Viscoelastic Ground Research Articles

An Integration of Contact Force Models with Multibody Dynamics Analyses for Human Joint Mechanisms and Effects of Viscoelastic Ground Contact

An Integration of Contact Force Models with Multibody Dynamics Analyses for Human Joint Mechanisms and Effects of Viscoelastic Ground Contact

Mathematical modelling for interaction between soft ground and small curvature shield tunneling considering viscoelastic characteristics influences

The current analytical solutions for predicting the ground settlements induced by small curvature tunneling in soft ground are generally conducted on the assumption of linear elastic foundation and provide little attention on the soil rheology. This paper introduces a mathematical model to estimate the small curvature tunneling induced adjacent ground settlement considering the soil viscoelasticity. By introducing the Boltzmann viscoelastic ground model under the Laplace transform, the time domain parameters converted from Poisson's ratio and shear modulus are derived to further obtain the viscoelastic ground loss solution and the Mindlin solution. Then, the proposed viscoelastic solutions are employed for the ground settlement caused by the over-excavation and imbalanced loads for the small curvature tunnel, which accounts for the soil rheology influence. The accuracy of the mathematical model is then verified by comparisons with in-situ observed data and 3D numerical simulation results, as well as good agreement is obtained. Finally, the parametric analyses are performed to estimate the influence for transverse and longitudinal surface settlements, including tunnel curvature radius, shield cutterhead face radius, over-excavation value, creep time and shear modulus ratio of viscoelastic ground.

Algorithm for simulation of vibration effects during track tests of aircraft and missile technology

Track high-speed ground tests of products of aviation and rocket technology make it possible to experimentally confirm the aerodynamic and strength characteristics of new aircraft or their components. Experimental installation Rocket rail track 3500, located on the territory of the Federal State Enterprise Scientific Test Range of Aviation Systems named after L. K. Safronov (FKP GkNIPAS named after L.K. Safronov), is a complex hydro-gas-dynamic engineering structure. The main part of this installation is a rail track placed on a special concrete base, which is based on piles to eliminate the influence of viscoelastic ground vibrations. Between the rails, taking into account the profile of the track, a hydrodynamic multi-level tray is made, designed for hydraulic braking of the stored track sled. The movable rocket track sled rests on slip shoes covering the top rail head. On the track sleigh, solid propellant rocket engines and the object of study are placed. The article describes the approach to the calculation of determining the dynamic loads acting on the elastic structure of the track sled with the test object. The design is represented by a schematic spatial model of elastic beams in the form of rods, plates, pipes with equivalent mass and stiffness, interconnected by elastic links. A model of non-stationary aerodynamic forces is formulated taking into account viscosity for numerical calculations of the flow around the sled structure. Programs have been developed and modeling of the aerodynamic interaction in the case of a supersonic air flow around the structure of a rocket sled has been carried out. The results of vibrational accelerations of elements, components of the sled and the test object, depending on the speed of movement, were obtained by calculation. The forms and frequencies of natural free vibrations of the sled structure are determined, and the densities of the vibration acceleration spectra are calculated.

Effect of ground tire rubber media's viscoelasticity and flow passage geometry on the abrasive flow finishing of helical gear

This work aims to elucidate the behavior of viscoelastic ground tire rubber media (GTRM) under abrupt contraction and expansion of the media at the entry and exit of the gear flow channel and its influence on polishing results. Due to the inherent nature of the abrasive flow finishing (AFF) process, the media flow converges at the entrance of the gear tooth as it flows from a larger fixture cross-section to a narrower volumetric space between gear teeth. The material removal and subsequent surface roughness rely heavily on the flow's pressure and velocity. A numerical simulation was performed to obtain the pressure and velocity along the gear flank face width (FFW). To investigate the effect of variation in the media deformation rate along the gear flow channel on AFF results, the material removal height and improvement in average surface roughness at different locations along the tooth flank face width were measured. AFF results reveal that the material removal near the two edges of the gear tooth is higher and has an inferior surface finish compared to the tooth's center. Due to the abrupt compression of the media at the flow channel entrance, the media act elastically dominant, resulting in high pressure and flow velocity near the tooth edge (flow channel's entry). Additionally, the effect of the helix angle on the AFF of various helical gear (HG) was investigated. Among the three HGs chosen, the 30° HG produces the lowest surface roughness under moderate pressure and high velocity. The microhardness and fretting wear analyses further confirm that the AFF polishing increases the microhardness and wear resistance of the gear tooth surface as a result of work hardening and minimizing surface defects.

