Elastic Foundation Beam Research Articles

Buried Pipeline Collapse Dynamic Evolution Processes and Their Settlement Prediction Based on PSO-LSTM

Based on the unit life and death technology, the dynamic evolution process of soil loss is considered, and a pipe-soil nonlinear coupling model of buried pipelines passing through the collapse area is constructed. The analysis shows that after the third layer of soil is lost, the existence of the “pipe-soil separation” phenomenon can be confirmed, which then supplements the assumption that “pipe-soil is always in contact” in the elastic foundation beam theory. Calculation of settlement deformation of buried pipelines It needs to be divided into two stages: cooperative deformation and non-cooperative deformation. Taking the settlement prediction of buried pipelines as the goal, the particle swarm algorithm (PSO) was used to optimize the number of neurons, Dropout, and Batch-size in the long short-term memory network (LSTM) structure. The optimization results were 60, 0.001, and 100, respectively. The PSO-LSTM model proposed in this article can accurately describe the dynamic evolution process of buried pipelines and has better prediction accuracy than the modified Gaussian curve method and LSTM neural network model. The use of this model can provide a reference for safety risk management, disaster early warning, and intelligent monitoring when buried pipelines suffer from soil collapse disasters.

Scratch-induced surface formation mechanism in C/SiC composites

Due to the extremely complex composition of C/SiC composites, their material removal mechanisms are significantly different from those of conventional single-phase ceramic materials. Therefore, the grinding removal mechanism of C/SiC composites must be investigated so that the components based on these composites can be machined efficiently and with low damage. In this paper, nano-scratch experiments with various cutting depths are carried out along different fiber orientations to simulate the material removal process in grinding and theoretically clarify the damage failure mechanism based on different cutting thicknesses. According to the assessment of surface and subsurface morphology of the various constituents in the scratch grooves regarding different fiber orientations, the multiple brittle breakage modes and surface integrity of carbon fiber are revealed. Green’s function is applied to establish a half-space anisotropic analytic elastic stress field considering the microstructural characteristics of material, and the crack nucleation and propagation principles during micro brittle fracture regime for nano-scratch experiment are elucidated based on the fracture mechanics and the maximum principal stress criterion. The formation mechanism of machined surface morphology in macro brittle removal process is investigated under the crack deflection effect at the weak interface and based on the elastic foundation beam theory. The related findings can provide a reasonable reference framework for optimizing the grinding technology, material and tool design regarding C/SiC composites.

A Novel Model for Mechanics and Safety Calculation of Pipe Roof Based on the Load Transfer Mechanism

A novel model is created in this paper to realize the systematic evaluation of the mechanical properties and construction safety of the pipe roof support system. The pipe roof is split into supported area, unloading area, and stable area based on the load distribution characteristics. Combining a statically indeterminate beam (for the area of unloading) with an elastic foundation beam (supported area and stability area) takes into account the mechanical effect of the pipe roof. The new model can better reflect the load transfer mechanism and the stability of the tunnel face under the pre-support. It is demonstrated that the novel model, when compared to the existing theoretical solution, is more closely related to the measured and simulated results than typical engineering cases and is practical for field application. It can provide a new idea for the design of pipe roof support and the safety evaluation of field construction.

Analytical solution for seismic response of vertical shaft with primary and secondary linings under SH wave excitation

This paper presents a novel mechanical model for seismic response analysis of vertical shafts. The model is based on elastic foundation beam theory and simplifies the shaft linings as parallel Euler Bernoulli beams. Their interaction is simulated using uniformly distributed springs. The governing differential equation for shaft vibration is derived for SH wave excitation. The seismic input motion is applied to the primary lining by converting the free field displacement into harmonic form. The closed-form solutions for seismic response of both primary and secondary linings are obtained via the transfer function method. The accuracy of analytical solution is validated by comparing with finite element analysis results. Additionally, the impact of foundation stiffness, secondary lining thickness, shaft outer diameter, and relative stiffness between linings on seismic response are investigated in the parametric analysis. The analytical solutions of the seismic response analysis of vertical shafts indicates that the relative stiffness between linings significantly affects the secondary lining's peak bending moment. Furthermore, higher stiffness of the elastic connection layer between the two linings can effectively reduce the peak displacement response of the secondary lining.

