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, SiO_{2}, and Al2O_{3}. 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·SiO_{2}, 2CaO·SiO_{2}, 3CaO·Al_{2}O_{3}, 4CaO·Al_{2}O_{3}·Fe_{2}O_{3}). 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 _{w}z+_{csb}z carries the self-weight of the CSB at depth z of the wall and at excess pore water pressure _{e}_{csb}z, where _{w} and _{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.

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
_{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
_{CSB}, Ø’_{CSB}, and _{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

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
_{h}_{m}_{0} is known as the coefficient of at-rest lateral earth pressure, the subsequent angle Ø_{0} can be described as
_{0} = 1 − sin Ø_{0}, then

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 Ø_{0} describes a displacement angle for active and at-rest values, respectively. So, the intermediate part at each depth can be defined as Ø_{0} < ψ < Ø. Furthermore, where δ is the cured slurry wall friction angle, so that;

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

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

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

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 Ø_{0} 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) = Ø_{0}. So it can be expressed as

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

This section presents an assessment of the validity of the proposed model to a case of CSB slurry wall. A CSB is constructed to intercept and impede the stream of polluted fluids towards the groundwater. CSB provides lower structural strength compared to diaphragm and concrete walls. An alternative explanation might be that the CSB wall is principally constructed as a plastic medium with stress-strain properties much closer to the soil than concrete walls. Consequently, it should not be considered a structural wall, instead, the CSB slurry wall can be modeled as elastic soil [15]. On the basis of the relationship between stress and void ratio for CSB samples, Opdyke and Evans [1] concluded that the coefficient of consolidation (_{v}^{-4} cm^{2}/s indicates the upper limit of natural clay soils, and the behavior is closely akin to overconsolidated soil. For remolded soils with liquid limits around 60%, Sridharan and Nagaraj [16] have provided an upper limit for the coefficient of consolidation of 3×10^{-4} cm^{2}/s. In addition, for marine clay treated with 8% lime and 20% slag, Rao and Raju [17] obtained a coefficient of consolidation of 5.17×10^{-4} cm^{2}/s. In this study, the time-rate of consolidation for CSB was investigated for loading increments from 200 kPa to 400 kPa. The laboratory experiment was conducted to investigate the consolidation parameters of the samples at 7 days and 28 days of curing time and other index properties (Table 1). Since the compressibility of CSB is similar to hard clay soil rather than a structural concrete wall, the authors decided to consider the performance of CSB as being similar to clay soil on the basis of elastic theory.

Consolidation and index properties.

Parameter | Unit | C50-S50-B5 | C50-S45-L5-B9 | ||||
---|---|---|---|---|---|---|---|

Curing age (days) | |||||||

7 | 28 | 7 | 28 | ||||

Value | |||||||

/ | 2.76 | 2.70 | |||||

% | 42 | 62 | |||||

% | 15 | 38 | |||||

% | 17 | 17 | |||||

% | 67 | 73 | |||||

% | 16 | 10 | |||||

_{v} | cm^{2}/s | 2.03×10^{-3} | 1.24×10^{-3} | 3.34×10^{-4} | 3.0×10^{-3} | ||

_{u}) | kPa | 78 | 380 | 80 | 505 |

Laboratory datasets were assumed to apply on a site; that is, saturated medium dense sand encapsulated a trench with a width and a depth of 1.2 m and 30 m, respectively. The Poisson’s ratio values were theoretically obtained for the samples at a given curing time and are related to Young’s modulus

The Young’s modulus

As the geotechnical status of the site shows, a direct relationship between the additional load module _{h}

Although the model provided by Li et al. [6] proposed a better estimation for σ′_{h}, the σ′_{v} achieved by this method was considered the major principal effective stress and was greater than σ′_{h}. This approach is not well suited to deep trenches and may raise a question where the lateral squeezing effect is considered to be specified on the basis of Filz’s [5] theory.

The development of lateral earth pressure behind a slurry wall creates inward displacement from mixture placement to consolidation completion. Laboratory investigation for increased strength of CSB also indicates that this deformation will stop to develop after 28 days of curing time because the unconfined compressive strength test values are greater than those provided by effective horizontal stress [19]. Vertical effective stress determination has various stages, starting from the at-rest condition (mixture placement) to the active condition (consolidation completion). In the analysis, the adjacent soil layer is assumed to have uniform properties with no change of layer type. The method of analysis estimates not only the progressive lateral earth pressure at each depth but also the dilatancy angle, ψ, development as 0 ≤ β ≤ 1. The predicted vertical effective stress using this method is in good agreement with those provided by Ke et al. [8] and remains below effective horizontal stress at each depth. Moreover, by considering the effects of both arching and lateral squeezing, this model presents a considerable improvement of stress estimation in CSB slurry walls. The stress values obtained by the proposed model are used to estimate the permeability (^{-1} is the equivalent major effective stress, σ′_{mean} is the mean effective stress in cured samples, and _{b} is assumed to be present as υ/ (1-υ) for the consolidation test. Li et al. [6] indicated that the mean effective stress, σ^{-1}, can be adjusted for the plain-strain problem as follows:

The estimated permeability profile controlled by the proposed effective stress at each depth is given in Figures 5 and 6. In the shallow depth (z ≤ 7 m) where the arching effect is still dominant, permeability is higher than 10^{-9} m/s as a result of lower effective stress and higher void ratio. The permeability decreases slightly with depth as stress increases and reaches 1×10^{-9} m/s in the region of 17 m and remains constant down to the trench’s floor for the method proposed here. Predicted permeabilities for CSB in this study (Figures 5 and 6) appear to be well substantiated by those achieved in previous studies for both laboratory and field monitoring [20, 9]. However, the permeability predicted by the geostatic method is lower than the presented method as a result of the greater stress values. According to the laboratory consolidation test results in this study, permeability decreases with depth as the void ratio decreases. Moreover, as specimens’ hydration improve with increased curing times, the particles of the cementitious materials fill the void between them. Simultaneously, for the amended specimen, the presence of further bentonite content in addition to lime gave lower values than (C50-S50-B5) specimens for both curing times. The laboratory study also shows that permeability values for both mixtures at each curing period are slightly higher than those achieved by the proposed method (Figures 5 and 6).

The consolidometer permeation values in soft-to-medium consistency materials are 10 to 100 times greater than those gained by the flexible wall permeation test [21, 19].

The proposed physical modeling in this study considers the effects of adjacent soil and mixture properties along with trench size on the steady-state effective stress profile. The values and the impact of corresponding parameters for both surrounded soils and mixtures are provided in Table 2. The width and depth of the trench are 1.2 m and 30 m, respectively [8]. The laboratory investigation was performed to define the CSB mixture’s properties and the impact of curing ages at 7 days and 28 days.

Geometric and mixture properties.

Parameter | Unit | C50-S50-B5 | C50-S45-L5-B9 | ||
---|---|---|---|---|---|

Curing age (days) | |||||

7 | 28 | 7 | 28 | ||

Value | |||||

B | m | 1.2* | |||

H | m | 30* | |||

γ′_{csb} | kN/m^{3} | 11.9 | 13.8 | 12.3 | 12.6 |

υ | / | 0.26 | 0.22 | 0.25 | 0.18 |

kPa | 66 | 133 | 67 | 160 | |

Ø′ | ° | 18 | 21 | 23 | 25 |

n_{h} | kN/m^{3} | 4500† | |||

/ | 0.1—0.25‡ |

Ke, H et al. 2018.

Das 1998.

Lam et al. 2014.

The values of subgrade modulus for granular soils _{h} = 4500 kN/m^{3} [13]. The impact of lateral squeezing throughout mixture consolidation and inward displacement is employed to determine σ′_{h} in the CSB slurry wall according to depth.

The shear strength reduction factor at the interface of the mixture-adjacent soil also vary with depth and is _{in} and Ø′_{in} parameters of the CSB wall are a function of _{v}, is determined by using various values of Ø′_{CSB}. As discussed before, the minor effective stress, σ′_{v}, value is a function of β, Ø′_{CSB}, and σ′_{h}, and must be determined for each depth. The described solution steps, however, need a parametric study to specify the impact of wall tilt, β, on the shear strength parameters. The values, as mentioned above for each parameter, are influenced by mixture properties at each curing age.

In this study, the effective horizontal stress, σ′_{h}, reduces owing to low lateral squeezing impact as

Such an investigation is developed in Equation 15, and the results are based on the determination of the intermediate value of Ø and Ø_{0} 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.

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 _{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.

#### Consolidation and index properties.

Parameter | Unit | C50-S50-B5 | C50-S45-L5-B9 | ||||
---|---|---|---|---|---|---|---|

Curing age (days) | |||||||

7 | 28 | 7 | 28 | ||||

Value | |||||||

/ | 2.76 | 2.70 | |||||

% | 42 | 62 | |||||

% | 15 | 38 | |||||

% | 17 | 17 | |||||

% | 67 | 73 | |||||

% | 16 | 10 | |||||

_{v} |
cm^{2}/s |
2.03×10^{-3} |
1.24×10^{-3} |
3.34×10^{-4} |
3.0×10^{-3} | ||

_{u}) |
kPa | 78 | 380 | 80 | 505 |

#### Geometric and mixture properties.

Parameter | Unit | C50-S50-B5 | C50-S45-L5-B9 | ||
---|---|---|---|---|---|

Curing age (days) | |||||

7 | 28 | 7 | 28 | ||

Value | |||||

B | m | 1.2 |
|||

H | m | 30 |
|||

γ′_{csb} |
kN/m^{3} |
11.9 | 13.8 | 12.3 | 12.6 |

υ | / | 0.26 | 0.22 | 0.25 | 0.18 |

kPa | 66 | 133 | 67 | 160 | |

Ø′ | ° | 18 | 21 | 23 | 25 |

n_{h} |
kN/m^{3} |
4500 |
|||

/ | 0.1—0.25 |

Mineral Chemistry of Pyroxene Gneiss in Obudu, SE Nigeria, and Its Petrological Significance Recycling of foundry sand wastes in self-compacting concretes: Use as cementitious materials and fine aggregates Empirical Relation Between Magnetic and Radiometric Survey in Bitumen Area, Ogun State, Nigeria Geology and Rare Earth Element Geochemistry of Magnesian Granitoids Within Proterozoic Schist Belt of Southwest Nigeria Physico-Chemical Trends in the Sediments of Agbede Wetlands, Nigeria