Intelligent model selection with updating parameters during staged excavation using optimization method

Abstract

Various constitutive models have been proposed, and previous studies focused on identifying parameters of specified models. To develop the smart construction, this paper proposes a novel optimization-based intelligent model selection procedure in which parameter identification is also performed during staged excavation. To conduct the model selection, a database of seven constitutive models accounting for isotropic or anisotropic yield surface, isotropic or anisotropic elasticity, or small strain stiffness for clayey soils is established, with each model numbered and deemed as one additional parameter for optimization. A newly developed real-coded genetic algorithm is adopted to evaluate the performance of simulation against field measurement. As the process of optimization goes on, the soil model exhibiting good performance during simulation survives from the database and model parameters are also optimized. For each excavation stage, with the selected model and optimized parameters, wall deflection and ground surface settlement of the subsequent unexcavated stage are predicted. The proposed procedure is repeated until the entire excavation is finished. This proposed procedure is applied to a real staged excavation with field data, which demonstrates its effectiveness and efficiency in engineering practice with highlighting the importance of anisotropic elasticity and small strain stiffness in simulating excavation. All results demonstrate that the current study has both academic significance and practical significance in providing an efficient and effective approach of adaptive optimization-based model selection with parameters updating in engineering applications.

Appendix A: Derivation of initial reference shear modulus and apparent swelling index

Based on Eq. (17), the shear modulus at 0.1% of strain and that at any strain level is defined as:

$$ \left\{ {\begin{array}{*{20}l} {G_{0.1\% } = \frac{{G_{0} }}{{\left( {1 + {{0.001} \mathord{\left/ {\vphantom {{0.001} {\gamma_{\text{ref}} }}} \right. \kern-0pt} {\gamma_{\text{ref}} }}} \right)^{2} }}} \hfill \\ {G = \frac{{G_{0} }}{{\left( {1 + {\gamma \mathord{\left/ {\vphantom {\gamma {\gamma_{\text{ref}} }}} \right. \kern-0pt} {\gamma_{\text{ref}} }}} \right)^{2} }}} \hfill \\ \end{array} } \right. $$

(27)

According to the elasticity, the corresponding bulk modulus at 0.1% of strain and that at any strain level is obtained:

$$ \left\{ {\begin{array}{*{20}l} {K_{0.1\% } = \frac{{2\left( {1 + \upsilon } \right)}}{{3\left( {1 - 2\upsilon } \right)}}G_{0.1\% } = \frac{{2\left( {1 + \upsilon } \right)}}{{3\left( {1 - 2\upsilon } \right)}}\frac{{G_{0} }}{{\left( {1 + {{0.001} \mathord{\left/ {\vphantom {{0.001} {\gamma_{ref} }}} \right. \kern-0pt} {\gamma_{ref} }}} \right)^{2} }}} \hfill \\ {K = \frac{{2\left( {1 + \upsilon } \right)}}{{3\left( {1 - 2\upsilon } \right)}}G = \frac{{2\left( {1 + \upsilon } \right)}}{{3\left( {1 - 2\upsilon } \right)}}\frac{{G_{0} }}{{\left( {1 + {\gamma \mathord{\left/ {\vphantom {\gamma {\gamma_{ref} }}} \right. \kern-0pt} {\gamma_{ref} }}} \right)^{2} }}} \hfill \\ \end{array} } \right. $$

(28)

Assuming the ordinary swelling index κ is adopted to computer the K_0.1% and a modified swelling index κ_s corresponding to any strain level is adopted to computer K

$$ \left\{ {\begin{array}{*{20}l} {K_{0.1\% } = \frac{{\left( {1 + e_{0} } \right)}}{\kappa }p^{{\prime }} } \hfill \\ {K = \frac{{\left( {1 + e_{0} } \right)}}{{\kappa_{s} }}p^{\prime}} \hfill \\ \end{array} } \right. $$

(29)

Combining Eqs. (28) and (29), and noting a reference value p_at for replacing p′, the initial reference shear modulus G_ref0 for replacing G₀ can be defined as:

$$ \left\{ {\begin{array}{*{20}l} {G_{{{\text{ref}}0}} = \frac{{3\left( {1 - 2\upsilon } \right)\left( {1 + e_{0} } \right)}}{{2\left( {1 + \upsilon } \right)}}\left( {1 + {{0.001} \mathord{\left/ {\vphantom {{0.001} {\gamma_{\text{ref}} }}} \right. \kern-0pt} {\gamma_{\text{ref}} }}} \right)^{2} \frac{{p_{\text{at}} }}{\kappa }} \hfill \\ {G_{{{\text{ref}}0}} = \frac{{3\left( {1 - 2\upsilon } \right)\left( {1 + e_{0} } \right)}}{{2\left( {1 + \upsilon } \right)}}\left( {1 + {\gamma \mathord{\left/ {\vphantom {\gamma {\gamma_{\text{ref}} }}} \right. \kern-0pt} {\gamma_{\text{ref}} }}} \right)^{2} \frac{{p_{\text{at}} }}{{\kappa_{s} }}} \hfill \\ \end{array} } \right. $$

(30)

Adopting the $\gamma_{\text{ref}} = {{7\varepsilon_{70} } \mathord{\left/ {\vphantom {{7\varepsilon_{70} } 3}} \right. \kern-0pt} 3}$ and adding a controlling factor of stiffness P_rev (with P_rev = 1 when loading and P_rev = 2 when unloading), Eq. (30) can be expressed as:

$$ \left\{ {\begin{array}{*{20}l} {G_{{{\text{ref}}0}} = \frac{{3\left( {1 - 2\upsilon } \right)\left( {1 + e_{0} } \right)}}{{2\left( {1 + \upsilon } \right)}}\left( {1 + P_{\text{rev}} \frac{3}{7}\left| {\frac{0.001}{{\varepsilon_{70} }}} \right|} \right)^{2} \frac{{p_{\text{at}} }}{\kappa }} \hfill \\ {G_{{{\text{ref}}0}} = \frac{{3\left( {1 - 2\upsilon } \right)\left( {1 + e_{0} } \right)}}{{2\left( {1 + \upsilon } \right)}}\left( {1 + P_{\text{rev}} \frac{3}{7}\left| {\frac{{\varepsilon_{\text{eq}}^{*} }}{{\varepsilon_{70} }}} \right|} \right)^{2} \frac{{p_{\text{at}} }}{{\kappa_{s} }}} \hfill \\ \end{array} } \right. $$

(31)

From the second equation in Eq. (31), the modified swelling index κ_s corresponding to any average equivalent strain level can be obtained as:

$$ \kappa_{\text{s}} = \frac{{3\left( {1 - 2\upsilon } \right)\left( {1 + e_{0} } \right)}}{{2\left( {1 + \upsilon } \right)}}\left( {1 + P_{\text{rev}} \frac{3}{7}\left| {\frac{{\varepsilon_{\text{eq}}^{*} }}{{\varepsilon_{70} }}} \right|} \right)^{2} \frac{{p_{\text{at}} }}{{G_{{{\text{ref}}0}} }} $$

(32)

This equation suggests that the apparent swelling index increases (corresponding to the decrease in shear modulus and bulk modulus) with the increase in average equivalent strain.