quantified. For example, attention has mostly been given to the impacts of some specific variables (such as fabric features, pore distribution, pore size and particle size) on the macro-mechanical behavior (19-20-21). This leads to the following reasonable question under consideration: is it necessary to obtain these micro-parameters for the purpose of characterizing the impacts of structure on the macro-mechanical behavior? The answer is obviously no, although such micro-features and micro-parameters help explain the impacts of structure from the micro perspective.

In addition to the strong connections and linkages, high-strength clays often have stable particle arrangements; however, the high strength does not suggest that the clay has strong structural characteristics. The clay with strong structural characteristics is clay whose particle connections are strongly influenced by environmental factors, and whose particle arrangements tend to be unstable when losing particle cementation. For example, in some special clays (such as loess, soft clay, swelling clay and laterite), there are special particle arrangements or particle cements that interact with water, and such materials are considered as having strong structural characteristics, which means that their mechanical behavior is strongly influenced by their structural changes. The purpose of quantification for clay structures is to determine some parameters that can quantitatively characterize the impact of microstructure on the macro-mechanical behavior. In general, the stronger the structural characteristics are, the stronger the influence of clay structure on its mechanical behavior is, and vice versa.

Clay materials comprise a system that has complex mechanical behavior and is often subjected to changeable boundary conditions and environmental loads. In a complex system, it is almost impossible to specifically characterize the mechanical behavior using some specific microstructural factors. For example, it is difficult and inapplicable to use some locally structural factors to describe the mechanical behavior of a building, even if each microstructure of the building is completely known. There may be some parameters that can quantitatively characterize the mechanical behavior of the material; however, such factors are not the specific geometric parameters (such as particle sizes, particle shapes, pore sizes and pore distributions) (22, 23) or the abstract parameters extracted from these specific geometric parameters (such as fractal dimension parameters and information entropy) (24, 25). The parameters required for structural characteristic quantification should be macro parameters that can comprehensively reflect mechanical behaviors. Therefore, it would be more appropriate to establish quantification parameters on the basis of the specific geometric parameters.

The aim and approach of quantifying the clay structure should be to quantify the impact of structural characteristics, which is strongly influenced by the effects of environmental loads (such as loading, wetting and perturbation) on the macro-mechanical behavior. For a clay material that has particular structure and boundary conditions, the mechanical behavior of this material is therefore specific, and the purpose of quantification for structural characteristics is to quantify the impacts of the structure changes on the macro-mechanical behaviors, which are induced by environmental factors. In clay mechanics, there are some successful examples using parameters to reflect the influence of structural changes on macro-mechanical behaviors, such as the sensitivity ratio and the coefficient of collapsibility of loess. The key to the quantification of clay structural characteristics is to use some parameters to extract the interaction information between the structural characteristics and macro-mechanical behavior; thus, we can obtain the quantitative parameters that can characterize the comprehensive structural-mechanical effects. Rather than simply assessing the specific features of the microstructure and its changes, the appropriate path to research clay structure is to examine the mechanical effects caused by the clay structure and the changes in its structure. Fortunately, many scholars have recognized the profound meaning of clay structure quantification, e.g., studies on the comprehensive structure potential by Xie and Qi (26), the structural potential by Tang et al (27), the structural stress share ratio by Qin et al (28), the strain comprehensive structure potential by Luo et al (29), the stress comprehensive structure potential by Shao et al (30), and the void ratio structural parameter by Chen et al (31).

The goal of quantification

The mechanical effects of clay structure, including clay fabric and components, are mostly shown in the forms of inter-particle forces. The clay structure actually denotes its mechanical behavior; therefore, the goal of quantifying clay structure is to quantify the mechanical behavior of the clay structure. Thus, we need to determine some parameters that can quantitatively describe the clay structure and can characterize its influence on the mechanical behavior of the material. The mechanical effects of clay structure include the following two aspects: (1) the strength behavior, which mainly refers to the influences of the structure on the strength parameters, and (2) the deformation behavior, which mainly refers to the influences of the structure on the deformation parameters.

