Determination of the poroelasticity of shale

Shales play important roles in various civil, energy and environmental engineering applications. Shales are categorized as poroelastic materials due to their tight and very stiff structure, and reliable poroelastic properties are required when dealing with shales. This paper presents simple procedures to determine the poroelastic properties of rocks using oedometer and triaxial consolidation tests. The procedures, which avoid the difficulty to perform determination of the unjacketed bulk modulus of the rock minerals, are demonstrated on a North Sea shale. The experimentally obtained Biot coefficient α and the drained bulk modulus K of the shale range from 0.95 to 0.99, and from 0.17 to 2.00 GPa, respectively. The Biot coefficient α and the drained bulk modulus K values determined from the oedometer and triaxial tests are compared and show good agreement and consistency between the two test procedures. The Skempton’s coefficient B-value of the triaxial samples was also experimentally measured prior to the triaxial consolidation tests. The theoretically predicted B-value varies from 0.81 to 0.96 which is, on the average, only about 10% higher than the experimentally obtained B-value which range from 0.80 to 0.85.

     

Influence of different strain rates on hydro-mechanical behaviour of reconstituted unsaturated soil

The hydro-mechanical behaviour of a reconstituted unsaturated soil under different suctions and strain rates was studied through various rate-controlled unsaturated/undrained triaxial tests. The fully saturated reconstituted specimens were desaturated to four different initial suctions (s₀?=?0, 100 kPa, 200 kPa and 300 kPa) and then triaxially sheared (conventional triaxial compression) at three different strain rates in undrained conditions (\(\dot{\varepsilon }_{1} = 0.001\) h^?1, 0.01 h^?1, and 0.1 h^?1). The observed hydro-mechanical behaviour during shearing including the volumetric strain, deviatoric stress, degree of saturation and suction is presented and discussed in this paper. The results indicate that when the strain rate rises at the given initial suctions (or pore water pressures), the maximum deviatoric stress (q_max), critical net stress ratio (M) and critical state suction (s_c) increase but the degree of saturation (S_rc) and volumetric strain at the critical state (ε^c_v ) reduce. The critical effective stress ratio (M′) is not dependent on the strain rate for saturated and unsaturated samples. The critical state lines for unsaturated soils with the constant strain rates are parallel with each other in the e???lnp′ space.

     

吸力历史对非饱和土力学性质的影响

现在被广泛公认的由Fredlund提出的非饱和土力学的双参数理论,即净应力和吸力为非饱和土的应力状态变量,不能直接考虑吸力历史及其饱和度对非饱和土的应力-应变关系和强度的影响。非饱和土三轴试验结果表明,即使净应力和吸力相同的条件下,经过干-湿循环试样与未经过干-湿循环试样的应力比-应变关系和强度是不相同的。在其他条件相同时,经历过干-湿循环的试样比未经过干-湿循环试样的应力比-应变关系要高、强度大和体变小。经过干-湿循环试样的饱和度低而强度高,主要是由于经过先期较高的吸力,相当于受过较大的前期有效压力,使试样成为超固结土。更多不同吸力历史的对比试验有待于进一步研究,以便为非饱和土的水力-力学特性耦合弹塑性本构模型定量地表示上述非饱和土的性质提供基础性试验数据。     

非饱和土增湿变形的实用计算方法

非饱和土力学研究目前还未进入实用阶段,主要原因在于吸力量测困难。本文提出了用等效吸力代替真实吸力的试验方法。首先以常规静三轴试验得到的原状饱和土以及非饱和土的应力-应变曲线为基础,根据变形等效的原则确定与某一饱和度相当的围压即为等效吸力;然后建立饱和度与等效吸力之间的非线性关系,并验证了该数学公式的正确性;再根据试验结果分析含水量对非饱和土强度的影响,建立了非饱和土的实用抗剪强度公式;最后按照邓肯-张模型的参数整理方法得到了不同饱和度非饱和土的模型参数,探索这些参数随饱和度的变化规律,建立了引入饱和度的非饱和黄土实用非线性模型,并进行了降雨入渗情况下非饱和土增湿变形的计算。结果表明,饱和度最大值为95%,等效吸力最大值为160 kPa,最大水平位移与竖向位移分别为0.6 cm和20.0 cm,均出现在浸水位置。计算结果合理地反映了非饱和土变形的分布趋势,验证了方法的合理性。     