Viscoelastic Burger's model for tunnels supported with tangentially yielding liner

This study proposed an analytical model for the tunnel supported with a tangentially yielding liner in viscoelastic ground. The efficiency of the developed analytical model was verified by comparing the calculated results with associated numerical simulation results. Using the analytical model, a comprehensive parameter sensitivity analysis was performed to examine the effects of the rate of tunnel face advancement, concrete liner thickness, installation time of liner, and strength and thickness of yielding elements on the tunnel responses. The results highlight the significant benefit of the tangentially yielding liner to relieve overstress in the tunnel liner and improve the stability of the tunnel. The yield efficiency of the tangentially yielding liner depends highly on the yielding strength and deformable capacity of the yielding elements and less on the installation time.

Homogenization of subwavelength free stratified edge of viscoelastic media including finite size effect

This paper proposes the homogenization for a stratified viscoelastic media with free edge. We consider the effect of two-dimensional periodically stratified slab over a semi-infinite viscoelastic ground on the propagation of shear waves hitting the interface. Within the harmonic regime, the second order homogenization and matched-asymptotic expansions method is employed to derive an equivalent anisotropic slab associated with effective boundary and jump conditions for the displacement and the normal stress across an interface. The reflection coefficients and the displacement fields are obtained in closed forms and their validity is inspected by comparison with direct numerics in the case of layers associated with Neumann boundary conditions.

Consideration of longitudinal vibration of automobiles in planar model with taking road deformation and loss of contact into account

This article considers longitudinal planar vibration of a two-axle automobile moving linearly with a constant velocity and subjected to pre-deterministic kinematic excitation caused by the rough road surface. The automobile is modeled as a vibration system which has three masses and four degrees of freedom. The deformed road is modeled as an elastic beam which is simply supported at the two ends and lying on Kelvin’s visco-elastic ground. The change in dimensions of the contact areas is considered. The loss of contact between the wheels and the road surface is taken into account by producing the contact state parameters in the differential equations of motion of the vibration system. The partial differential equation which describes the motion of deformed road is then transformed into a set of all ordinary differential equations by applying the Bubnov-Galerkin’s method. Some typical results coming from numerical consideration are also presented in the article.

Consideration on lateral vibration of automobiles in quasi-planar model with wheel separation and road deformation taken into account

This article considers lateral vibration of an automobile in a so-called quasi-planar model where both the loss of contact and road deformation are taken into account. The automobile with dependent suspension is modeled as a vibration system which has two masses and four degrees of freedom. The deformed road is modeled as an elastic beam which has uniform rectangular cross-section, is simply supported at the two ends and lies on the Kelvin's visco-elastic ground. The loss of contact and the change in dimensions of contact areas are considered. The differential equations of motion of the vehicle-road coupled system which contains a partial differential equation are transformed into a set of all ordinary differential equations by applying the Bubnov-Galerkin’s method. A procedure for numerically solving the transformed differential equations of motion is proposed. Some illustrating results coming from numerical consideration are also presented in the paper.

Dynamic responses of long tunnels in layered viscoelastic ground subjected to inclined SH waves

Dynamic responses of a long tunnel in a horizontally layered viscoelastic ground subjected to inclined SH waves are analyzed by Fourier transform in this paper. The tunnel is assumed to be a beam. The free field displacement of the horizontally layered viscoelastic ground is imposed on the long tunnel through the viscoelastic foundation model. The analytical solution is verified through comparison with numerical solutions and other solutions in the literature. Based on the solution, the difference between rigid bases and elastic bases is clarified, and the influence of pressure-dependent effect is discussed. Parametric analyses on the incident angle and the flexibility ratio are also performed. The solution can be easily used in the preliminary seismic analysis and design of tunnels.

Consideration of the problem about vibration of automobile in one fourth model with taking road deformation and the loss of contact into account

This paper presents an approach to the problem about vibration of automobiles in one-fourth model where both road deformation and the loss of contact are taken into account. Contact characteristics such as the geometry of the contact area, pressure distribution, the relation between the contact force and the dimensions of the contact area, and therefore the change in dimensions of the contact area with respect to time are mentioned. Deformed road is modeled as an elastic beam which is simply supported at the two ends and lies on Kelvin’s visco-elastic ground. The differential equations of motion for both states of contact and losing contact are unified by introducing a so-called contact state parameter. The partial differential equation among the differential equations of motion of the vehicle-road coupled system is transformed into a system of all ordinary differential equations by applying the Bubnov-Galerkin’s method. A procedure for numerically solving the ordinary differential equations of motion of the vibration system under consideration is proposed and some numerical results for illustration are also presented in the paper.

