Longitudinal Deformation of Deep Shield Tunnels Caused by Upper Load Reduction

Above-crossing excavations may cause uplift damages on existing shield tunnels. Therefore, to accurately calculate the deformation of shield tunnels is very necessary for geotechnical engineers. At present, the single-sided elastic foundation beam model is usually used in longitudinal deformation calculations for shield tunnels, which overestimates the uplift of deep shield tunnels. Because of the existence of the ground arch, deep shield tunnels are subjected to two-sided foundation reaction forces. Therefore, this paper proposes a partial missing double-sided elastic foundation beam model and the related fourth-order partial differential equations. In this model, the shield tunnel is subjected to double Winkler foundation springs and is simply considered a Euler–Bernoulli beam. A two-stage analysis method is used to solve the problem. First, the vertical unloading stress due to the above-crossing tunnelling at the tunnel location is calculated through Mindlin’s solution. Second, the deformation response of the beam subjected to an unloading stress is calculated by the finite difference method. Two engineering cases are used to verify the research. The results indicate that the proposed model is more accurate than traditional models in predicting the maximum uplift value, which is basically consistent with the observations. Due to the existence of segment staggering, the longitudinal influence range of the calculation by two models is larger than the actual measurement.

Internal force calculation of long span suspension bridge under vertical load based on elastic foundation beam algorithm

The calculation of suspension bridge under vertical load is the most important content of suspension bridge design calculation and the most important basis of main component design. Combined with the knowledge of structural mechanics, this paper puts forward the elastic foundation beam algorithm, and deduces the important formulas for the cross-section design and strength comparison of sling, cable and stiffening beam. In use, as long as the parameters are brought into the formula, it is more convenient and fast compared with the complex software modeling. The method proposed in this paper is used to check the strength of the completed Japanese Guanmen bridge, and the results are accurate enough. It is fast and reliable to use this method in the preliminary design and rapid safety assessment of suspension bridge.

Analysis of Deformation and Stress Characteristics of Anchored-Frame Structures for Slope Stabilization

In recent years, anchored-frame structures are widely being used in road slopes for stabilization and improvement. The technology of frame structure with anchors is becoming more and more mature, but the pertinent theory lags behind the application. While more attention is being paid to the control of deformation, there is still no uniform solution to the calculation of deformation in the anchored-frame structures. According to the classical laterla earth pressure theory and static equilibrium, this paper improves the calculation method of lateral earth pressure and derives the calculation formula of slope-induced lateral earth pressure. At the same time, based on the elastic foundation beam model, the columns and beams are treated as a whole system, and the appropriate elastic frame beam model is established. The formula of the deformation and bending moments for the columns and beams in the anchored-frame structures are derived. Additionally, the calculated results based on the abovementioned newly derived formulas are compared with those of finite element simulations for a simulated case study. The results of simulation and analytical calculation are basically consistent, which prove the feasibility of the new analytical method.

Study on the Mechanical Relationship among the Backfilling Mining Support, Roof Rock Beam, and Gangue Filling Body in Comprehensive Mechanized Filling Mining Process

Based on the theory of elastic foundation beam, the mechanical model of the backfilling mining support-roof rock beam-gangue filling body under the condition of comprehensive mechanized filling mining is established. The foundation coefficient of each part is determined, and the subsidence of each part of roof rock beam is calculated. It is found that the initial filling height is the decisive factor to control the subsidence and migration stability of each part of the roof rock beam. Properly increasing the pushing force of backfilling-coal mining hydraulic support on the filling body can also effectively control the roof subsidence. The comprehensive mechanized filling mining process was studied by similar simulation experiments, it is found that the influence law of initial filling height on roof rock beam subsidence is the same as that of theoretical analysis, and the experimental measurement values and fitting function relationships are consistent with the theoretical calculation results.