A Hybrid Method for Vehicle–Track Coupling Dynamics by Analytical and Finite Element Combination Technique

Globally, rail transit is developing toward higher speeds, larger axle weights, and greater environmental friendliness. The more and more complex wheel–rail interaction will result in the dynamic responses of vehicles, tracks and other structures needing more in-depth theoretical research. However, most existing models for dynamic simulations of the vehicle–track coupling system need to extend the model on both sides of the concerned region to eliminate the boundary effect. To a certain extent, this kind of process method increases the computational effort. To overcome this disadvantage, a hybrid model combined with the analytical method and finite element method was proposed. The moving support system (including transition nodes) was specially established referring to the analytical solution of rail deflection based on the Winkler elastic foundation beam theory to realize the combination of the two methods. Two examples were presented to verify the stability and accuracy of the proposed model. The comparison results show that simulation results of vertical wheel–rail forces and track vibrations are almost consistent with the existing model. Furthermore, the calculation efficiency was discussed and certificated under different long-marshalling trains, with an obvious speedup factor that could be more than 2.5 for 16-marshalling train. The proposed model has a wide application prospect in the vehicle–track coupling analysis of long-marshalling trains, especially for heavy haul railways with hundreds of vehicles.

Analysis of interfacial stresses on narrow beams strengthened by FRP straps with a side anchorage system

AbstractInterfacial stress concentrations at fiber‐reinforced polymer (FRP) ends can easily cause premature debonding failure of FRP‐strengthened beams. To solve this problem in narrow beams, a hybrid strengthening method was proposed in our previous study, but the theoretical stress analysis was lacking due to the complexity at the anchorage zone. In this study, the interfacial stresses of the hybrid strengthened beam were initially analyzed by decomposing it into a purely bonded beam under three different effects, including the load on the beam, the tensile force at the end of the FRP strap released from anchor plates and a pair of eccentric forces induced by the side anchorage system towards the midspan. By summing the special solutions of the three cases, the expressions for the total interfacial stresses of a hybrid strengthened beam were determined. Moreover, a formula for the shear stiffness of the side anchorage system was proposed, in which the side plate and the bolt were compared to a deep cantilever beam and an elastic foundation beam, respectively. Finally, a finite element model was developed to verify the applicability of the proposed theoretical model. The theoretical and simulated results were in satisfactory agreement for a hybrid strengthened beam.

State analysis of the inclinometer tube for monitoring relative slippage between backfill and surrounding rock mass

ABSTRACT This paper presents a methodology for analysing the state of an inclinometer tube used for in-situ monitoring of the relative slide between backfill and surrounding rock mass, based on the principles of elastic beam and elastic foundation beam theory. Through the utilisation of this approach, it becomes feasible to evaluate the appropriate depth for installation, the extent of measurement, and the operational state of the inclinometer tube. The mechanical response of the inclinometer tube was analysed using the new method and finite element method, with Longshou Mine serving as the background. The feasibility of the new method was subsequently confirmed.

Investigation of stress distribution and damage behavior caused by forced installation of a composite bolted joint with a hole-location error

In this paper, the influence of forced installation caused by a hole-location error on the 3D stress distribution and damage of a composite bolted joint is investigated. An analytical model of stress distributed on composite holes is promoted, in view of non-uniform extrusion caused by forced installation. At first, non-uniform extrusion of the hole edge caused by forced installation is analyzed. According to the contact state, expression of hole deformation is given. Then, based on Hertz theory, the maximum extrusion load is obtained with help of deformation expression. By constructing an elastic foundation beam model, 3D stress distributed on a hole could be analyzed according to the extrusion load. Then, stress distribution predicted by the above analytical method is compared with that provided by FE considering composite damage. Finally, a forced installation experiment is carried out to analyze the damage distribution of the joint. Results show that a central-symmetrically distributed stress is introduced by the hole-location error. With an increment of the error, strength of composite decreases due to extrusion damage. Therefore, stress presents a concave distribution on the hole. As the hole-location error exceeding 3%, stress decreases gradually due to failure of composite. Damage of holes does not exhibit a centrosymmetric distribution. Serious damage is mainly distributed on the entrance of the hole at the lower sheet.

