Lateral squeezing effects on cement-slag-bentonite slurry wall performance

Cement-slag-bentonite (CSB) slurry walls as nonstructural barrier techniques have been widely employed to decrease contaminants’ migration into the groundwater stream. Within this area of consideration, a proper estimation of the wall permeability is an important parameter for the slurry wall design. For groundwater control applications, a permeability of 1×10^-9 m/s is specified for CSB slurry walls, although a permeability of 1×10^-8 m/s or higher would be sufficient for most remediation applications [1]. Even though the self-hardening property of the CSB mixture exerts effects on permeability reduction, several studies have also shown that permeability decreases as the weight of the joint increases [2-4]. Consequently, an appropriate prediction of the lateral earth pressure development within the slurry wall is important. The hypothesis of the lateral squeezing modeling was initially proposed by Filz [5], and this method for modeling was then developed by many researchers considering the arching and squeezing effect for deep trenches [6-8].

Observations differ for the analysis of the mechanism; however, the results of all approaches indicate that the stress state in the trench (below the depth of 5–7 m) remains lower than the geostatic approach. It has been suggested that the major principal stress in deep-narrow slurry walls is horizontal, and it is vertical in shallow-wide slurry walls [5, 9, 8]. However, the specific mechanism behind the lateral squeezing models [9, 5] has not been fully addressed for modeling of one sort or another. Proposed theories are based on the assumption that either the earth pressure coefficient is in the at-rest condition for surrounding soils or neglects the down-drag force between the mixture placements and completed consolidation.

This paper describes a model to estimate effective stress in CSB slurry walls employed at 7 days and 28 days of curing ages based on laboratory consolidation and index tests. To consider both arching and lateral squeezing mechanisms, the method provided by Li et al. [6] is used to obtain major principal stress (horizontal stress) with depth. Earth pressure transition from at-rest to the active condition presented by Bang and Kim [10] is then applied to evaluate minor principal stress (vertical stress). Then, the permeability of the wall can be predicted based on obtained stresses at a given curing age and compared with those achieved in the laboratory for the same stress values.

To identify the stress-state in a CSB slurry wall, two different mixtures with 20% of cementitious material mixed with 80% of the bentonite-water slurry are used. For the first mixture, ground granulated blast furnace slag (GGBS) is replaced with 50% cement type I by dry weight to make up the 20% of cementitious material. In this mixture, the bentonite-water slurry contains 5% of bentonite mixed into distilled water to make up the 80% batch slurry which is allowed to hydrate for one week. Hence, one kilogram of this mixture comprises the following: 100 g cement, 100 g GGBS, 40 g bentonite, and 760 g distilled water (C50-S50-B5). In the second mixture, 5% lime is employed for the cementitious mixture mentioned above and replaced with a 5% portion of GGBS as well as increasing the bentonite content of the batch slurry to 9%. Consequently, one kilogram of this mixture includes the following proportions: 100 g cement, 90 g GGBS, 10 g lime, 72 g bentonite, and 728 g distilled water (C50-S45-L5-B9). The following chemical reactions are expected among the materials in the mixture. The lime in a hydrated form (Ca(OH)₂) reacts with the montmorillonite structure containing alumino-silicates and also reacts with GGBS, which is a pozzolanic material and has CaO, SiO₂, and Al2O₃. These silica and aluminum particles react with lime in a hydrated structure to form calcium silicate hydrate (CSH), calcium aluminate silicate hydrate (CASH), and calcium aluminate hydrate (CAH), which are separated into gap minerals in response to calcium particles. CSA and CAH are cementitious objects, such as those in the form of a Portland concrete grid (3CaO·SiO₂, 2CaO·SiO₂, 3CaO·Al₂O₃, 4CaO·Al₂O₃·Fe₂O₃). The matrix formed is permanent. The state of stress in slurry walls depends on inward pressure from adjacent soils and the weight of the wall [5, 11]. A two-dimensional CSB slurry wall, with width and depth of B and H, respectively, surrounded by submerged medium dense sand, is investigated in this paper. It is assumed that the mixture placed into the trench along with the surrounding soils is homogeneous and isotropic, and the groundwater table is at the surface [5-8]. Since the horizontal strain of mixtures after placement is expected to be zero, the geometry of the problem is identified as plain-strain. Subsequently, in this two-dimensional coordinate system, inward horizontal deformation is assumed to be positive, and the ground surface is indicated as the origin of z (Figure 1). Consequently, in the following problem, the longitudinal direction implies the transverse direction. Once the fresh mixture is placed, it is assumed that the pore water pressure u=γ_wz+γ′_csbz carries the self-weight of the CSB at depth z of the wall and at excess pore water pressure u_e = γ′,_csbz, where γ_w and γ′_csb are the unit weight of water and floating unit weight of CSB, respectively, and the vertical and horizontal effective stress in the wall is σ′_h=σ′_v=0. During the consolidation procedure, the pore water pressure is intended to decline to hydrostatic pressure, and the magnitude of effective stresses need to be specified.

