Vlasov Foundation Research Articles

Analytical Solution to Estimate the Effect of Underlying Tunnel Excavations on the Existing Tunnel

ABSTRACTThe tunneling underlying inevitably leads to the displacement of adjacent soil, greatly influencing the deformation of the tunnel above. Most theoretical studies primarily concentrate on analyzing the mechanical equilibrium of individual tunnel sections, ignoring the energy generated by the system during tunnel deformation. Based on this, in view of the energy relationship, the overlying tunnel's deformation is simulated by using the Rayleigh–Ritz method. Further, its potential energy equation can be established based on the Vlasov foundation. The corresponding energy variational solution is solved according to the minimum potential energy principle, leading to an analytical solution for the shield tunneling‐induced overlying tunnel's response. The efficacy of the suggested method is verified by contrasting it with centrifuge experiments and field case studies derived from prior studies. Relative to the Winkler foundation model, which deviated from the suggested approach, the results derived from the suggested method show a closer correlation with the collected measurement data. Further parameter studies show that the vertical clearance and skew angle between two tunnels, the volume loss rate, and elastic modulus are significant factors affecting the tunnel behaviors due to tunneling underneath. The suggested theoretical model can be applied to forecast potential risks that an existing tunnel may encounter during the excavation of a new tunnel underlying in similar engineering projects.

On the Applications of a New Advanced PEPFG Mathematical Model for HTM Dynamic Behavior of SDF Sandwich Plates

Considering the crucial role of the flexoelectricity phenomena (the electrical polarization–strain gradient coupling) in the mechanical behavior of different structures on the micro/nanoscale, this paper is derives the motion equations of a size-dependent flexoelectric (SDF) sandwich plate to study its hygro-thermo-mechanical (HTM) dynamic behavior. The model is a three-layer microplate including a porous exponential and power–law functionally graded (PEPFG) mid-layer, and two flexoelectric face sheets. The whole structure is under hygrothermal loading and the Vlasov foundation serves as the stand for the structure. Then, Hamilton’s principle and modified couple stress theory (MCST) are implemented to derive the motion equations. The new PEPFG utilization besides evaluating the impact of the length scale parameter, hygrothermal loading, materials composition, porosity, foundation parameter, and boundary conditions on the normalized natural frequency (NNF) of such an SDF sandwich model is the novelty of this paper. It is revealed that the lateral ratio enhancement causes NNF and stiffness reduction in the model. Furthermore, among all considered boundary types, simply supported and clamped refer to the lowest and the highest NNFs, respectively. This paper serves as a good source to provide a better understanding of the dynamic response of high stiffness-to-weight ratio structures to different variable variations.

Theoretical Solutions for Forecasting the Response of the Existing Pipeline Induce by Tunneling underneath

In order to accurately and efficiently assess the impact of tunnel excavation on overlying existing pipeline, an analytical method is proposed to solve this problem. First, the vertical free displacement of the surrounding soil due to tunnel excavation can be derived by the Loganathan formula. Next, the overlying existing pipeline can be treated as a Timoshenko beam resting on the Vlasov foundation model, and the influence of the surrounding soil on the both sides of the existing pipeline is taken into consideration. Finally, an analytical solution for the longitudinal deformation of the existing pipeline can be obtained by using the integral method. Case analysis results demonstrate that the calculated results of this method closely in line with measured data. Compared to the degenerate analytical solution given by this method, the result from this method is more consistent with the measured data. Further parameter studies show that the volume loss rate, diameter of new tunnel, skew angle, and vertical distance between tunnel and pipeline are significant factors affecting the existing pipeline response due to tunneling underlying.