Force Calculation of Mechanical Model of Pile-anchored Support Structure Based on Elastic Foundation Beam Method

With the widespread use of deep foundation pit engineering in engineering construction, the force calculation problem about deep foundation pit support engineering has become a common problem in today’s engineering construction process. In this paper, based on the elastic foundation beam method, a simplified mechanical model of pile-anchored structure is proposed, and a systematic and practical calculation method is proposed for the force and deformation calculation of deep foundation pit support structure. The method simplifies the support structure as a vertically placed elastic foundation beam, the support, anchor and geotechnical body are replaced by a spring system, the spring stiffness of geotechnical soil can be calculated by the deformation modulus of geotechnical soil, and a systematic calculation method is proposed for the dynamic characteristics of the construction and structure of the foundation pit project; Based on the monitoring data of a deep foundation pit project, the calculation method of the simplified mechanical model proposed in this paper is verified, and the theoretical calculation value is compared with the field monitoring results; Single factor analysis is carried out on the detailed parameters of pile-anchor supporting structure to study the influence of cable prestress, cable dip Angle, pile diameter, pile length and other related parameters on the deformation and stress characteristics of supporting structure. Then the orthogonal combination of all factors is carried out to propose the optimization design. The results show that the maximum settlement deformation of the calculated value is 23.437 mm, and the maximum settlement deformation of the monitored value is 26.517 mm, and the difference between them is small. The maximum bending moment is 1210 kN⋅m after 150 kN and 250 kN horizontal prestressing is added to the second- and third-layer anchors respectively. After optimization, the maximum bending moment of pile row is 336.87 kN⋅m, and the maximum horizontal displacement of pile body is 16.505 mm, which is reduced by 11.97% compared with the original design.

A hybrid method to determine optimal design axial forces of servo steel struts in excavations with high deformation requirements

PurposeThe application of servo steel struts enables the active control of the excavation-induced deformation in foundation pits. However, there is currently only one design axial force for each servo steel strut, which requires in-situ axial force adjustments based on the experience of site engineers. The purpose of this study is to develop a method for determining the design axial forces of servo steel struts at different excavation steps.Design/methodology/approachIn this study, a hybrid method for determining the design axial forces of servo steel struts in different excavation steps was established based on the combination of the elastic foundation beam model and nonlinear optimisation.FindingsThe hybrid method is capable of providing a better set of design axial forces than the original design method. The lateral wall displacement and bending moment could be better controlled. Ordinary steel struts should be prevented from being set between servo steel struts to avoid axial force losses.Practical implicationsThe axial forces of the servo steel struts at different excavation steps should be designed to achieve better deformation control effects. Moreover, a well-designed set of axial forces can also reduce the internal forces of the retaining structure.Originality/valueThe hybrid method enables the determination of the design axial forces of servo steel struts at different excavation steps, which can guide axial force adjustments in practical projects.

Analytical solutions of the tunnels under the fault creeping by elastic foundation beam model with considering tangential interaction

The fault zone plays a vital role in the internal force responses of the tunnel. An analytical solution of the tunnel under the fault zone creeping is developed by taking account of normal and tangential interaction between the ground and tunnel. First, the elastic foundation beam model is used. Wherein, the normal interaction is considered by applying the displacements of the free field on the distal end of normal foundation springs. And the tangential interaction is transformed into bending moment applied on the beam. The analytical solution of the tunnel's response is gotten based on the model. Secondly, the numerical solutions from finite element model of 3D are provided to verify the validity of the proposed analytical solutions. Finally, the effect of the fault zone width, the elastic modulus of the fault and the concrete's grade of the lining are investigated. The results show that with the width of the fault zone increasing, the internal force decrease. The concrete's grade of the lining has opposite effects on the internal force of the tunnel. And with the growth of the elasticity modulus of the fault zone, the shear force and bending moment increase and decrease, respectively.

Stiffness evaluation of UHPC-filled socket column-foundation joints: Numerical investigation and analytical model

Socket connections are widely used to connect precast columns to the foundation and the initial stiffness of the socket joints is of great significance for seismic design. The connection efficiency of precast socket column has an important influence on its initial stiffness. Therefore, based on the previous experiment research on socket column by authors’ team, a finite element model (FEM) of ultra-high performance concrete (UHPC)-filled socket precast bridge column-foundation joints was established and verified by the local damages, failure mode and hysteresis curves. The key parameters that influencing the initial stiffness of socket joints were studied by numerical analysis, and a simplified calculation formula of initial stiffness was proposed. In addition, based on the theory of elastic foundation beam, an analysis model for predicting the initial stiffness of socket joints considering rotating stiffness of the connection was developed. The theoretical results are verified by the proposed simplified equations and experiments results in the literature. The method presented in this paper can conveniently predict the initial stiffness of RC socket column-foundation joints with reasonable accuracy.