Figure 1:

According to Filz [5], inward displacement of the trench sidewalls should take place to keep horizontal stress equilibrium applied to the sidewalls. Alternatively, the interface frictional stress τ between the trench wall and adjacent soil during the consolidation procedure [3, 6, 7] follows the Mohr-Coulomb strength criterion as 1 τ=C′in+σ′htan∅′in $${\rm{\tau }} = {{\rm{C}}^\prime }_{{\rm{in}}} + {{\rm{\sigma }}^\prime }_{\rm{h}}\tan {\emptyset ^\prime }_{{\rm{in}}}$$ where C′_sin and Ø′_in are the solidity and internal in friction angle of the sidewall interface, respectively, and as mentioned by Potyondy [12], the relationship is as follows 2 C′in=RC′CSB and 3 tan∅′in=Rtan∅′in where C′_CSB, Ø’_CSB, and R are the cohesion, internal friction angle, and shear strength reduction factor of the cured wall, respectively. It is assumed that effective horizontal stress at the ground surface and the top of the CSB wall is σ′_h = 0 at z = 0. A model proposed by Li et al. [6] for a lateral squeezing effect caused by the inward displacement of side walls is 4 σ′h=Bγ′CSB2tan∅′in(1+A−2c′inBγ′CSB)×[ 1−exp(−2tan∅′inBDz) ] where the coefficient of A and D can be outlined as 5 A=2Eυ(1+υ)BK so that 6 D=1−υυ+A

According to Das [13], an elastic medium of soils can be expressed as a series of infinitely elastic springs (Figure 1), and the subgrade module for cohesive soils at depth z can be characterized as 7 kz=nhz where n_h is the constant of modulus of horizontal subgrade reaction. As reported by Filz [5], the following relationship between vertical and horizontal effective stress in the lateral squeezing model is 8 σ′v=kmσ′h where k_m is the coefficient of lateral earth pressure employed into the trench wall. The conventional consideration is that there is no need to evaluate wall-to-soil shear resistance or down-drag force when the coefficient of at-rest earth pressure is assumed for the surrounding soil [14]. However, during fresh mixture placement into the trench, the mixture will settle corresponding to the sidewall under its weight and deploys a down-drag force. This phenomenon then develops until consolidation completion. The role of an at-rest earth pressure condition in a slurry wall, that is, no inward displacement of surrounding soils into the trench, is assumed. Besides, Clough and Duncan [14] pointed out that where the proposed backfill material is cohesive, a moderate earth pressure between at-rest and active conditions must be mobilized for design. To illustrate lateral earth pressure transition from at-rest to active condition, a method proposed by Bang and Kim [10] is investigated to analyses the relationship between the major and minor principal effective stresses. Where k₀ is known as the coefficient of at-rest lateral earth pressure, the subsequent angle Ø₀ can be described as 9 sinϕ0=1−k01+k0 where k₀ = 1 − sin Ø₀, then 10 sinϕ0=sinϕ/(2−sinϕ)

