“…The LB and UB calculations are formulated as SOCP to obtain the FSs of PIP braced excavations. Till now, OptumG2 has been successfully employed to solve various undrained stability problems, including excavations (Keawsawasvong & Ukritchon, 2017a, Keawsawasvong & Ukritchon, 2019Chen et al, 2020), slopes (Yang et al, 2016;Oberhollenzer et al, 2018), pile foundations (Keawsawasvong & Ukritchon, 2017b;Zhou et al, 2020b), marine infrastructures (Ke et al, 2020), earth retaining structures (Lai et al, 2022b;Yang et al, 2022), and trapdoor problems (Keawsawasvong & Ukritchon, 2017c;Lai et al, 2020a;Shiau et al, 2021Shiau et al, , 2022.…”