Mechanical Properties of Ballastless Track Considering Freeze–Thaw Deterioration Damage

In order to investigate the stress characteristics of ballastless track under high latitude, and multi-source and multi-field extreme temperature conditions. Based on the finite element theory and the elastic foundation beam–plate principle, a finite element model of the ballastless track considering the limit convex abutment, gel resin, and interlayer bonding is established. The mechanical characteristics of the ballastless track under the slab–CAM layer bonding state, mortar separation, freeze–thaw degradation and forced deformation of the foundation are studied. Considering the deterioration of materials, the bending moment and reinforcement of track structures in cold regions are checked and calculated. The studies show that under the action of negative temperature gradient load, the edge of the track slab is subjected to tension, and structural separation occurs at the edge of the slab. When the interface between the track slab–CAM layer is poorly bonded, the bearing capacity can be improved, and the amount of separation can be reduced by increasing the structural stiffness of the CAM layer. Under the action of freeze–thaw cycles, the material performance deteriorates seriously, the separation between the track structures intensifies, the baseplate is seriously powdered and cracked, and the maximum tensile stress exceeds 6 MPa. The CAM layer and the baseplate are weak structures, and the foundation frost heave occurs at the expansion joint of the baseplate, which is the frost heave condition. Under freeze–thaw deterioration, the original reinforcement design of the substructure structure does not meet the requirements of structural cracks and reinforcement yield stress. In severely cold areas, the structural reinforcement scheme should be reasonably determined.

Analysis of Stress and Deformation Law of Tunnel Crossing Sliding Body Based on Pasternak Two Parameter Foundation Assumption

Because the landslide has an important influence on the internal force and deformation of the existing tunnel, and the research on the stress and deformation of the tunnel in the landslide area tends to field engineering monitoring, the corresponding theoretical analysis is relatively small, and there are some defects. First, Pasternak two parameter foundation model is introduced to establish the elastic foundation beam model of tunnel landslide interaction, which solves the soil discontinuity of Winkler foundation in the previous theory, and the transfer matrix method is used to derive the transfer matrix formula. Then, Matrix Laboratory (MATLAB) is used to compile the corresponding calculation program to analyze the distribution characteristics of internal force and deformation of the tunnel. Finally, the influence of relevant parameters such as the elastic coefficient of foundation inside and outside the landslide deformation area, the magnitude and distribution of landslide thrust, and the foundation shear stiffness inside and outside the landslide area are analyzed.

Calculation and Analysis of Pipe Joint Settlement Control in Large Back Silting Immersed Tube Tunnel

The use of the segmental pipe section immersed tunnel suffers from several problems, such as complex construction, weak foundation, great water depth, great thickness of siltation back on the top of the tube, and difficult settlement control. Based on Winkel’s elastic foundation beam theory, a mechanical calculation model is established according to the case of an inhomogeneous soil layer, and the force and deformation of the structural system of the immersed tube tunnel are calculated based on a bridge in Zhuhai as an example of an immersed tube tunnel. The results show that the derived formula for calculating the allowable differential settlement per unit length of the longitudinally immersed tube is applicable to the sudden change type foundation stiffness deformation model of the natural foundation section of the tube tunnel of the aforementioned bridge in Zhuhai. The relationship between the settlement control index and related influencing factors is analyzed. Hence, a formula for calculating the stratified ground foundation’s integrated bed coefficient is derived, and the equations for tunnel deflection curves and shear forces are solved. A set of calculation methods that are applicable to the foundation settlement control criteria of the segmental immersed tunnel is provided, and the results provide a significant reference for the optimization of the foundation scheme and improvement of the construction process for similar projects.

Analytical solution for circular tunnel under obliquely incident shear waves

The incident direction plays an important role in the seismic response of long lined tunnels. A simplified analytical solution is developed for estimating the seismic response of the circular tunnel under obliquely incident shear waves, including the principle stress and the internal forces and deformations on the cross section and longitudinal of the tunnel. Based on the elastic wave theory, the oblique incident shear wave can be decomposed into an axially propagating shear wave and a shear wave propagating transversely to the tunnel axis. A modified elastic foundation beam model is used to calculate the tunnel longitudinal response, which is based on Timoshenko beams resting on Winkler foundations with considering different tangential contact conditions. Furthermore, by adopting wave theory and Fourier transform, longitudinal response of tunnels under arbitrary seismic load can be obtained. Moreover, the flattening effect and out-plane response of tunnel cross-section caused by longitudinal bending are considered. The proposed analytical solution is verified by comparing with the dynamic numerical results. The effect of the incident angle, ground condition and contact condition on the seismic response of long lined tunnel is investigated by the simplified analytical solution. It is demonstrated that the proposed solution can be adopted to predict internal forces and deformations of circular tunnels under obliquely incident shear wave in preliminary design.