A Study on the Influence of Dewatering in the Excavation of Adjacent Tunnels under Lateral Soil Effects

The dewatering of foundation pits leads to changes in the water level and effective stress within the surrounding strata. When existing tunnels are present within the dewatering influence zone, the impact of dewatering on these tunnels cannot be ignored. The Vlasov foundation beam model was used to simulate the interaction between the tunnel and the soil, and the key parameters of the model were precisely investigated. In addition, the constraining effect of the lateral soil on the tunnel was also considered. By integrating the principles of effective stress and Dupuit’s assumption, in this work we calculated the additional load on the tunnel caused by foundation pit dewatering, which was then applied to determine the tunnel stress and deformation induced by dewatering. The accuracy of this approach is validated through comparative analysis with finite element results. Furthermore, the relationships between the permeability coefficient (kt), the spacing (d) between the tunnel and the dewatering well, the water level drop (sw), and tunnel stress and deformation were further studied. The key findings are summarized as follows. Firstly, accounting for lateral soil effects enhances computational accuracy. Secondly, an increase in soil kt leads to a greater tunnel settlement with relatively minor changes in bending moments. Thirdly, as d increases, both tunnel settlements and bending moments decrease. Additionally, as the water level dropped from 10 m to 30 m, the maximum additional stress on the tunnel increased by 94.50%, and the settlement increased by 127.43%. Consequently, it is essential to pay close attention to the tunnel segment nearest to the water level.

Analytical prediction for longitudinal deformation of shield tunnel subjected to ground surface surcharge considering the stiffness reduction

AbstractThis paper presents an improved longitudinal beam‐spring model on the Vlasov foundation for estimating the longitudinal deformation of the shield tunnel when subjected to the ground surface surcharge. This model incorporates an improved subgrade modulus and treats each segmental ring as a Timoshenko short beam, with each circumferential joint modeled by two mechanical springs. It can accurately reflect the discontinuous deformation, and capture the dislocation and opening deformation of shield tunnels. Two‐stage analysis methodology is adopted to consider soil and tunnel interaction. The feasibility of this model is verified by comparing it with two well‐documented field monitoring cases. The computed results are also compared with those based on other analytical models. The results show that the Timoshenko continuous beam overestimates the dislocation deformation, while underestimates the opening deformation. In addition, the settlement curve exhibits neither smooth nor differentiable features. Finally, this paper also conducted some parameter analysis to examine the impact on tunnel deformation, encompassing dimensions of ground surface surcharge, the dual‐area loading, and the joint reinforcement. This approach provides valuable insights into how the deformation characteristics of shield tunnels are influenced by ground surface surcharge.

Analysis of longitudinal stress and deformation characteristics of shield tunnel under faulting dislocation

Fault dislocation seriously threatens the structural security of cross-fault tunnels during operation. Regarding the mechanical response of the tunnel across faults, the tunnel was equated as the Timoshenko beam on the Vlasov foundation in the present study, and the mechanical analytical model of the cross-fault tunnel was established and solved by the finite difference method. Published cases were utilized to validate the reasonableness of the analytical model. The influence law of critical parameters of the model on the response of the tunnel was investigated by parameter sensitivity analysis. Finally, the mechanical properties of the tunnel under the non-homogeneous foundation conditions were discussed. The calculation results of the proposed analytical model were similar to the existing model test monitoring data, and the trend was the same, demonstrating the correctness of the analytical model. The tunnel-fault distance, foundation reaction coefficient, foundation shear stiffness, and effective factor of bending stiffness changed the maximum tunnel bending moment, while the fault inclination changed the position where the maximum bending moment occurred. For the non-homogeneous foundation, the difference of adjacent foundation parameters significantly affected the response law of tunnel longitudinal internal forces, and the maximum tunnel bending moment presented a particular nonlinearity with the change of foundation parameters.

