Revisiting the methods of determining hydraulic conductivity of saturated expansive clays in low-compressibility zone

Wei Su, Yu-Jun Cui, Feng Zhng, Weimin Ye

a Key Laboratory of Geotechnical and Underground Engineering of Ministry of Education, Tongji University, Shanghai, 200092, China

b Ecole des Ponts ParisTech, UR Navier/CERMES, 6-8, av. Blaise Pascal, Cité Descartes, Marne-la-Vallée, 77455, France

Keywords:Expansive clays Laboratory tests Hydraulic conductivity Terzaghi’s consolidation equation Modified effective stress

ABSTRACT The hydraulic conductivity of saturated clays is commonly determined either directly by monitoring water flux or indirectly based on Terzaghi’s consolidation equation.Similar results are generally obtained from the two methods, but sometimes a significant difference can be observed, in particular for expansive soils. In this study, the hydraulic conductivities determined by the two methods are first compared based on existing data in the literature. The indirect method is then revisited attempting to explain the difference identified. A modified effective stress, considering physico-chemical interaction between face-to-face oriented particles, is finally introduced to better describe the compressibility of expansive clays and to further improve the indirect method in determining hydraulic conductivity of such soils in the low-compressibility zone. Extra tests were performed on Gaomiaozi (GMZ) bentonite slurry and the results obtained allowed the modified indirect method to be verified.

1. Introduction

The hydraulic conductivity k is one of the key parameters in geotechnical and geo-environmental engineering. Many efforts have been devoted to the measurement of this parameter in both field and laboratory conditions. In the laboratory, the hydraulic conductivity is commonly determined either directly by monitoring water flux or indirectly based on Terzaghi’s consolidation equation. Tavenas et al. (1983) compared the direct and indirect measurement methods for natural clays and observed that the indirect method overestimated the values at relatively large void ratios while underestimated the values at smaller void ratios.They attributed the difference to the adopted assumptions of constant k,compressibility and coefficient of consolidation during each consolidation stage, as well as the ways of interpreting the consolidation-time curves on the basis of Terzaghi’s consolidation theory. Mesri et al. (1994) reported that the indirect method typically underestimates the value of permeability by a factor of 2.Therefore, in estimation of the settlement of Kansai International Airport Islands,the values of hydraulic conductivity of the involved Holocene marine clay determined by the indirect method were multiplied by 2 (Mesri and Funk, 2015).

This paper aims at better clarifying the indirect method of determining the hydraulic conductivity of expansive clays. First,reported k data for remoulded,undisturbed and compacted clayey soils, determined directly and indirectly in one-dimensional condition, were collected. Then, the parameters used for indirectly determining k were analysed one by one in order to better understand the difference between the direct and indirect methods.Thereby, the significance of physico-chemical effects between the bound water around clay particles in controlling the response of dense clay to external loading was identified. A modified effective stress concept based on this was postulated and introduced in the Terzaghi’s consolidation theory, aiming to narrow the difference between the direct and indirect methods. Finally, the modified method was verified based on existing data from the literature and complementary data from tests on Gaomiaozi (GMZ) bentonite.This study suggests the necessity of introducing the modified effective stress concept into the Terzaghi’s consolidation theory for active expansive clays in the low-compressibility zone.

2. Direct and indirect methods for k determination

Generally, in a conventional step-loading oedometer test,k can be indirectly calculated at each loading step based on Terzaghi’s consolidation theory as follows:

where cvis the consolidation coefficient(m2/s),mvis the coefficient of compressibility (kPa-1), γwis the unit weight of water (taken equal to 10 kN/m3in this study).

Parameter cvreflects the rate at which a saturated clay undergoes consolidation when subjected to an incremental load. In practice, the methods proposed by Casagrande and Fadum (1944)and Taylor (1948) are routinely used to estimate cvfrom the settlement-time curve at each loading step. It appears that this parameter shows mineral-dependence and varies with the stress state of soil(Retnamony et al.,1998;Sridharan and Nagaraj,2004).

At the end of a loading step i,with corresponding void ratio e,mvcan be determined as follows:

Meanwhile,at the end of each consolidation stage,the hydraulic conductivity k can be determined directly based on Darcy’s law by connecting the base of the soil specimen to a burette using falling head method or to a pressure/volume controller using constant head method (ASTM D5856,1993; ASTM D7100, 2011).

