## 8 Conclusions  
A mathematical model of unsteady groundwater flow in a limited confined aquifer was established in this investigation to obtain the drawdown distribution outside a strip excavation pit. The approach uses the Laplace transform and Fourier transform to derive an analytical solution to evaluate the two-dimensional drawdown. In addition, the time-domain result is obtained by the Laplace inversion transform which is based on the work of [PERSON]. The semi-analytical solution was compared with numerical simulation via the finite element method. From the analytical analysis of the barrier effect of the cut-off wall on the groundwater seepage, these main conclusions can be drawn:  
1. The existence of the cut-off wall has a barrier effect on the distribution of groundwater head, as the cut-off wall increases the seepage path. The groundwater flow in the confined aquifer changes from a simple one-dimensional flow to a two-dimensional flow around the cut-off wall, which indicates the change in the flow velocity and direction.
2. From the time-domain results, the distribution of drawdown in the horizontal direction changes from a cone-shaped distribution to a straight line over time in a limit confined aquifer, which shows the process of transition from unsteady flow to steady flow. The barrier effect reduces with the increase in pumping time.
3. The dimensionless drawdown decreases with the increase in anisotropic degree (\(k=k_{\text{h}}/k_{\text{v}}\)). The effect of anisotropy is obvious near the cut-off wall, and weakened with the horizontal distance. The effectiveness of excavation dewatering is significantly influenced by the lateral boundary distance, with closer boundaries requiring higher pumping rates to achieve desired drawdown depths, while increased distances result in improved dewatering effects.
4. The impacts on drawdown in a limited confined aquifer due to the barrier effect are correlated with the penetrating depth of the cut-off wall. When the cut-off wall is not buried deep enough to cut off the confined aquifer completely, it is thought that there is an optimum penetrating depth ratio to achieve a balance between the barrier effect and economy, when determining the parameters.
5. A case study was conducted on a practical municipal engineering scenario involving the dewatering of a long rectangular excavation. The practical scenario was conceptualized and analyzed using the presented analytical solution, as well as finite element numerical methods. Comparison with field data validates the engineering applicability of the approach proposed in this paper.  
Conceptualization, X.W. and J.X.; methodology, X.W.; software, Y.C.; Validation, L.L.; formal analysis, Y.C.; investigation, Y.C.; writing--original draft, Y.C.; writing--review & editing, J.X.; visualization, L.L.; supervision, X.W.; project administration, X.W.; funding acquisition, J.X. All authors have read and agreed to the published version of the manuscript.  
National Natural Science Foundation of China (No. 41272303).  
Not applicable.  
The data presented in this study are available on request from the corresponding author.  
The authors declare no conflict of interest.