Meshless Analysis of a box culvert resting on Modified Vlasov Foundation

Meshless Analysis of a box culvert resting on Modified Vlasov Foundation

Static Analysis of thin Rectangular Plate Resting on Elastic Foundation Using Modified Vlasov Model

A four-nodded rectangular plate bending element based on Kirchhoff theory resting on elastic foundation using modified Vlasov model. For evaluate the two soil parameter for Vlasov foundation the modulus of elasticity and Poisson ratio of the soil is assumed constant from top surface to the top of bottom rigid base. All the deformation stiffness matrix of plate and subsoil are evaluated using finite element method. A Matlab code is developed and convergence study is carried out and then some realistic cases of plate under static load on elastic foundations are solved to determine the static response. The results, thus obtained, are compared, with the available results obtained by other researchers. It behaves extremely well for thin plates and convergence rate is high.

Modelling the performance of immersed tunnel via considering variation of subsoil property

This paper presents a theoretical model to evaluate the time-dependent behaviour of an immersed tube tunnel by considering the changes in soil properties over time. The proposed model simplifies the tunnel as a Timoshenko beam on a Vlasov foundation with a stiffness change. Subsequently, the partial differential equation for calculating the stress and deformation of the immersed tube tunnel was derived. A new approach to solving this partial differential equation is proposed, which is different from the existing solution in the literature. The proposed model can analyse the joint force transmission characteristics of an immersed tube tunnel. This was verified by the field-observed settlement data of the immersed tube tunnel of the Hong Kong-Zhuhai-Macao transportation pass. The results show that the calculated results of the proposed model are consistent with the measured data, and the structural stress of semi-rigid elements can be quantitatively analysed by calculating the settlement of elements caused by flexible and rigid joints and the vertical differential settlement of joints.

Two Novel Vlasov Models for Bending Analysis of Finite-Length Beams Embedded in Elastic Foundations

The issue of soil–structure interaction (SSI) is essentially to analyze the influence of complex media on the mechanical behavior of supported structures. With the development of underground space, geological structures and space constraints put forward higher requirements for foundations and buildings. In this paper, the effects of soil heterogeneity and embedment depth on the bending of finite-length beams embedded in two novel Vlasov elastic foundations are investigated. Firstly, the constitutive relations of subsoil are simulated by Gibson and transversely isotropic soils, and the type of elastic foundation is described by the modified Vlasov model. Then, based on variational principles, the governing differential equations for the deformation and attenuation parameters of beams embedded in elastic foundations are derived by taking the variation of the minimum potential energy of the system, and the characteristic coefficient related to the embedment depth is introduced. Finally, the mechanical performance of the beam and foundation is obtained by an iterative technique and the Fourier series method, and an extensive parametric study is performed to examine influence of some basic parameters on the deformation and internal forces of the system. The results show that the mathematical expressions of two refined elastic models are in good agreement with those of the traditional Vlasov foundation after degradation. The iterative technique based on the principles of solid mechanics can be employed to obtain more reliable model parameters. More importantly, with the increase in the embedment depth, the mechanical responses of the beam and subgrade forces decrease. The main reason is that the restraint effect of the soil media around structures, which leads to the reduction of the characteristic coefficient affecting the displacement of beams. Moreover, the heterogeneity of soil, including Gibson characteristics and transverse isotropy, should be considered according to specific working conditions in civil engineering.

The modified Vlasov model on a nonhomogeneous and nonlinear soil layer

This study presents a novel approach to account for the soil nonlinearity of nonhomogeneous soil deposits in foundation deflection analyses in the context of a modified Vlasov foundation model. We present an extension of the previously proposed formulation by developing a new formulation employing an improved algorithm that takes the modulus degradation curves at varying strain levels into account in an iterative manner. This new model, which takes the nonlinear soil behavior into account, was first verified against a linear elastic soil model given in the literature to ensure that the new model algorithm can capture the original solution when the soil behavior is assumed to be linear elastic. Later, the experimental data reported in the literature for a specific type of dense and loose sands were used in the example analyses. Example problems were considered for different cases, which presented (i) how the model captures nonlinear behavior and (ii) the significant effect of the nonlinear soil behavior. The result of the new model was also compared with the finite element model results, assuming elastoplastic soil. The results obtained from both models match well, especially for the maximum deflection value, provided that laterally constrained sections underneath the foundation are used.