3. Comparison of the two methods based on the literature data

In this section, the direct and indirect results reported in the literature are collected and compared. The sources of data are summarized in Table 1. The reliability of indirect k values is evaluated by the ratio kd/kind, where kdand kindare the direct and indirect hydraulic conductivities, respectively. The kd/kindresults in the high-compressibility zone are plotted in Fig. 1, together with the e-log10σ′vcurves.It is observed that the values of kd/kindexhibit a large scatter. However, most of them are close to unity (mostly from 0.5 to 1.1).This suggests that at this stage,the indirect method is reasonably valid.Nevertheless,in the case where very high stress is applied and the soil compressibility changes to very small value,kd/kindturns to be much larger than unity (see Fig.1b and c), suggesting that the indirect method becomes less valid. Further examination of Eq. (1) shows that the reliability of indirect value k mainly depends on the accuracy of cvand mv. As pointed out by Tavenas et al. (1979), clays in the normally consolidated state exhibit significant variations in terms of cvand mvwith changes in void ratio. This is confirmed by the results of three bentonite specimens shown in Figs. 2 and 3: a decreasing trend is identified for cv(Fig.2)and mv(Fig.3).Tavenas et al.(1983)also reported that reduction of cvnear the drainage boundary is much faster than that in other parts of specimen. Obviously, this finding is contradictory to the assumption of constant cvat each loading step.Thereby,the indirect value k is affected by this assumption, explaining the fluctuation observed in Fig.1a.

Fig.1. Evolution of kd/kind during consolidation,together with the compression curves:(a)Slurry in the loading range of 1-2000 kPa;(b)Slurry in the loading range of 0.001-100 MPa; and (c) Compacted and undisturbed clays in the loading range of 0.01-100 MPa.

Table 1Main information of consolidation-permeability tests from the literature.

Fig. 2. Evolution of cv during consolidation of three bentonites, together with the compression curves: (a) Compacted GMZ bentonite; and (b) Kunigel bentonite slurry and Fourges slurry.

Fig. 3. Evolution of mv together with the compression curves: (a) Compacted GMZ bentonite; and (b) Kunigel bentonite slurry and Fourges slurry.

As the consolidation process steps into the low-compressibility zone, small strain is recorded and the variations in cvand mvbecome moderate (Figs. 2 and 3). These observations are more consistent with the Terzaghi’s assumptions, theoretically making this theory more applicable in this zone. However, it is observed that kd/kindstarts to be larger than unity (see Fig. 1b and c). It is commonly admitted that in this zone, all macro-pores have collapsed and further loading gives rise to compression of well orientated face-to-face particles.In such orientated microstructure,the physico-chemical interaction between clay particles and absorbed water is enhanced and starts to govern the global volume change behaviour of specimen (Cui et al., 2013). Mesri and Olson(1971) also pointed out that while investigating the hydraulic conductivity of soils, it is important to consider not only the mechanical variables (mainly the size, shape and geometrical arrangement of the clay particles), but also the physico-chemical variables (surface charge density and distribution, valence of the adsorbed cations as well as the properties of the involved fluid).From this point of view,the stress induced by the physico-chemical interactions should be accounted for when calculating the effective stress, which could impact the determination of mvby Eq. (2).

4. Introduction of a modified effective stress in the indirect method

For saturated soils subjected to an external loading, Terzaghi(1936) introduced an effective stress in form of Eq. (3) and stated that mechanical responds, such as compression, distortion and changes in shearing resistance, are exclusively due to changes in effective stress:

where σ′is the effective stress (ML-1T-2), σtis the total external stress(ML-1T-2),and uwis the pressure(ML-1T-2)of the free bulk water.

However, for expansive clayey soils, in addition to free pore water, there are another two kinds of water: (1) crystalline water which is strongly adsorbed and attached to clay sheets; and (2)double layer water which is well adsorbed to clay particles. Under mechanical loading, free pore water was compressed, generating pore water pressure. The dissipation of such pressure leads to the volume change of soil and this process is commonly known as soil consolidation. However, for the adsorbed water, the change of its pressure is controlled by the physico-chemical interactions between the bound water around clay particles and this pressure is interparticle distance-independent.

Depending on the circumstances, these two kinds of water pressures could act separately or together to control the volumetric behaviour of clayey soils. In consolidated clay with high compressibility, a large number of large pores exist and the drainage of “free” water in the large pores is responsible for the volume change. This is accompanied by the development of particles reorientation and thus the progressive enhancement of physico-chemical interactions between bound water and clay particles (Bolt, 1956; Maˇsín and Khalili, 2015); as the consolidation keeps proceeding in the low compressibility zone, the large pores disappear as all clay particles are normally well orientated, the“free” water is thoroughly drained out and all water can be considered as adsorbed water. Thus, the common pore water pressure can be taken equal to zero and the physico-chemical effects will control the response of the dense clay to applied loading.However, water can still flow under very high gradients (Pusch et al., 1987). In such case, the physico-chemical stress can be taken equal to the swelling pressure (Zhang, 2017).