An advanced hydro-mechanical constitutive model for unsaturated soils with different initial densities

This paper presents an advanced constitutive model for unsaturated soils, using Bishop’s effective stress (σ′) and the effective degree of saturation (S_e) as two fundamental constitutive variables in the proposed constitutive model. A sub-loading surface and a unified hardening parameter (H) are introduced into the σ′–S_e modelling framework to interpret the effects of initial density on coupled hydro-mechanical behaviour of compacted soils. Compared with existing models in the literature, the main advantage of the proposed model that it is capable of modelling hydro-mechanical behaviour of unsaturated soils compacted to different initial densities, such as the dependence of loading–collapse volume on initial void ratio and density effect on the shearing-induced saturation change. The proposed model requires 13 material parameters, all of which can be calibrated through conventional laboratory tests. Numerical studies are conducted to assess the performance of the model for a hypothetical soil under two typical hydro-mechanical loading scenarios. The proposed advanced unsaturated soil model is then validated against a number of experimental results for both isotropic and triaxial conditions reported in the literature.     

Influence of matric suction on shear strength behavior of a residual clayey soil

In this paper, the shear strength with respect to the matric suction of unsaturated soils was studied. For this purpose, unsaturated triaxial testing procedures were applied to the undisturbed residual soil specimens. An apparatus for performing triaxial tests was designed and constructed. In the tests, matric suction was controlled by using the axis translation technique, and pore water volume changes were measured by means of a volume change transducer with 10⁻⁸ m³ sensitivity. The test results indicated that the matric suction contributes to the shear strength of unsaturated soil specimens, and this contribution called suction strength varies non-linearly with respect to the matric suction. The logarithmic model needing to know the air-entry value and the internal friction angle of a soil specimen for prediction of the suction strength were presented and compared with the test results. It was found that suction strength values predicted from the proposed model were in satisfactory agreement with the experimental results.     

Effect of degree of saturation on mechanical behaviour of unsaturated soils and its elastoplastic simulation

The two stress-state variable approach has been widely used in interpreting unsaturated soil behaviour. However this approach cannot take into account the effect of degree of saturation or water contents on the stress–strain behaviour and strength of unsaturated soils. The triaxial test results presented in this paper show that even if the same path of net stress and suction is followed, the stress–strain relation and strength are different due to different degrees of saturation. When other conditions are the same, the higher the degree of saturation for the soil sample is, the higher the stress ratio corresponding to a given axial strain will be. This effect can be modeled by using an elasto-plastic constitutive model coupling hydraulic and mechanical behaviour of unsaturated soils. Comparisons between the predicted and measured results are presented, which demonstrate that the model can quantitatively simulate the influence of the degree of saturation on stress–strain behaviour and strength of unsaturated soils.     

饱和度对非饱和土力学性质的影响

现在被广泛公认的由Fredlund提出的非饱和土力学的双参数理论,即净应力和吸力为非饱和土的应力状态量,不能直接考虑饱和度或含水率对非饱和土的应力-应变关系和强度的影响。在非饱和土三轴试验结果表明,即使在净应力和吸力路径相同的条件下,具有不同饱和度试样的应力-应变关系和强度也是不同的。其他条件相同时,试样饱和度越高,其应力比-应变关系曲线越高,强度越大。最新的水力-力学特性耦合的弹塑性本构模型可以定量地表示上述非饱和土的性质     

Improving a thermal conductivity model of unsaturated soils based on multivariate distribution analysis