Dynamic stability analysis of pile groups under wave load

As marine resources have been exploited in recent years, the number of offshore buildings has greatly increased. Foundations of these buildings are mainly pile and pile group foundations. Compared with the single pile, the interaction between piles in the pile group is more complicated. The dynamic stability analysis of pile groups under wave load has not been reported thus far. On this basis, based on the theory of diffraction, the modified Vlasov foundation model and the principle of dynamics, the high-order vibration differential equation is obtained. The interaction factor method and transfer matrix method are combined to establish dynamic stability equations of the active pile and passive pile. The dynamic interaction factor between piles and the group pile impedance are obtained. Parametric analysis is carried out. The ratio of the pile spacing to the pile diameter S/Dis found to be the major factor in pile group dynamic interaction. As for the pile group, the displacement of the pile u increases with increasing wave height Hlinearly and increases with increasing wavelength Lnonlinearly, both increments are much lesser than that of the single pile. the topsoil is of vital importance to the pile group impedance. In engineering practice, the pile group stability can be improved by increasing Young's modulus of the topsoil.

Influence of Inertial Vlasov Foundation Parameters on the Dynamic Response of the Bernoulli-Euler Beam Subjected to A Group of Moving Forces-Analytical Approach.

The subject of this study is the vibration of the Bernoulli–Euler beam on a three-parameter inertial foundation caused by a group of moving forces. The solution to the problem is obtained analytically. The influence of deformable foundation properties on the dynamic response of the beam in the case of forced vibration and the case of free vibration after the load has left the beam is analysed. The influence of velocity on the dynamic response of the beam is also investigated in both cases. The results can be used as a benchmark for calculating more complex engineering structures under moving loads caused by road or railroad vehicles. The results of the investigation are presented in the figures. It is evident that the coefficient determining the foundation inertia has a significant influence on the dynamic deflection of the beam. Taking shear into account in the Vlasov foundation model has little effect on the dynamic deflections of the beam. The equivalent damping number introduced into the Kelvin–Voigt model takes into account the structure damping and mass damping of the beam.

Meshless Analysis of a box culvert resting on Modified Vlasov Foundation

Meshless Analysis of a box culvert resting on Modified Vlasov Foundation

Dynamic Lateral Response of the Partially-Embedded Single Piles in Layered Soil

Scouring can reduce the strength and rigidity of the pile–soil system and become one of the major causes for the failure of the structure of the partially-embedded single pile. The stratification of the soil fields has a significant influence on the internal force and deformation of laterally-loaded piles. A dynamic model of the laterally-loaded single pile in layered soil is established employing Hamilton’s principle based on the modified Vlasov foundation model. Then, the finite difference method is used to obtain the numerical matrix containing the control equations of the single pile to achieve accurate modeling of the soil–structure interaction (SSI) system affected by scouring, so as to solve the natural frequencies of the single pile. Green’s function method obtains the analytical solution of the forced vibration of the single pile. The effects of scouring and the layered soil on the dynamic response of the single pile are studied by numerical calculation and parameter analysis. It is shown that the dynamic model of the partially-embedded single pile in layered soil based on the modified Vlasov foundation model can accurately predict the dynamic characteristics of pile foundation affected by scouring. As the scouring degree intensifies, the first-order natural frequencies of the single pile in layered soil decrease significantly. The subgrade reaction coefficient of each layer of soil in the modified Vlasov foundation model decreases, and the shear coefficient increases. The first-order natural frequencies of the single pile at each scour level increase with the increase in the thickness of the underlying soil. When the elastic modulus of the first layer of soil is increased by one time, the first-order natural frequencies of the single pile are increased by about 20%.