Sridharan and Rao (1973) suggested accounting the electrical forces acting in the water-films around clay particles into the common Terzaghi’s effective stress equation. Lambe (1960)included the electrical attractive and repulsive forces between water-films around clay particles as follows:

where σsis the mineral to mineral contact stress(ML-1T-2),R is the total interparticle repulsion divided by total interparticle area(ML-1T-2), A is the total interparticle attraction divided by total interparticle area (ML-1T-2). R-A is a general term representing all possible attractive and repulsive stresses between clay particles.

By examining the effective stress in a stiff indurated clay rock theoretically and experimentally,Zhang(2017)concluded that in a dense clay-water system,the effective stress is transferred through the solid-solid contact between non-clay mineral grains and for the most part, the bound pore water in narrow pores, i.e.

where σlrepresents the average net repulsive force acting on the bound water-film area divided by the total cross-sectional area(ML-1T-2).The experimental results of Zhang(2017)suggested that for stiff indurated clay rock,the swelling pressure is almost equal to the effective stress. Maˇsín and Khalili (2015) referred the net electrical stress acting on water-films between clay particles as σR-Aand argued that this kind of stress mainly controls the mechanical behaviour of soils with prevailing face-to-face particle arrangement. In this regard,σland σR-Arefer to the same kind of stresses acting in the dense clay-water system.

Therefore, for the low-compressibility zone where the particle arrangement is dominated by the face-to-face feature,the termin Eq.(2)should be revisited.At each loading step,σR-Ais assumed to be equal to the swelling pressure Psat the corresponding density.The vertical effective stressat a given step i is determined by subtracting Ps,ivalue from the applied vertical stress σv,ibased on Eq. (6). Then, a newis determined using the modifiedfollowing Eq.(7).Thus,a modified indirect valuecan be further calculated by substituting the newin Eq. (1). With such modifications, the newis expected to be closer to the direct value.

It is worth noting that the modification is proposed by incorporating the physico-chemical effects into the effective stress equation for dense expansive clays. In other words, the proposed approach is an extension of Terzaghi’s consolidation theory.

5. Complementary experiment

To evaluate the validity of the proposed modification, an oedometer test was performed on GMZ bentonite slurry.The bentonite,originated from Inner Mongolia, China, is a Na+bentonite with a montmorillonite fraction of 75.4%. The total cation exchange capacity is 77.3 meq/100 g with 43.36, 29.14, 12.33 and 2.51 meq/100 g for Na+, Ca2+, Mg2+and K+, respectively. The bentonite powder,with particle sizes smaller than 0.2 mm and a solid particle density of 2.66 Mg/m3,has a liquid limit of 276%and a plastic limit of 37%.

The slurry was prepared by mixing de-aired distilled water with the bentonite powder to reach a water content of 1.5 times its liquid limit.Care was taken to avoid trapping air bubbles inside.After 24 h sealing for water homogenisation, the slurry was carefully poured into the oedometer cell with 50 mm inner diameter to the marked height of 30 mm.The oedometer has a steel porous disk and a filter paper previously placed at the base. Afterwards, a saturated filter paper, a steel porous disk and the piston were placed at the top of the specimen in sequence. The slurry was allowed to preconsolidate under a stress of 0.013 MPa, which corresponds to the piston weight. The positions of the piston during the preconsolidation were monitored using a cathetometer to determine the void ratio change.

When the pre-consolidation was completed,the oedometer cell was placed in a high-pressure load frame, which enables a maximum vertical pressure of 50 MPa to be applied on the specimen. More details about this loading system can be found in Ye et al. (2012). Conventional step loading was applied with ultimate load equal to 41.25 MPa.

The values of the coefficient of consolidation cvat the last three consolidation steps,where specimen was expected to be in the lowcompressibility zone, were estimated using Casagrande’s method for indirectly determining the hydraulic conductivity. Constant head permeability tests were also carried out after consolidation completion at these three steps under water injection pressure of 1 MPa, using a volume/pressure controller connected to the oedometer cell. In addition, swelling pressure tests using constantvolume method were performed on statically compacted GMZ bentonite specimens with void ratios taken from the compression curve.