Soil thermal conductivity (k) is a key parameter for the design of energy geo-structures, and it depends on many soil properties such as saturation degree, porosity, mineralogical composition, soil type and others. Capturing these diversified influencing factors in a soil thermal conductivity model is a challenging task for engineers due to the nonlinear dependencies. In this study, a multivariate distribution approach was utilized to improve an existing soil thermal conductivity model, Cote and Konrad model, by quantitatively considering the impacts of dry density (ρ_d), porosity (n), saturation degree (S_r), quartz content (m_q), sand content (m_s) and clay content (m_c) on thermal conductivity of unsaturated soils. A large database containing these seven soil parameters was compiled from the literature to support the multivariate analysis. Simplified bivariate and multivariate correlations for improving the Cote and Konrad model were derived analytically and numerically to consider different influencing factors. By incorporating these simplified correlations, the predicted k values were more concentrated around the measured values with the coefficient of determination (R²) increased from 0.83 to 0.95. It is concluded that the developed correlations with the information of different soil properties provide an efficient, rational and simple way to predict soil thermal conductivity more accurately. Moreover, the quartz content is a more important factor than the porosity that shall be considered in the establishment of thermal conductivity models for unsaturated soils with high quartz content.

     

干湿路径影响粉土小应变剪切模量的试验研究

天然土尤其是地表浅层土常处于非饱和状态,其小应变剪切模量是预测地基变形及土工结构物动力反应的一个重要参数。通过对非饱和压实粉土三轴样进行弯曲元试验,研究了吸力和干湿路径对其小应变剪切模量的影响。试验结果表明,非饱和压实粉土样的小应变剪切模量各向异性忽略不计;小应变剪切模量G0(vh)、G0(hh)和G0(hv)均随吸力增大而非线性增大;同一吸力下不同干湿路径上的土样,饱和度不同,其小应变剪切模量随饱和度升高而减小,主要原因是土的平均骨架应力和土中毛细水的作用。根据试验结果对非饱和土小应变剪切模量的半经验公式进行了改进,同时考虑了吸力与饱和度的作用。     

Coupled modelling of hydro‐mechanical behaviour of unsaturated compacted expansive soils

The Barcelona basic model cannot predict the mechanical behaviour of unsaturated expansive soils, whereas the Barcelona expansive model (BExM) can only predict the stress–strain behaviour of unsaturated expansive soils without the water‐retention behaviour being incorporated. Moreover, the micro‐parameters and the coupling function between micro‐structural and macro‐structural strains in the BExM are difficult to determine. Experimental data show that the compression curves for non‐expansive soils under constant suctions are shifted towards higher void ratios with increasing suction, whereas the opposite is true for expansive soils. According to the observed water‐retention behaviour of unsaturated expansive soils, the air‐entry value increases with density, and the relationship between the degree of saturation and void ratio is linear at constant suction. According to the above observation, an elastoplastic constitutive model is developed for predicting the hydraulic and mechanical behaviour of unsaturated expansive soils, based on the existing hydro‐mechanical model for non‐expansive unsaturated soil. The model takes into consideration the effect of degree of saturation on the mechanical behaviour and that of void ratio on the water‐retention behaviour. The concept of equivalent void ratio curve is introduced to distinguish the plastic potential curve from the yield curve. The model predictions are compared with the test results of an unsaturated expansive soil, including swelling tests under constant net stress, isotropic compression tests and triaxial shear tests under constant suction. The comparison indicates that the model offers great potential for quantitatively predicting the hydraulic and mechanical behaviour of unsaturated expansive soils. Copyright © 2011 John Wiley & Sons, Ltd.     

Some investigations to quantify hysteresis associated with water retention behaviour of fine-grained soils

The soil water retention characteristics curve (SWRC) has been reported to be quite useful for estimation of unsaturated soil properties. However, the uniqueness of SWRC is questionable due to hysteresis associated with the drying- and wetting-path SWRCs and this poses great challenge in utilising the SWRC for reliable estimation of unsaturated soil properties. Although hysteresis associated with SWRCs has been extensively studied for coarse-grained soils, due to limited studies on wetting-path SWRC for fine-grained soils, the hysteresis for fine-grained soils is not well understood. The present work attempts to address this gap, by studying the drying- and wetting-path SWRCs for eight different fine-grained soils by employing Dew point Potentiameter (WP4C®), Environmental Chamber and Controlled Water Sprinkling method. The study employs the concept of ‘Suction Hysteresis’, ψ_h, for quantification of hysteresis. Further, the influence of various soil-specific properties on the variation of ψ_h-water content relationship (viz., slope of variation of suction hysteresis, S_ψh) has also been studied and demonstrated. The findings of the study are quite encouraging and it has been realised that extensive studies on soils of different characteristics would be quite useful in quantifying the variation of SWRC during drying and wetting cycles.     