If the angle, ψ, refers to the relationship between major (horizontal) and minor (vertical) principal effective stress, then considering a ψ value between Ø and Ø₀ describes a displacement angle for active and at-rest values, respectively. So, the intermediate part at each depth can be defined as Ø₀ < ψ < Ø. Furthermore, where δ is the cured slurry wall friction angle, so that; 11 sinΔ=sinδ/sin∅

Since ψ (z) can be used instead of Ø, and δ (z) is the developed cured slurry wall friction at depth z, Equation (11) can be modified to result in 12 sinΔ(z)=[ sinδ(z)/sinψ(z) ]

And the variation of δ (z) can be considered to be zero for at-rest and to be δ_max in an active max condition. The average stress for plain-strain at any depth is 13 σ=σv+σh2

Subsequently, the complete solution once σ along the ground surface up to the entire depth (z), that is, developed at the face of the slurry wall, the intermediate earth pressure coefficient can be analyzed from 14 km=[ sin(Δ(z)−δ(z))/sinΔ(z) ]cosδ(z)|z=zy

However, Equation (14) requires detailed solution steps, which is a function of, ψ (z), and provides lateral earth pressure transition from at-rest to the active condition. The variation for ψ (z), is from Ø₀ for at-rest to Ø for active condition. In other words, if the stage of the sidewall from mixture placement to consolidation completion denotes β, then β=0 and β=1 can describe the at-rest and active conditions, respectively (Figure 2). Accordingly, the deformation development of the surrounding soils at z = 0 is 0 ≤ β ≤ 1, whereas the variation of ψ (z) is assumed to be ψ (z) = Ø, and at z = H it is determined to be ψ (z) = Ø₀. So it can be expressed as 15 ψ(z)=∅0+(∅−∅0)(1−zH)β where 16 ∂ψ(z)∂z=−β(∅−∅0)/H

Figure 2:

Consequently, for β=0, at both depth z=0 and depth z=H, wall tilt is considered to be ψ(z) =Ø₀ and ψ(z) = Ø, respectively. The solution to β=β at depth z=0 can be expressed as Ø₀<ψ(z) <Ø, and at depth z=H ψ(z) =Ø₀, ψ(z) decreases linearly between z=0 and z=H. Using β=1 at depth z=0 ψ(z)=Øand at depth z=H ψ(z) =Ø₀, the variation of ψ(z) between z=0 and z=H reduces linearly.

In this study, the effective horizontal stress, σ′_h, reduces owing to low lateral squeezing impact as K increases linearly, and the maximum values are between 15 m to 20 m for both samples (Figures 3 and 4). The major and minor effective stress values for both samples are decreased as z > 20 m and reached lower than 62 kPa for the C50-S45-L5-B9 and 54 kPa for C-50-S50-L5 mixtures at a depth of 30 m. The parametric study also shows that the faster the hydration rate of a sample develops, the higher the effective stresses on the self-hardening walls. However, horizontal and vertical effective stress magnitude between two curing times do not exceed 10 kPa for either mixture with depth. Besides, the properties of the CSB wall depend on mixture design and bentonite content. Considering reports from previous studies, this paper reveals that cementitious properties of slurry wall materials experience up to the 25 kPa of major and minor effective stresses with depth. The laboratory tests revealed that the hydration progression of each sample has a slight influence on the proposed effective stress values to control the lateral squeezing effect. An alternative explanation might be that the increasing values of cohesion C and internal friction angle Ø of each mixture due to curing age does not have considerable impact on stress values. Measurements were taken as shear strength reduction factor R changes with depth, that is, the function of β, and gives effective stress distribution values from the at-rest to the active condition. Moreover, the constrained modulus D and Young’s modulus E values of the CSB mixtures are stress dependent and increase with depth. The results show that since the differences between the maximum and minimum value of E for both mixtures at 7-day and 28-day curing ages are relatively low, it does not have a major impact on the effective stress in the wall. The coefficient of lateral earth pressure has a significant effect on the vertical effective stress prediction. Ke et al. [8] indicated that this prediction accuracy could be improved by inputting a distribution of the lateral earth pressure coefficient with depth.