The term “clay structure” can be understood as the comprehensive characteristics of particle arrangements and particle linkages. In terms of mechanical effects, there are relations and differences between these two factors. The change of clay structure is merely the change of its comprehensive characteristics. The research of clay structure cannot focus on the description of the clay deformation and strength characteristics using only micro-morphology or mineralogical and chemical analysis results because these methods cannot comprehensively reflect the clay particle arrangement and cementation characteristics, and the results of this research cannot be conveniently explicated in the study of clay deformation and strength. From a more profound sense, these methods do not aid in the comprehensive characterization of clay in the two structural aspects of particle arrangement and cementation. Clay structure quantification requires the adoption of some macroscopic variables to characterize the influence of structural changes on the mechanic effects from one structural state to another structural state, including strength behavior and deformation behavior. This is the key and most important academic thought in the quantification process. In other words, if we choose the strength behavior and deformation behavior as the main objectives of such structural quantification, then the aim and approach of the quantification is more understandable and explicit. Thus, this practice should be the appropriate way in which we conduct clay structure quantification.

Quantification model for clay structure

According to the system theory, any system has a particular structure, and each type of structure contains a particular energy of its own. Therefore, we can investigate the clay structure by observing both the external influences (energy input) and the changes in mechanical behavior (energy output). The external influence-induced changes of the comprehensive characteristics of clay further affect the mechanical behavior of the system. Moreover, according to the law of energy conservation, the structural changes in clay certainly will consume a portion of energy. In other words, the input energy will induce changes in structure and, therefore, the changes in mechanical behavior. Based on the above deductions, in this paper, a quantification model for clay structure is proposed, and experimental studies are conducted.

The following situations are assumed to illustrate the quantification model. There is a clay specimen at a height of H and with an initial structure state of A₀ (Fig. 1A). When the specimen is subjected to an axial normal stress of σ, the clay structure changes to another state of A₁ (Fig. 1B); the compression deformation is S, resulting in a compression strain of e = S/H. According to the shear strain energy theory, the structure change induced by the normal stress indicates that some stain energy U_σ is absorbed by a unit volume of the clay, and U_σ in Figure 1 can be expressed as Eq. [1]:

Fig. 1

Schematic diagrams for the structure state and mechanical effects of clay.

U_{σ} = σ \cdot ε / 2

Thus, the change in the clay structure characteristics can be reflected by the stain energy U_σ.

Considering the Mohr-Coulomb strength criterion, the shear strength of clay can be expressed as:

τ = c + σ \tan φ

We further assume that shear tests are conducted on two clay specimens with structure states of A₀ and A₁ (Figs. 1C-D), and the test results are as follows: (1) shear failure occurs in each specimen when the shear stain is γ; (2) the shear strength of the specimens are t_fA and t_fB, respectively. In this case, the difference of the absorbed shear-strain energy Ut between these two specimens is:

U_{τ} = (τ_{f A} - τ_{f B}) \cdot γ / 2 = Δ τ \cdot γ / 2

Obviously, U_τ is attributed to the difference of the initial structure state of the specimens, which is induced by U_σ. The relation between these two parameters (i.e., the clay from structure states of A₀ to A₁) can be expressed as:

U_{τ} = N \cdot U_{σ}

Eq. [4] can be rewritten as:

N = [(τ_{f A} - τ_{f B}) \cdot γ / 2] / [σ \cdot ε / 2] = Δ τ / σ \cdot ε / γ

where N is a structural transition parameter (STP) used to characterize the difference in the mechanical behavior influenced by the structural transition of clay, which can also be used as a quantitative parameter to characterize the structural features from an energy perspective.

The external influences imposed on clay mass can be classified into the following three main types: the disturbance effect, external loading and wetting. To investigate the relation between these external influential factors and the clay structure and to adequately consider the structural strength behavior and structural deformation behavior, series tests were conducted on undisturbed clay, saturated and remolded specimens. All three specimen types were initially subjected to an axial compression stress σ, and then their shear strengths under shear stain γ were obtained. Therefore, the three corresponding structural transition parameters (N₀, N_s, and N_r) are:

N_{0} = Δ τ_{0} / σ \cdot ε_{0} / γ

N_{s} = Δ τ_{s} / σ \cdot ε_{s} / γ

N_{r} = Δ τ_{r} / σ \cdot ε_{r} / γ

where N₀, N_s, and N_r denote the STPs of the undisturbed clay specimen, saturated specimen and remolded specimen, respectively.

