An enhanced ensemble Kalman filter scheme incorporating model error in sequential coupling between flow and geomechanics

Abstract

Summary In this work, we construct a new methodology for enhancing the predictive accuracy of sequential methods for coupling flow and geomechanics while preserving low computational cost. The new computational approach is developed within the framework of the fixed‐stress split algorithm procedure in conjunction with data assimilation based on the ensemble Kalman filter (EnKF). In this context, we identify the high‐fidelity model with the two‐way formulation where additional source term appears in the flow equation containing the time derivative of total mean stress. The iterative scheme is then interlaced with data assimilation steps, which also incorporate the modeling error inherent to the EnKF framework. Such a procedure gives rise to an “enhanced one‐way formulation,” exhibiting substantial improvement in accuracy compared with the classical one‐way method. The governing equations are discretized by mixed finite elements, and numerical simulation of a 2D slab problem between injection and production wells illustrate the tremendous achievement of the method proposed herein.

Data assimilation for surface wave method by ensemble Kalman filter with random field modeling

“…Inada 38 derived Equation (17) for sandy grounds to calculate the N-value in SWS tests. 𝑁 = 0.067𝑁 𝑆𝑊 + 0.002𝑊 𝑆𝑊 (17) in which 𝑁 is the N-value derived from the SWS tests, 𝑁 𝑆𝑊 is the number of half rations and 𝑊 𝑆𝑊 is the total weight of the loads (unit: N).…”

“…In contrast, there have been relatively few studies, which have applied the EnKF for the parameters of the soil strength or rigidity. The study of Caballero 17 involved Young's modulus of the ground, but the tests require a lot of time. In the present study, the Young's modulus of an earth‐fill dam is identified using the travel time to the first arrival of the surface waves, which has a strong correlation with the rigidity of the soil.…”

Developments of inverse analysis by Kalman filters and Bayesian methods applied to geotechnical engineering

“…Several attempts have been made to adopt the EnKF, the PF, and the UKF for DA in civil engineering applications, for example, the transient flows in geologic formations 87 ) (Chen and Zhang, 2006), identification of elastic constants in foundations under embankment loading 88 ) (Hommels et al , 2009), reservoir characterization in an underground gas storage field 89 ) (Jha et al , 2015), integration of microseismic monitoring data into coupled flow and geomechanical models 90 ) (Tarrahi et al , 2015), capacity to reduce the uncertainty of geomechanical parameters by assimilating a given number of surface displacements 91 ) (Bau et al , 2016), sequential reduction of slope stability uncertainty via hydraulic measurement 92 , 93 ) (Vardon et al , 2016; Liu et al , 2018), uncertainty reduction in soil deposits with spatial variability 94 ) (Li and Liu, 2019), sequential methods for coupling flow in geomechanics 95 ) (Caballero et al , 2019), prediction of spring water for mountain tunnel excavation 96 ) (Mori, et al , 2020), simultaneous estimation of strength and stiffness parameters for a fully coupled hydro-mechanical slope stability analysis 97 ) (Mohsan et al , 2021), prediction of soil settlement with quantified uncertainties 98 ) by the EnKF (Tao et al , 2020), parameter identification of an elastoplastic constitutive model for a foundation ground under embankment loading by the PF 37 , 38 ) (Shuku et al , 2012; Murakami et al , 2013), reduction of forecast uncertainty by using settlement observations 99 ) (Huber, 2016), model calibration of soil parameters for geomechanical modeling in mechanized tunneling 100 ) (Nguyen and Nestorovic, 2016), estimation of spatial distribution of Young’s moduli for earthfill dams 101 ) (Ren et al , 2022), multislip surface searching 102 ) (Zhang et al , 2022), and nonlinear structural dynamical system identification by the UKF 103 , 104 ) (Ghanem and Ferro, 2006; Chatzi and Smyth, 2009) and the PF 105 – 107 ) (Namdeo and Manohar, 2007; Sajeeb et al , 2009, 2010). Novel approaches based on nonlinear Kalman filters are still being proposed, such as a UKF algorithm coupled with a modified constitutive relation error observation 108 ) (Diaz et al , 2023) and a constrained UKF method for both updating structural parameters and identifying unknown external excitations 109 ) (Li et al , 2022).…”