Influence of Infiltration of Sodium Chloride Solutions on SWCC of Compacted Bentonite–Sand Specimens

The degree of saturation of compacted bentonite buffer in deep geological repositories is subject to alterations from infiltration of groundwater and heat emanated from the waste canisters. The matric suction (ψ)–degree of saturation (S _r ) relations of unsaturated clays is represented by soil–water characteristics curves (SWCC) that are influenced by soil structure, initial compaction condition and stress history. Infiltration of groundwater besides increasing the degree of saturation can also alter the pore water chemistry; the associated changes in cation hydration and diffuse double layer thickness could impact the micro-structure and matric suction values. This study examines the influence of infiltrating sodium chloride solutions (1,000–5,000 mg/L) on the transient ψ–S _r relations of compacted bentonite–sand specimens. Analysis of the ψ–S _r plots, and X-ray diffraction measurements indicated that infiltration of sodium chloride solutions has progressively less influence on the micro-structure and SWCC relations of bentonite–sand specimens compacted to increasingly higher dry densities. The micro-structure and SWCC relations of specimens compacted to 1.5 Mg/m³ were most affected, specimens compacted to 1.75 Mg/m³ were less affected, while specimens compacted to 2 Mg/m³ remained unaffected upon infiltration with sodium chloride solutions.     

Predicting effective stress parameter of unsaturated soils using neural networks

In the effective stress equation for unsaturated soils proposed by Bishop, shear strength in these soils depends on the effective stress parameter, χ, a function of soil suction [1]. To estimate the shear strength of unsaturated soils, one must already know this parameter and its variation with soil suction. Though theories on the shear strength of unsaturated soils are consistent with experimental measurements, estimating the effective stress parameter directly from tedious laboratory tests is impractical. Thus, researchers have performed numerous intensive studies to effectively obtain the unsaturated shear strength using simplified empirical methods.This paper shows an adaptive learning neural network method for predicting this parameter, χ. The proposed network is a multilayer perceptron network with six neurons in the input layer representing the air entry value, the volumetric water content at residual and saturated conditions, the slope of soil water characteristic curve, the net confining stress and suction. The available literature uses a database prepared from triaxial shear test results to train and test the network. The results show the suitability of the proposed approach for estimating the effective stress parameter. Network analysis indicates that the χ-parameter depends strongly on the net mean stress.     

非饱和土的本构模型研究

引用平均土骨架应力的概念,研究推导出非饱和土的刚度参数随吸力变化而变化的关系式,进而推导得到用平均土骨架应力表述的非饱和土LC屈服面函数以及硬化规律。从土力学原理推导,得到土样由于在净应力和吸力作用下产生体积变形引起土样饱和度变化的关系式。由平均土骨架应力推广,得到三轴应力状态的椭圆屈服函数,这一非饱和土本构模型的优点在于考虑了应力作用后土样饱和度的变化,通过对已有试验数据的初步验证,表明提出的非饱和土本构模型的合理性和适用性。     

三门峡地区黄土状粉质黏土非饱和性质试验研究

以三门峡地区黄土状粉质黏土为研究对象,通过控制重塑土样的干密度及含水率制备不同状态下的试样,在改进的三轴仪上采用不排水试验法,分别对试样进行非饱和土三轴试验。试验结果表明,黄土状粉质黏土的基质吸力变化规律与土的基本状态有着密切关系,尤其是在相同含水率、相同围压、不同干密度的状态下基质吸力会随着饱和度的增加,出现先增后减的变化规律。通过单元土体中土颗粒组成的结构体参数,分析了这种变化规律。     

A bounding surface model for unsaturated soils considering the microscopic pore structure and interparticle bonding effect due to water menisci

