The issue of geotechnical hazards induced by excavation in soft soil areas has become increasingly prominent. However, the retaining structure and surface settlement deformation induced by the creep of soft soil and spatial effect of the excavation sequence are not fully considered where only elastic–plastic deformation is used in design. To understand the spatiotemporal effects of excavation-induced deformation in soft soil pits, a case study was performed with the Huaxi Park Station of the Suzhou Metro Line S1, Jiangsu Province, China, as an example. Field monitoring was conducted, and a three-dimensional numerical model was developed, taking into account the creep characteristics of mucky clay and spatiotemporal response of retaining structures induced by excavations. The spatiotemporal effects in retaining structures and ground settlement during excavation processes were analyzed. The results show that as the excavation depth increased, the horizontal displacement of the diaphragm walls increased linearly and tended to exhibit abrupt changes when approaching the bottom of the pit. The maximum horizontal displacement of the wall at the west end well was close to 70 mm, and the maximum displacement of the wall at the standard section reached approximately 80 mm. The ground settlement on both pit sides showed a “trough” distribution pattern, peaking at about 12 m from the pit edge, with a settlement rate of −1.9 mm/m per meter of excavation depth. The excavation process directly led to the lateral deformation of the diaphragm walls, resulting in ground settlement, which prominently reflected the time-dependent deformation characteristics of mucky soft soil during the excavation process. These findings provide critical insights for similar deep excavation projects in mucky soft soil, particularly regarding excavation-induced deformations, by providing guidance on design standards and monitoring strategies for similar geological conditions.

Cracks and other diseases may occur in the long-term operation of highway tunnels and reduce the structural load-carrying capacity. Strengthening using carbon fiber reinforced polymer (CFRP) sheets and other materials could extend the service time of the tunnels. However, the process of strengthening tunnels is remarkably different from the process of strengthening aboveground structures because of the secondary load. In order to understand the development of stress and deformation of strengthened tunnels under secondary load, a 1 : 10 scaled model was tested to simulate the tunnel strengthened with CFRP under different damage states. The test results show that CFRP strengthening improved the stiffness of the structure and inhibited the propagation of the existing cracks. The peeling of the CFRP sheets made the strengthened structure quickly lose its load-carrying capacity, causing the instability of the structure. The failure loads of the structures strengthened at different damage states were essentially the same, with an average value of 184% of the original failure load. Nevertheless, the early strengthening helped control the structural deformation. The test results also demonstrate that the bonding strength between the CFRP and the lining is essential for strengthening effectiveness. This study provides a theoretical basis for similar engineering reinforcement designs.

Coupled electro-elastic analysis of functionally graded piezoelectric material plates three-dimensional analysis;coupled electro-elastic analysis;static;finite layer methods;functionally graded materials;piezoelectric plates; A unified formulation of finite layer methods (FLMs), based on the Reissner mixed variational theorem (RMVT), is developed for the three-dimensional (3D) coupled electro-elastic analysis of simply-supported, functionally graded piezoelectric material (FGPM) plates with open- and closed-circuit surface conditions and under electro-mechanical loads. In this formulation, the material properties of the plate are assumed to obey an exponent-law varying exponentially through the thickness coordinate, and the plate is divided into a number of finite rectangular layers, in which the trigonometric functions and Lagrange polynomials are used to interpolate the in- and out-of-plane variations of the primary field variables of each individual layer, respectively, such as the elastic displacement, transverse shear and normal stress, electric potential, and normal electric displacement components. The relevant orders used for expanding these variables in the thickness coordinate can be freely chosen as the linear, quadratic and cubic orders. Four different mechanical/electrical loading conditions applied on the top and bottom surfaces of the plate are considered, and the corresponding coupled electro-elastic analysis of the loaded FGPM plates is undertaken. The accuracy and convergence rate of the RMVT-based FLMs are assessed by comparing their solutions with the exact 3D piezoelectricity ones available in the literature.

In this paper, a localized boundary knot method is adopted to solve two-dimensional inverse Cauchy problems, which are controlled by a second-order linear differential equation. The localized boundary knot method is a numerical method based on the local concept of the localization method of the fundamental solution. The approach is formed by combining the classical boundary knot method with the localization method. It has the potential to solve many complex engineering problems. Generally, in an inverse Cauchy problem, there are no boundary conditions in specific boundaries. Additionally, in order to be close to the actual engineering situation, a certain level of noise is added to the known boundary conditions to simulate the measurement error. The localized boundary knot method can be used to solve two-dimensional Cauchy problems more stably and is truly free from mesh and numerical quadrature. In this paper, the stability of the method is verified by using multi-connected domain and simply connected domain examples in Laplace equations.

The localized method of fundamental solutions (LMFS) is a domain-type, meshless numerical method. Compared with numerical methods that have a high grid dependence, it does not require grid generation and numerical integration, so it can effectively improve computational efficiency and avoid complex integration processes. Moreover, it is formed using the traditional method of fundamental solutions (MFS) and the localization approach. Previous studies have shown that the MFS may produce a dense and ill-conditioned matrix. However, the proposed LMFS can yield a sparse system of linear algebraic equations, so it is more suitable and effective in solving complicated engineering problems. In this article, LMFS was used to solve eigenfrequency problems in electromagnetic waves, which were controlled using two-dimensional Helmholtz equations. Additionally, the resonant frequencies of the eigenproblem were determined by the response amplitudes. In order to determine the eigenfrequencies, LMFS was applied for solving a sequence of inhomogeneous problems by introducing an external source. Waveguides with different shapes were analyzed to prove the stability of the present LMFS in this paper.