Assessing uncertainty propagation in CPTu-based hydro-mechanical subsoil characterization using a multivariate stochastic simulation approach

Abstract

Estimating the spatial distribution of hydromechanical properties in the investigated subsoil by defining an Engineering Geological Model (EGM) is crucial in urban planning, geotechnical designing and mining activities. The EGM is always affected by (i) the spatial variability of the measured properties of soils and rocks, (ii) the uncertainties related to measurement and spatial estimation, as well as (iii) the propagated uncertainty related to the analytical formulation of the transformation equation. The latter is highly impactful on the overall uncertainty when design/target variables cannot be measured directly (e.g., in the case of piezocone Cone Penetration Test–CPTu measurements). This paper focuses on assessing the Propagated Uncertainty (PU) when defining 3D EGMs of three CPTu-derived design/target variables: the undrained shear resistance ($s_u$), the friction angle (${\phi }^{\prime }$), and the hydraulic conductivity ($k$). We applied the Sequential Gaussian Co-Simulation method (SGCS) to the measured profiles of tip ($q_c$) and shaft resistance ($f_s$), and the pore pressure ($u_2$), measured through CPTus in a portion of Bologna district (Italy). First, we calculated 1000 realizations of the measured variables using SGCS; then, we used the available transformation equations to obtain the same number of realizations of $s_u$, ${\phi }^{\prime }$, and $k$. The results showed that PU is larger when the transformation equation used to obtain the design/target variable is very complex and dependent on more than one input variable, such as in the case of $k$. Instead, linear (i.e., for $s_u$) or logarithmic (i.e., for ${\phi }^{\prime }$) transformation functions do not contribute to the overall uncertainty of results considerably.