6. Application to existing data

The attempts of introducing a modified effective stress to the indirect method are made on the tested GMZ bentonite slurry, as well as three bentonites in the low-compressibility zone from the literature.Results are summarised in Table 2 and graphically shown in Fig.4.It is worth noting that the values of swelling pressure Psof GMZ bentonite were deduced from the swelling pressure-dry density relationship determined by Ye et al. (2007), while those for Kunigel and Fourges bentonites were deduced from the correlations established by Wang et al. (2012) based on the literature data.All these swelling pressure-dry density expressions are given in Table 2.

As expected, since the external stress is partially supported by the physico-chemical forces between inter-particles, the modified compressibility coefficientincreases as less incremental stress is required to cause a certain decrease in void ratio in each loading step according to Eqs. (6) and (7). In other words, from the perspective of permeability, as compared to the circumstance before modification,it is easier for the specimen in loading step i to drain water with volume change of Δeisince less incremental effective stress is needed. Therefore, the modified indirect valueincreases and becomes much closer to the direct value kd,making a significant decrease ofratio.This,in turn,supports the idea of σR-A=Psin the case of compression of orientated faceto-face particles.Note that parameter cvis determined based on the settlement-time curves at each loading step using the common Casagrande’s method. As negligible free water is expected to be involved in the low-compressibility zone,the consolidation process must mainly depend on adsorbed water, thus physically muchmore complicated.However,as the void ratio changes a little in this zone,the values of cvshould change slightly too.This is evidenced by the similar cvvalues at different stresses for a given soil in Table 2. Further examination shows that the improvement of kd/k′indresults of GMZ bentonite, ranging from 1.2 to 1.9, is more significant than that of other soils ranging from 1.7 to 3.8(Table 2).It is basically due to the different accuracies of obtaining swelling pressures: tested on compacted specimens for GMZ bentonite slurry, deduced from different expressions by Ye et al. (2007) for compacted GMZ bentonite and Wang et al. (2012) for the rest two slurries. Furthermore, it is important to note that the swelling pressures used for the three slurries are determined/estimated from the experiments on compacted soils. As for GMZ bentonite,better improvement in kd/k′indis found in the compacted specimens than that in the slurry ones (see also Table 2), indicating that in highly compacted bentonite, the net stress σR-Aacting on waterfilms between clay particles is equal to its swelling pressure, and that it is necessary to determine the σR-Avalue in slurry at different void ratios. Better results of kd/k′indare expected when the σR-Ais obtained with the soils tested in slurry state.

Table 2Information of indirect k before and after modification.

Fig. 4. Comparisons of kind and modified k′ind, together with the compression curves:(a) GMZ bentonite; and (b) Kunigel bentonite slurry and Fourges slurry.

7. Conclusions

The data of hydraulic conductivity k of undisturbed,remoulded and compacted expansive soils, determined in the laboratory by direct and indirect methods,are collected and compared,showing that in the primary compression zone characterised by a high compressibility,the two methods give similar results;while in the low-compressibility zone, the indirect method gives much lower hydraulic conductivity value.

In the low-compressibility zone, cvis found to be almost constant and the difference between the direct and indirect methods is attributed to the effect of physico-chemical interaction.The results of the first attempt in consideration of a modified effective stress accounting for such interaction show that much closer hydraulic conductivity can be obtained between the direct and indirect methods, showing the relevance of such an approach.

It is worth noting that when directly measuring the hydraulic conductivity(kd),there must be a certain range of error in the test results even though the test is carried out by strictly following the testing standards.However,as the data obtained here are quite rich,showing the same variation trend,it is believed that this kind of test error does not affect the general conclusion drawn in this paper.More data about more expansive clays are of course needed to further verify this approach.

Declaration of competing interest

The authors wish to confirm that there are no known conflicts of interest associated with this publication and there has been no significant financial support for this work that could have influenced its outcome.

Acknowledgments

The authors wish to acknowledge the support of the European Commission by the Marie Sk?odowska-Curie Actions HERCULES -Towards Geohazards Resilient Infrastructure Under Changing Climates (Grant No. H2020-MSCA-RISE-2017-778360) and Shanghai Pujiang Talent Program (Grant No.18PJ1410200).

Notation

cvConsolidation coefficient

mvCoefficient of compressibility

m′vModified coefficient of compressibility

γwUnit weight of water

e Void ratio

σ′Effective stress

σvVertical total stress

σ′vVertical effective stress

σsMineral to mineral contact stress

R Total interparticle repulsion divided by total interparticle area

A Total interparticle attraction divided by total interparticle area

σlAverage net repulsive force acting on the bound waterfilm area divided by the total cross-sectional area

σR-ANet stress acting on water-films between clay particles

PsSwelling pressure

k Hydraulic conductivity

kd, kindHydraulic conductivity determined directly and indirectly