Figure 3:

Figure 4:

Such an investigation is developed in Equation 15, and the results are based on the determination of the intermediate value of Ø and Ø₀ at each depth. The proposed physical model provides a relatively good estimation of the stress distribution within CSB slurry walls. The trends of both major and minor effective stress achieved by this model are in good agreement with those calculated from CPTu data sets provided by Ke et al. [8]. The proposed stresses are used to estimate the permeability of the CSB wall and compare it with those evaluated in the laboratory for the same stress profile. Estimated permeability and laboratory test results for the C50-S50-B5 mixture and the C50-S45-L5-B9 mixture are presented in Figures 5 and 6. The permeability results of both would seem to suggest that permeability is relatively high in the shallow depth where stress is lower and it decreases as stress increases.

Figure 5:

Figure 6:

The use of vertical curtains in order to contain the advance of contaminating plumes towards groundwater is increasing throughout the world [19]. These are trench-shaped excavations that can reach up to tens of meters in depth and are strategically placed to contain, diverge, or encapsulate the underground contaminating flow. Simultaneously with the excavation process, the trench is filled with a mixture of bentonite and water, called bentonite mud, which has functions of geotechnical stabilization and reduced permeability [7]. After the excavation, the trench is re-ground, so that part of the introduced bentonite mud is expelled, and the remaining part tends to remain, covering the walls and the bottom of the ditch and forming a thin layer (filter cake) [2].

This thin layer, if well constituted, is mainly responsible for the reduction of the permeability of the curtain [11]. The backfill, normally constituted of the excavated material itself, can be mixed with bentonite and/or cement, in order to further reduce its permeability and increase its mechanical resistance. Geomembranes can also be applied next to the backfill to further decrease the hydraulic conductivity of the curtain [2]. Lateritic soils, in turn, cover approximately 65% of the country’s territory. In general, they are characterized by a mineralogical composition dominated by quartz, Fe-Al-Mn oxides/hydroxides, and kaolinite as the predominant clay. In the field, they usually present high porosity and drainability, in profiles of alteration of great thicknesses, and are quite homogeneous. Because of its wide occurrence, lateritic soils have great potential for application in vertical curtains.

This paper has investigated the physical model to predict effective stresses in CSB slurry walls, and considerable progress has been made for both arching and lateral squeezing effect. Taken together, the proposed model was then employed to evaluate the influence of two different self-hardening mixtures on estimated stress profile. A bentonite filter cake prior to mixture hardening reduces the shear strength between adjacent soils and the trench wall, and the provided R, C′_CSB, and Ø′_CSB values change with depth according to β tilt. The principal stress of the trench wall at z > 7 m is horizontal, and maximum stress values are appear at 15 ≤ z ≤ 20 m. A parametric study implies that the stresses in the CSB wall are initially dominated by the arching effect at shallow depth; later at z ≥ 7 m, stresses are caused by lateral squeezing. The effective vertical stresses are then predicted based on obtained horizontal effective stresses and the transition of the lateral earth pressure coefficient from at-rest to the active condition. The proposed stresses are used to estimate the permeability of the CSB wall and compare it with those evaluated in the laboratory for the same stress profile. The permeability results of both would seem to suggest that permeability is relatively high for the shallow depth as a result of its low-stress stage, and permeability decreases as stress increases. Finally, considerable insight has been gained with regard to an appropriate stress stage prediction in the CSB wall, in which the development is consistent with calculations from CPTu data provided by previous studies.