## 2 Soil-Bentonite Vertical Cut-Off Wall Service Performance and Improvement Measures
### Main Factors Affecting the Long-Term Service Performance of Vertical Walls
#### 2.3.1 Service Time Evaluation Methodology  
When a pollutant penetrates the cut-off walls, causing the outer concentration to reach a specified threshold, the cut-off walls are considered penetrated, and the corresponding duration is referred to as the penetration time [17]. [PERSON] [50] suggested that the service life is influenced by the physical and chemical aging of the material. [PERSON] et al. [51] emphasized that the assessment of service life should consider three distinct zones of the cut-off walls: the erosion zone, the central effective zone, and the outer stretching zone. Additionally, [PERSON] et al. [52] identified deformation, stress, and damage distribution as critical determinants of service life, based on simulations employing a coupled finite element method (FEM)-Peridynamics (PD). [PERSON] et al. [53] further confirmed these findings, noting that the primary factors affecting service life include the deformation modulus of the soil matrix and the creep effect, as determined through a combination of FEM, PD, and centrifuge model testing. The transport of pollutants must account for diffusion, adsorption, and degradation processes, leading to extensive research on analytical models. [PERSON] [54] and [PERSON] et al. [55] developed a coupled analytical model addressing seepage and dissolution. [PERSON] et al. [56] created a transient two-dimensional transport model that incorporates advection, dispersion, adsorption, and biodegradation within a multilayered system, overcoming the limitations of traditional wall models that primarily address non-point source pollution at constant concentrations. Furthermore, [PERSON] et al. [57] proposed a two-dimensional analytical model that considers transient diffusion, adsorption, and degradation processes of organic pollutants within a composite geomembrane containment wall (GCCW) and a \begin{table}
\begin{tabular}{c c} \hline
**Case Studies** & **Practical Application Performance** \\ \hline Karkheh Dam, south-west Iran [45] & The impermeable walls reduced total seepage and permeability by 25\% at the right dam shoulder. \\ Landfills in the Tropics [46] & Tropical soils amended with bentonite exhibit reduced hydraulic conductivity, suitable for waste disposal facility liners. \\ \hline Taihu Meilangwan Whitetall Storage Yard [47] & Bentonite reduces permeability; higher pressure minimizes permeability changes with bentonite. Dredged material \\  & meets landfill requirements; 1.5–3–5 bentonite aids long-term self-healing. \\ \hline Changzhou City Smitry Landfill [48] & PBFC slurry cut-off wall has high load-bearing capacity and ductility, matching landfill conditions. \\ \hline Landfill in the Lagouat region, Algeria [49] & Waste leachate cuts bentonite mixtures’ compressibility and permeability but raises their strength. \\ \hline \end{tabular}
\end{table} 
Table 4: Practical case studies. continuous aquifer. For evaluating the service life of composite cut-off walls consisting of a geomembrane and a soil-bentonite mixture for organic pollutants, [PERSON] et al. [58] developed a geometric model (Figure 3). In this model, \(R_{\rm d}\) is the delay factor of the soil-bentonite cut-off wall, \(C_{1}\) is the pollutant concentration at any location x in the soil-bentonite cut-off wall, \(D_{1}\) is the effective diffusion coefficient of the soil-bentonite cut-off wall, \(v_{1}\) is the pollutant's average linear velocity in the soil-bentonite cut-off wall, \(\rho_{\rm d}\) is the dry density of the soil-bentonite cut-off wall; \(n_{1}\) is the porosity; \(K_{\rm d}\) is the distribution coefficient. The impacts of soil-bentonite cut-off wall defects and their locations were quantitatively analyzed through the modeling of control Equations (1) and (2).