Estimating water fluxes in the critical zone using water stable isotope approaches in the Groundnut and Ferlo basins of Senegal

Sustainable water management in semi-arid agriculture practices requires quantitative knowledge of water fluxes within the soil-vegetation-atmosphere system. Therefore, we used stable-isotope approaches to evaluate evaporation (E_a), transpiration (T_a), and groundwater recharge (R) at sites in Senegal's Groundnut basin and Ferlo Valley pasture region during the pre-monsoon, monsoon, and post-monsoon seasons of 2021. The approaches were based upon (i) the isothermal evaporation model (for quantifying E_a); (ii) water and isotope mass balances (to partition E_a and T_a for groundnut and pasture); and (iii) the piston displacement method (for estimating R). E_a losses derived from the isothermal evaporation model corresponded primarily to Stage II evaporation, and ranged from 0.02 to 0.09 mm d⁻¹ in the Groundnut basin, versus 0.02–0.11 mm d⁻¹ in Ferlo. At the groundnut site, E_a rates ranged from 0.01 to 0.69 mm d⁻¹; T_a was in the range 0.55–2.29 mm d⁻¹; and the T_a/ET_a ratio was 74%–90%. At the pasture site, the ranges were 0.02–0.39 mm d⁻¹ for E_a; 0.9–1.69 mm d⁻¹ for T_a; and 62–90% for T_a/ET_a. The ET_a value derived for the groundnut site via the isotope approach was similar to those from eddy covariance measurements, and also to the results from the previous validated HYDRUS-1D model. However, the HYDRUS-1D model gave a lower T_a/ET_a ratio (23.2%). The computed groundwater recharge for the groundnut site amounted to less than 2% of the local annual precipitation. Recommendations are made regarding protocols for preventing changes to isotopic compositions of water in samples that are collected in remote arid regions, but must be analysed days later. The article ends with suggestions for studies to follow up on evidence that local aquifers are being recharged via preferential pathways.     

A variationally consistent hyperstatic reaction method for tunnel lining design

In this technical note, a consistent finite element formulation of the Hyperstatic Reaction Method (HRM) for tunnel linings design is proposed by introducing a variational consistently linearized formulation. It permits to consider a nonlinear interaction between a lining structure and the surrounding ground. Recent advances of the HRM in regard to the consideration of the nonlinear response of the segmented tunnel lining exposed to design loads use an iterative algorithm for solving the nonlinear system of equations. In the proposed Variationally consistent Hyperstatic Reaction Method (VHRM), a distributed nonlinear spring model representing the interaction between the lining and the ground soils is considered in a variationally consistent format. Computing the tangential spring stiffness via consistent linearization, and using Newton-Raphson iteration, requires significantly smaller number of iterations as compared to the original HRM model based on nodal springs. Furthermore, the method is applicable for simulations using solid finite elements (2D and 3D), as well as beam or finite shell elements, respectively.