Two parameters are defined here. N_0r is defined as the ratio of N_r (STP of the remolded clay) to N₀ (STP of the undisturbed clay), and N_0s is defined as the ratio of N_s (STP of the saturated clay) to N₀, as expressed in Eq. [9] and Eq. [10]:

N_{0 r} = N_{r} / N_{0} = Δ τ_{r} / Δ τ_{0} \cdot ε_{r} / ε_{0}

N_{0 s} = N_{s} / N_{0} = Δ τ_{s} / Δ τ_{0} \cdot ε_{s} / ε_{0}

Furthermore, M(p, w) is defined as the product of N_0r and N_0s, as shown in Eq. [11]:

M (p, w) = N_{0 r} \cdot N_{0 s} = m_{d} \cdot m_{s}

m_{d} = ε_{r} \cdot ε_{s} / ε_{0}^{2}

m_{s} = Δ τ_{r} \cdot Δ τ_{s} / Δ τ_{0}^{2}

In this paper, m_d and m_s are called deformation structure potential (DSP) and strength structure potential (SSP), respectively; and their product M(p, w) is called the comprehensive structure potential (CSP). The expression of parameter m_d (in this paper) is similar to the parameter m_p by Xie and Qi (26), and this result indicates that both m_d and m_p follow the law of the conservation of energy and the system theory. Xie and Zhang (32) discussed whether the comprehensive structure potential can reflect the law of energy conservation, and the results in this paper provide an affirmative (yes) answer.

The parameters of m_d and m_s are used to characterize the deformation behavior and strength behavior, respectively. m_d, m_s and M(p, w) are functions of compression stress and water content; the magnitudes of m_s and m_d are 0<m_s≤1 and 1≤m_d<K (K is a particular value for a clay with a particular fabric and composition), respectively. A higher m_d indicates a greater DSP, which implies that the influence of clay structure on deformation behavior is stronger; however, a smaller m_s indicates a greater SSP, which implies that the influence of clay structure on strength behavior is stronger. The comprehensive structure potential M(p, w) is used to characterize the relative magnitude of the influence of clay structure on deformation behavior and strength behavior. A greater M(p, w) indicates a stronger influence of clay structure on deformation behavior, but a weaker influence on strength behavior, and vice versa.

Experiment

Material and methodology

All the clay samples used in the tests are composed of undisturbed red silty clay. The mechanical properties of the clay are as follows: a natural water content of 20.3%, a dry density of 1.47 g/cm³, a void ratio of 0.864, a relative density of 2.63, and a plastic index I_p of 13.6. The effective internal friction angle of 19° and the effective cohesion of 21.6 kPa are obtained by the direct shear test.

According to the method of sampling and sample preparation by Shao et al (30), by adopting the freeze-drying method (for protecting the natural clay fabric) and vapor adsorption method (curing in an airtight container for more than 48 hours), the undisturbed specimens and remolded specimens with different water contents are prepared. The diameter of the specimen is approximately 6.13 cm. The five different water contents are 5%, 10%, 20%, 30%, and 35%, i.e., all unsaturated.

According to Eq. [11], the specimens are initially subjected to axial compression stress in a confined compression test; then, direct shear tests are conducted on the specimens with different normal pressures. The five different normal pressures are 25 kPa, 100 kPa, 175 kPa, 325 kPa, and 425 kPa. The shear strain rate is approximately 0.2 mm/min.

Results and discussion

Variation in structure potential with compression stress

Figure 2 shows the variation in structure potential with normal stress. The water content of all the specimens are 10.2%. The DSP m_d decreases with the increase in normal stress (ignoring the small experimental error existing in the initial stage) and tends to be stable, and this variation tendency of m_d is similar to the result presented by Xie et al (33). These experimental results show that the impact of clay structure on the deformation behavior and strength behavior weakens with the increase in normal stress.

Fig. 2

Variation in structure potential parameters with normal stress.

The variation in structure potential shows that (1) in the initial region, the increasing compression stress will induce the redistribution and adjustment of clay particles, and thus the initial structure potential increases; (2) subsequently, M(p, w) decreases with increasing compression stress. This result indicates that when the clay is compacted under compression stress, the clay structure tends to reach a stable level as the compression stress increases. In other words, both the influences of clay structure on deformation behavior and strength behavior decrease with an increase in compression stress, but the decreasing rate of this influence on strength behavior is still smaller than that on deformation behavior.

Variation in structure potential with water content

Figure 3 shows the variation in structure potential with water content, and all the specimens are initially compacted under a vertical stress of 25 kPa. The result shows that the DSP m_d decreases but the SSP m_s increases with increasing water content; additionally, both of these two parameters tend to be stable. The value of CSP M(p, w) fluctuates around one, and this phenomenon implies that the clay structure characteristics synchronously influence both the deformation behavior and strength behavior as the water content changes; in other words, the magnitudes of these influences on these two behaviors decrease almost synchronously. The fact that water content strongly influences the parameters of structure potential confirms that water content (or moisture condition) is one of the most important components of the clay structure.