Two elastic supporting models to simulate the submerged floating tunnel and their equivalence on the free/forced vibrations

By applying two elastically supporting styles, the elastic supports beam (ESB) and elastic foundation beam (EFB) are proposed to simulate the underwater submerged floating tunnel (SFT) under hinged boundaries. Their equivalence is investigated through the frequencies/modes and forced responses caused by equidistant moving loads. The ESB model is built by regarding each tether as an elastic support and using the novel isolating/assembling technique between beam-segments and global tube, and the order of characteristic matrix for any number of intermediate elastic supports is reduced to 4 × 4. Then, the stiffness of all elastic supports and the uniformity/non-uniformity are well considered in the ESB model. The governing equations of the EFB model with a uniform linear elastic support are also given. The newly discovered results, which are verified by the finite element method (FEM), indicate the merging phenomena appear in the frequency spectrum in the ESB model. The equivalence holds for some uniform cases in the ESB model based on the peak values of responses by using the stiffness relationship and a correction coefficient, whereas the equivalence does not exist for the uneven case of elastic supports.

Dynamic Response Analysis of Offshore Flaoting Hose Strings Under Wave Load

A floating hose is key item for offshore oil transportation. In this paper, a mathematical model is derived for the overall dynamic performance of a single point-moored floating hose string under wave and current load. Airy wave theory was selected to calculate the wave force on the floating hose string. The dynamics of buoy, floating hose string and FSO were modelled using elastic foundation beam theory and discretised by using a fixed grid finite difference method. Discontinuities in the bending stiffness due to the flange connections are also considered. To verify the accuracy of the mathematical model, the finite element model of the buoy, floating hose string and FSO as a system was established by use of Orcaflex software tool. Numerical results for the displacement and bending moment at each section of the floating hose under severe sea conditions were obtained.

Seismic performance of precast double-column pier with UHPC-filled socket connections

Precast piers have been extensively investigated and applied in low seismic intensity areas, owing to the faster construction speed, limited traffic interruption, and environmental friendliness. However, few studies and engineering practices of the precast double-column piers (PDPs) located in high-intensity seismic areas have been reported. Therefore, in this study, a novel socket connection filled with ultra-high-performance concrete (UHPC) was proposed for the PDPs. The socket connections with concrete filled steel tube (CFST) are used to enhance the strength of the column-cap beam joints, at the same time the socket connections with the tooth-shaped shear keys are adopted at the column-footing joints to reduce the required anchorage length. The PDP with a scale ratio of 1:3 was constructed and then tested under the quasi-static load to investigate its seismic performance. Finally, a simplified analytical model of the socket connections was proposed based on the concept of the elastic foundation beam. The test results demonstrate that the damage of the specimen PDP was mainly concentrated at the bottom of the columns, and the damage at the damage ends of the PDP specimen was severer than that of the cast-in-place (CIP) specimen. The load-bearing capacity of the PDP is slightly higher than that of the corresponding CIP specimen, while the energy dissipation and displacement ductility of PDP are slightly smaller than those of the CIP specimen. The proposed model could accurately and efficiently capture the hysteretic behavior of the proposed PDP with socket connections.

Analytical solution of longitudinal seismic response of circular tunnel across soil-rock stratum based on improved elastic foundation beam model

This study aims to analysis the longitudinal seismic responses of circular tunnels across soil-rock stratum longitudinally (“soil-rock” means two different stratums, not just the soil and rock ground). Based on an improved elastic foundation beam model, an analytical solution is derived to investigate the seismic response of long tunnels across soil-rock stratum, subjected to sinusoidal shear motions. The improved elastic foundation beam model adopts the Timoshenko beam and Winkler foundation, with considering tangential contact conditions at the ground-tunnel interface. The free field reaction considers the reflection and transmission by the soil-rock interface and the wave passage effect. Explicit formulations are obtained for tunnel displacement, rotation angles, bending moments and shearing forces. The proposed solution is verified by comparing with the dynamic numerical results, as well as traditional analytical solutions. Finally, a parametric study is conducted to investigate the influence of traveling wave effect, earthquake frequency, shear wave velocity ratio of two stratums, lining stiffness and contact condition on tunnel seismic responses. The proposed analytical solutions can be used to predict the longitudinal seismic response of deep circular tunnels crossing soil-rock stratum in engineering design.