The interparticle bonding effect due to water menisci plays an important role in the hydromechanical coupling properties of unsaturated soils. This paper presents an unsaturated hydromechanical coupling model that considers the influence of matric suction, degree of saturation, and microscopic pore structure on the interparticle bonding effect. The enhanced effective stress and bonding variable are selected as constitutive variables. The bonding variable is correlated with the ratio between unsaturated void ratio and saturated void ratio. The deformation characteristics of unsaturated soils are described based on the bounding surface plasticity theory. A soil–water characteristic model that considers deformation and hydraulic hysteresis is integrated into the constitutive model to achieve hydromechanical coupling. The proposed model can effectively describe the hydromechanical coupling characteristics and the meniscus bonding force of unsaturated bimodal structure soils; the model parameters can be easily obtained through routine experiments. The experimental results of unsaturated isotropic compression, the wetting/drying cycle, and unsaturated triaxial shear tests are used to validate the capability of the proposed model.

     

非饱和土中的饱和度的求解方法

探讨非饱和土的饱和度测量几种测量方法。由于非饱和土试验方法的不同,造成饱和度的测量的偏差。本文根据GDS的试验结果,对几种测量饱和度的方法进行比较和分析,指出假设土样颗粒体积不变,土样体积改变是因为土样孔隙大小的改变的合理性,认为直接法是一种有效的方法。     

Influence of frozen conditions on the oxygen diffusion coefficient in unsaturated porous materials

The efficiency of soil covers used as oxygen barriers to control the generation of acid drainage from sulfidic mine wastes can be evaluated in terms of the diffusive oxygen flux reaching the underlying wastes. Oxygen diffusion has been extensively investigated over the last few decades for unsaturated porous materials that are not frozen. However, little attention has been paid to materials that are fully or partially frozen, and thus, the diffusion of oxygen through soil covers during the winter freezing period has been generally neglected. This paper presents a laboratory method developed to evaluate the effective diffusion coefficient of oxygen (D_e) in frozen, inert materials. The method is a modified version of the conventional double-chamber cell in which the temperature and unfrozen volumetric water content of the sample are measured in addition to the more commonly monitored change in oxygen concentration. Several tests were conducted on non-reactive materials: that is, a sand at multiple degrees of saturation (S_r?=?20, 30, 39, and 42%), a silt (S_r?=?47%), and a mixture of the two (S_r?=?90%). Experimental data were interpreted using the POLLUTE code. Values of D_e for frozen materials were slightly lower than those obtained at ambient laboratory temperatures. In addition to the development of an empirical method for determining D_e, a preliminary model based on the model proposed by Aachib et al. (Water Air Soil Pollut 156:163–193, 2004) was created for the prediction of D_e in frozen materials by defining the involved parameters as temperature-dependent. The results indicate that predicated values of D_e are slightly higher than experimental values, suggesting that there remains room for improvement in the model.

     

Role of degree of saturation in denitrification of unsaturated sand specimens

Nitrate contamination of groundwater arises from anthropogenic activities, such as, fertilizer and animal manure applications and infiltration of wastewater/leachates. During migration of wastewater and leachates, the vadose zone (zone residing above the groundwater table), is considered to facilitate microbial denitrification. Particle voids in vadose zone are deficient in dissolved oxygen as the voids are partially filled by water and the remainder by air. Discontinuities in liquid phase would also restrict oxygen diffusion and therefore facilitate denitrification in the vadose/unsaturated soil zone. The degree of saturation of soil specimen (S _r) quantifies the relative volume of voids filled with air and water. Unsaturated specimens have S _r values ranging between 0 and 100 %. Earlier studies from naturally occurring nitrate losses in groundwater aquifers in Mulbagal town, Kolar District, Karnataka, showed that the sub-surface soils composed of residually derived sandy soil; hence, natural sand was chosen in the laboratory denitrification experiments. With a view to understand the role of vadose zone in denitrification process, experiments are performed with unsaturated sand specimens (S _r = 73–90 %) whose pore water was spiked with nitrate and ethanol solutions. Experimental results revealed 73 % S _r specimen facilitates nitrate reduction to 45 mg/L in relatively short durations of 5.5–7.5 h using the available natural organic matter (0.41 % on mass basis of sand); consequently, ethanol addition did not impact rate of denitrification. However, at higher S _r values of 81 and 90 %, extraneous ethanol addition (C/N = 0.5–3) was needed to accelerate the denitrification rates.