Fig. 3

Variation in structure potential parameters with water content.

Possible application in the constitutive relation

In this paper, the following issues require further discussion. (1) What are the rules of these three quantitative parameters (m_d, m_s and M(p, w)) on the clay constitutive relation? (2) What is the relation between the structure potential parameters and the inter-particle forces (the absorbed suction and particularly the structural suction)? Some scholars have attempted to introduce the structural parameters into a constitutive model of clay (34). Generally, the structural parameters are introduced into classical constitutive models, such as the double hardening model, the Cam Clay model and the Modified Cam Clay model. Kasama et al (35), Ortiz and Pandolfi (36) and Suebsuk et al (37) developed structural models based on the Modified Cam Clay model due to its simple pattern recognition. There have been increasingly more structural models applied due to the rapid advances in computer software (38, 39).

Conclusions

(1)

The quantification of clay structure refers to quantifying the impact of structural changes, which are induced by some external factors (such as loading, wetting and perturbation), on the macro-mechanical behavior of the material. Therefore, the goal of clay structure quantification is to determinate the parameters that can quantitatively characterize the influences of the structure on the deformation behavior and strength behavior of clay. Such explanation provides a more explicit approach for clay structure quantification. These quantitative parameters, combined with the existing mechanical property indexes or parameters (e.g., the compressibility coefficient, collapsibility coefficient, and expansion coefficient), are likely to be introduced to the constitutive models of clay.

(2)

Based on the law of energy conservation and the system theory, a quantification model involving three quantitative parameters (i.e., deformation structure potential m_d, strength structure potential m_s, and comprehensive structure potential M(p, w) is proposed. The parameters m_d and m_s are used to characterize the influence of clay structure on the deformation behavior and strength behavior, respectively. The parameter M(p, w) is used to characterize the relative magnitude of structural influence on the above two quantitative parameters. The similar results by Xie and Qi (26) confirm that the parameters proposed in this paper follow the law of energy conservation.

(3)

The experimental results demonstrate that these quantitative parameters can be obtained by simple laboratory tests. These quantitative parameters have explicit mechanical meanings, so they can be used to characterize the structural influences of clay on its mechanical behavior.

Footnotes

Financial support: The research described in this paper was financially supported by the National Natural Science Foundation of China (No.41572277 and No.41402239), the Specialized Research Fund for the Doctoral Program of Higher Education (No.20120171110031), the Natural Science Foundation of Guangdong Province, China (No. 2015A030313118).

Conflict of interest: None of the authors has financial interest related to this study to disclose.

References

Terzaghi

Erdbaumechanik. Vienna: Franz Deuticke 1925; 18-25. Available from: http://www.ejge.com/People/Terzaghi/Terzaghi.htm.

Shen

Mathematical model of structural characteristic of soil.

Chinese Journal of Geotechnical Engineering. 199618l95–97.

Mitchell

Fundamentals of soil behavior, 2nd ed.

New York:

John Wiley and Sons Inc. 1993;56-66.

Osipov

Physical-chemical fundamentals of soil micromorphology, Proceedings of the 6th Congress of the IAEG, Amsterdam, Rotterdam, August 1990, Balkema, paper 35-40.

Gao

Micro-structure classification and inundation of loess.

Science China. 1980121204–1208.

Gao

Micro-structure of Chinese loess.

Chin Sci Bull. 1980 20945–948.

Gao

Modern soil science, 2nd ed. Beijing: Science Press 2013;223-234.

Wang

Xiao

A quantitative study of the micro structure characteristics of soil and its application to the engineering.

Journal of Chengdu University of Technology. 2001 284148–153.

Cárdenas

Santiago

Tarquis

Losada

Borondo

Benito

Soil porous system as heterogeneous complex network.

Geoderma. 2010160113–21.

10.

Schäffer

Stauber

Mueller

Müller

Schulin

Soil and macro-pores under uniaxial compression.

I. Mechanical stability of repacked soil and deformation of different types of macro-pores. Geoderma. 20081461-2183–191.

11.

Taina

Heck

Elliot

Application of X-ray computed tomography to soil science: a literature review.

Can J Soil Sci. 20088811–20.

