# Numerical Implementation of the Barcelona Basic Model Based on Return-Mapping Integration
###### Abstract  
This paper implemented the Barcelona basic model (BBM) into the OpenGeoSys (OGS) platform for numerical modeling of the coupled hydro-mechanical (HM) behavior of unsaturated soil. Within the implicit integration approach in the OGS, the integration rule of the BBM was developed first and the integration form of the BBM under a return mapping algorithm was built. The closest point projection method was used for calculating the return mapping directions with the associative flow rule. The numerical simulation results show that the BBM is feasible in fitting the experimental results. The numerical integration algorithm can reflect the elastic-plastic mechanical behavior of materials, and improve the calculation accuracy. The material exhibits obvious elastic-plastic characteristics during numerical simulation and experiment, and the water absorption process can lessen the mixture's compression stiffness while enhancing its recovery stiffness. hydro-mechanics coupling; Barcelona basic model; implicit integration; OpenGeoSys +
Footnote †: journal: Medical  
conduct numerical simulation studies on the coupling process of bentonite-based buffer materials in the international cooperation project DECOVALEX II [18; 19; 20; 21]. Since the BBM can describe many typical features of the mechanical behavior of unsaturated soils [22], including the swelling or collapse strain caused by wetting, the BBM is widely used in the simulation of HLW buffer materials in countries such as Europe and Japan [23]. [PERSON] et al. [24] used BExM and implemented in TOUGHREACT-FLAC3D, which is a multi-phase reactive transport and geomechanics simulator, to simulate the coupled thermal-hydraulic-mechanical-chemical (THMC) processes, with a focus on the influence of chemical changes on mechanical process over time. [PERSON] et al. [25] employed the thermo-elasto-plastic version of the BBM to characterize the mechanical behavior for the numerical simulations of full-scale engineered barriers experiment (FEBEX) and obtained approximate results in simulations including temperature, relative humidity, total stress, and displacement. Although research related to the mechanical constitutive model of the coupling process was widely performed, studies that evaluated the influence of integral algorithms on numerical simulation are limited. The integration method of constitutive equation is directly related to the accuracy and stability of calculation [26; 27; 28]. Different from the general unsaturated soil constitutive model, the integration algorithm of expansive unsaturated soil is more complicated due to the consideration of plastic characteristics and the effect of plastic deformation on water retention characteristics [29; 30]. At present, implicit integration algorithms [31; 32] and explicit integration algorithms [33] are commonly used in the field of numerical simulation. TOUGHREACT-FLAC3D uses an explicit integration algorithm, which does not require iteration and has high calculation efficiency. However, it does not strictly meet the consistency conditions in the integration process, which ultimately leads to the stress point possibly deviating from the yield surface, resulting in error accumulation and limiting the algorithm's accuracy [32; 34; 35]. In contrast, the implicit integration algorithm corrects plastic stress using a nonlinear equation iterative method, which is widely used due to its high calculation accuracy and efficiency [33; 36]. The application of the return mapping algorithm allows the deviation of the initial stress to the yield surface to be predicted elastically, and the implicit integration algorithm can correct the deviated stress plastically and pull the deviated stress back to the yield surface to complete the calculation [37; 38; 39; 40]. In this paper, an implicit algorithm is used to study the numerical calculation of the elastic-plastic mechanical model of expansive unsaturated soil.