Experimental Study on Stiffness Softening of Soil-Rock Mixture Backfill under Metro Train Cyclic Load

Due to the thick soil layer, short backfill time, and low degree of consolidation of the soil-rock mixture backfill in Chongqing city, metro train tunnels passing through this type of strata are prone to large settlements during operation, which greatly affects the stability of the tunnel and the safety of metro train operations. In response to this problem, the dynamic triaxial test of the soil-rock mixture backfill under cyclic loading was carried out to study the dynamic characteristics of the soil-rock mixture backfill under cyclic loading. The effect of initial consolidation degree, effective consolidation confining pressure, and rock content on the stiffness softening of soil-rock mixture backfill was analyzed. The results show that the initial consolidation degree, effective consolidation confining pressure, and rock content are all important factors affecting the stiffness of soil-rock mixture backfill under cyclic loading. As the number of cycles increases, the lower the initial consolidation degree and effective consolidation confining pressure, the faster the attenuation of the softening index, and the larger the amplitude. As the rock content increases, the softening index increases and the stiffness of the backfill changes from softening to hardening. Based on the test data, the softening-hardening model of the soil-rock mixture is established, which is in good agreement with the field test results. This study can provide a reference for predicting and controlling the postconstruction settlement of the metro tunnel in the soil-rock mixture backfill.

Applications of the RST Algorithm to Nonlinear Systems in Real-Time Hybrid Simulation

Real-time substructure testing (RST) algorithm is a newly developed integration method for real-time hybrid simulation (RTHS) which has structure-dependent and explicit formulations for both displacement and velocity. The most favourable characteristics of the RST algorithm is unconditionally stable for linear and no iterations are needed. In order to fully evaluate the performance of the RST method in solving dynamic problems for nonlinear systems, stability, numerical dispersion, energy dissipation, and overshooting properties are discussed. Stability analysis shows that the RST method is only conditionally stable when applied to nonlinear systems. The upper stability limit increases for stiffness-softening systems with an increasing value of the instantaneous degree of nonlinearity while decreases for stiffness-hardening systems when the instantaneous degree of nonlinearity becomes larger. Meanwhile, the initial damping ratio of the system has a negative impact on the upper stability limit especially for instantaneous stiffness softening systems, and a larger value of the damping ratio will significantly decrease the upper stability limit of the RST method. It is shown in the accuracy analysis that the RST method has relatively smaller period errors and numerical damping ratios for nonlinear systems when compared with other two well-developed algorithms. Three simplified engineering cases are presented to investigate the dynamic performance of the RST method, and the numerical results indicate that this method has a more desirable accuracy than other methods in solving dynamic problems for both linear and nonliner systems.

Modal Coupling Effect in a Novel Nonlinear Micromechanical Resonator

Capacitive micromechanical resonators share electrodes with the same bias voltage, resulting in the occurrence of electrostatic coupling between intrinsic modes. Unlike the traditional mechanical coupling, the electrostatic coupling is determined by the structural electric potential energy, and generally, it only occurs when the coupling modes operate in nonlinear regions. However, previous electrostatic coupling studies mainly focus on the stiffness softening region, with little attention on the opposite stiffness hardening condition. This paper presents a study on the electrostatic modal coupling effect in the stiffness hardening region. A novel capacitive micromechanical resonator with different modal nonlinearities is designed and fabricated. It is demonstrated that activating a cavity mode can shift the fundamental resonance of the manipulated mode by nearly 90 times its mechanical bandwidth. Moreover, the frequency shifting direction is found to be related to the manipulated mode’s nonlinearity, while the frequency hopscotch is determined by the cavity mode’s nonlinearity. The electrostatic coupling has been proven to be an efficient and tunable dynamical coupling with great potential for tuning the frequency in a wide range. The modal coupling theory displayed in this paper is suitable for most capacitive resonators and can be used to improve the resonator’s performance.

Noniterative Integration Algorithms with Controllable Numerical Dissipations for Structural Dynamics

A new family of noniterative algorithms with controllable numerical dissipations for structural dynamics is studied. Particularly, this paper provides nine members of the proposed algorithms and two existing methods are included as two special cases. The proposed algorithms achieve unconditional stability and are second-order accurate for linear elastic systems. The explicit expressions of stability conditions for nonlinear stiffness systems are completely presented, which shows that new algorithms possess unconditional and conditional stability for stiffness softening and hardening systems, respectively. A comprehensive stability and accuracy analysis, including numerical energy dissipations and dispersions, are studied in order to gain insight into spectral properties of new algorithms. Due to the existence of the nonzero spurious root, this paper also pays attention to the influence of the spurious root, which shows that the spurious root does not influence numerical accuracy at low-frequency domains. Although the proposed algorithms exhibit the unusual overshoot behaviors in either displacement or velocity, numerical damping ratios in new algorithms can significantly eliminate this overshoot at a few steps. The new dissipative algorithms are appropriate to solve numerical transient responses of the structure. Numerical examples are also presented to demonstrate the analytical results.