12.

Moore

Donaldson

Quantifying soil microstructure using fractals.

Geotechnique. 1995451105–116.

13.

Sun

On fractal structure of expansive soils in China.

Journal of Hohai University. 199726121–26 Available from: http://en.cnki.com.cn/Article_en/CJFDTOTAL-HHDX701.003.htm. Accessed May 2, 2016.

14.

Rui

Zhang

The variation of microstructure during soft soil solidification.

Earth Sci Front. 200071147–152 [In Chinese].

15.

Dong

Fractal models for the soil-water characteristics of unsaturated soils.

Rock and Soil Mechanics. 2002234400–405 Available from: http://en.cnki.com.cn/Article_en/CJFDTOTAL-YTLX200204002.htm. Accessed May 2, 2016.

16.

Shi

Quantitative assessment of changes of microstructure for clayey soil in the process of compaction.

J Geotech Eng. 199618457–62.

17.

Shi

Research on the analysis techniques for clayey soil microstructure.

Chinese Journal of Rock Mechanics and Engineering. 2001206864–870.

18.

Jiang

Shen

Microscopic analysis of shear band in structured clay.

J Geotech Eng. 1998202102–108.

19.

Xue

Mao

Fractal study on the microstructure variation of soft soils in consolidation process. China Civil Engineering Journal.

20061092–96.

20.

Wang

Deng

Huang

Quantitative analysis of microstructure of loess seismic subsidence.

Chinese Journal of Rock Mechanics and Engineering. 200726S13025–3031.

21.

Wang

Quantitative analysis of loess microstructure based on CT and SEM images.

Rock and Soil Mechanics. 2012331243–248.

22.

Zhong

Yuan

Microfabrics and constitutive relations of granular materials. Journal of Geotechnical Engineering.

1992 4S39–48.

23.

Xiong

Tang

Liu

Zhang

Using SEM photos to main the pore structural parameters of soil samples.

Earth Sci. 2007323415–419.

24.

Tao

Zhang

Zhuang

Zhang

A fractal model describing the relation between clay content and soil-water characteristic curve.

J Hydraul Eng. 2014454440–446.

25.

Xiu

Physical entropy, information entropy and their evolution equations.

Science in China. 200131177–84 Series A.

26.

Xie

Soil structure parameter and its relations to deformation and strength.

J Geotech Eng. 1999216651–656.

27.

Tang

Liao

Zhang

Structural entropy of soil and quantitative research for soil structure characteristics.

Chinese Journal of Rock Mechanics and Engineering. 200625101997–2002.

28.

Qin

Wei

Experimental study of the structural parameter of unsaturated loess.

Rock and Soil Mechanics. 201132S1265–269.

29.

Luo

Xie

Shao

Structural parameter of soil under complex stress conditions.

Chinese Journal of Rock Mechanics and Engineering. 200423244248–4251.

30.

Shao

Zhou

Long

Structural properties of loess and its quantitative parameter.

J Geotech Eng. 2004264531–536.

31.

Chen

Gao

Research on relationship between structure and deformation property of intact loess.

Rock and Soil Mechanics. 200627111891–1896.

32.

Xie

Zhang

Discussion on ‘Soil structure parameter and its relations to deformation and strength’.

J Geotech Eng. 2000224512–513.

33.

Xie

Zhu

Soil structure parameter and its relations to deformation and strength.

J Hydraul Eng. 199930101–5.

34.

Xie

Zhang

A constitutive law considering soil structural properties.

China Civil Engineering Journal. 200033435–41.

35.

Kasama

Ochiai

Yasufuku

On the stress-strain behavior of lightly cemented clay based on an extended critical state concept.

Soil Found. 200040537–47.

36.

Ortiz

Pandolfi

A variational Cam-clay theory of plasticity.

Comput Method Appl M. 200419327-292645–2666.

37.

Suebsuk

Horpibulsuk

Liu

Modiﬁed structured cam clay: a generalized critical state model for destructured, naturally structured and artiﬁcially structured clays.

Comput Geotech. 2010377-8956–968.

38.

Neher

Wehnert

Bonnier

An evaluation of soft soil models based on trial embankments. Computer Methods and Advances in Geomechanics.

Tucson, New Mexico 2001;1:373-378 07.-12.01.2001.

39.

Raisa

A study of geotechnical constitutive models using PLAXIS 2D.

ICE G&S Papers Competition. 2013 2013.