Vibration of FG Porous Three-Layered Beams Equipped by Agglomerated Nanocomposite Patches Resting on Vlasov's Foundation

Vibration of FG Porous Three-Layered Beams Equipped by Agglomerated Nanocomposite Patches Resting on Vlasov's Foundation

Analysis of sandwich single cantilever beam test specimen with graded core

In previous research, an analysis model named the ‘beam on Vlasov foundation model’ was proposed to theoretically analyze the compliance and energy release rate of sandwich single cantilever beam (SCB) test specimens. The validity of the analytical model was confirmed when it was applied to sandwich specimens with homogeneous cores. In this study, the analysis model is applied to the analysis of a sandwich SCB test specimen where the Young’s modulus of the core varies along the thickness direction. The procedures to obtain the solution for two specific cases are described. One is the case that the Young’s modulus of the core varies in the thickness direction as an exponential function. The other is the case that the Young’s modulus of the core varies as a combination of exponential functions which is symmetric with respect to the midplane of the core. By comparing with finite element analysis, it is confirmed that the beam analysis model can provide reliable results even when the core is inhomogeneous in the thickness direction.

Effects of Shear Deformation and Rotary Inertia on a Simple-free Anisotropic Plate on Vlasov Foundation Traversed by a Distributed Moving Mass

Effects of Shear Deformation and Rotary Inertia on a Simple-free Anisotropic Plate on Vlasov Foundation Traversed by a Distributed Moving Mass

Bending Analysis of Circular Thin Plates Resting on Elastic Foundations Using Two Modified Vlasov Models

The influence of soil heterogeneity is studied on the bending of circular thin plates using two modified Vlasov foundation models. The model parameters are determined reasonably using an iterative technique. According to the principle of minimum potential energy and considering transversely isotropic soils and Gibson soils, the governing differential equations and boundary conditions for circular thin plates on two modified Vlasov foundations are derived using a variational approach, respectively. The determination of attenuation parameters is a difficult problem, which has hindered the further application of the Vlasov foundation model. The equation that must be satisfied by the attenuation parameter is determined, and an iterative method is used to solve the problem. A comparative analysis is conducted between two modified Vlasov models and the traditional Vlasov model. The results show that the governing equations and boundary conditions for circular thin plates resting on two modified foundations are consistent with those for a circular thin plate on traditional two-parameter foundation after degradation. The accuracy and reliability of the proposed solutions are demonstrated by comparing the obtained results with those reported in the literature. The heterogeneity of soils, including the transversely isotropic soils and Gibson soils, has a certain effect on characteristic parameters of the foundation models as well as the deformations and internal forces of circular thin plates. The present study could be employed as a reference for future engineering designs.

Bending and buckling analysis of sandwich Reddy beam considering shape memory alloy wires and porosity resting on Vlasov's foundation

The aim of this research is to analyze buckling and bending behavior of a sandwich Reddy beam with porous core and composite face sheets reinforced by boron nitride nanotubes (BNNTs) and shape memory alloy (SMA) wires resting on Vlasov\'s foundation. To this end, first, displacement field\'s equations are written based on the higher-order shear deformation theory (HSDT). And also, to model the SMA wire properties, constitutive equation of Brinson is used. Then, by utilizing the principle of minimum potential energy, the governing equations are derived and also, Navier\'s analytical solution is applied to solve the governing equations of the sandwich beam. The effect of some important parameters such as SMA temperature, the volume fraction of SMA, the coefficient of porosity, different patterns of BNNTs and porous distributions on the behavior of buckling and bending of the sandwich beam are investigated. The obtained results show that when SMA wires are in martensite phase, the maximum deflection of the sandwich beam decreases and the critical buckling load increases significantly. Furthermore, the porosity coefficient plays an important role in the maximum deflection and the critical buckling load. It is concluded that increasing porosity coefficient, regardless of porous distribution, leads to an increase in the critical buckling load and a decrease in the maximum deflection of the sandwich beam.