Analytical Study of Soil Displacement Induced by Twin Shield Tunneling in Semi‐Infinite Viscoelastic Ground

Effective measures are needed to strictly control soil displacement caused during the process of shield construction excavation for urban subway tunnels. When calculating the displacement of soil caused by loading or unloading, many previous analytical studies have assumed that the soil was a linear elastic body and ignored the viscosity of the soil. In this study, the Boltzmann viscoelastic model and the Mindlin basic solution were combined to consider the effects of the additional support pressures, the shield shell frictions, the grouting pressures, and the ground loss, and a three‐dimensional viscoelastic solution for soil displacement caused by shield tunneling was derived. According to the calculation results of an example, the analytical solution was able to consider the asynchronous construction of the left and right tunnels and the mutual influence of the double shield tunnel. The rationality of the approach proposed in this study was verified by comparing the theoretical solution with the measured settlement values. In addition, the influence of differences in the viscoelastic parameters (the viscosity coefficient, the shear modulus of the elastic element, and the shear modulus of the viscous element) and the geometric parameters (the distance from the excavation surface, the calculated depth, and tunnel spacing) on soil displacement is discussed. The calculation method in this study provides a theoretical basis for predicting the three‐dimensional soil deformation caused by shield tunneling, especially in soft clays.

Analytical study on interaction between existing and new tunnels parallel excavated in semi-infinite viscoelastic ground

Abstract A new tunnel is usually excavated in close proximity to existing ones, which leads to significant negative influence on the existing tunnels. Moreover, the rheology of the ground probably induces quite different time-dependent ground deformation if the new tunnel is excavated at different time. This study focuses on the interaction between the existing and the new tunnels which excavated in rheological ground at a shallow depth. Through the strict derivation, a new analytical solution is proposed for ground stress and displacement induced by the interaction of new and existing tunnels. The ground rheology, excavation delay of the new tunnel, tunnel size and various tunnel arrangement, are all taken into account. The complex variable theory combined with the extension of corresponding principle are employed in the derivation. By deriving the potentials in complex variable theory for the problems in all the excavation stages, the time-dependent stresses and displacements are finally addressed for the whole excavation process, where the ground is simulated by any linear viscoelastic models. To verify and validate the analytical solutions, the analytical solution is compared with numerical results under simplified and complex ground conditions, which shows good consistency except the solution for Case 1 (considering gravity gradient). A parametric study is finally preformed to find the influence of excavation time and location of the new tunnel, the tunnel spacing and relative size of the new tunnel, on stresses/displacements around tunnels and surface settlements. The results show that the excavation time of the new tunnel (t2) significantly influence the additional displacements around the existing tunnel which is a decrease exponential function of t2; when the distance from center to center is larger than 2.5R1 (2.0R1), the interaction between two tunnels can be neglected from perspective of displacement (stress).

Viscoelastic ground responses around shallow tunnels considering surcharge loadings and effect of supporting

Tunnels in urban areas inevitably lie near the ground surface, and will be affected significantly by the loads on the surface. This study provides a new analytical approach to efficiently predict the time-dependent ground stresses and displacements induced by shallow tunnelling under initial stresses due to both gravity and surcharge loads. The viscoelasticity of the ground, inclination of ground surface, effect of support and its delayed installation, are all taken into account.The elastic potentials were first derived for tunnels subjected to boundary stresses induced by gravity, surcharge loads and tunnel supports, respectively. Based on the extension of correspondence principle, the time-dependent ground stresses and displacements were then provided analytically for any type of linear viscoelastic ground. The FEM analysis was performed to verify the analytical solutions, which demonstrates a well agreement between the analytical and numerical results. Additionally, by the qualitative comparison of surface movements and initial failure zone around tunnel between analytical solution and results from other numerical model of elastoplastic cases, it was proved that the analytical solution can predict the initial failure zone and can qualitatively provide the reliable ground deformations. Finally, a parametric study was carried out to find the influence of timing for support installation, the slop angle and the surcharge loads on stresses and displacements around tunnels. The proposed solutions provide a quick alternative method to predict the time-dependent ground responses of shallow tunnelling in rocks, or medium/stiff clays.

Dynamic Responses of Ground Vibration due to a Moving Load by using Cole–Cole Model

The dynamic responses of viscoelastic ground vibration due to moving loads by using Cole-Cole model is investigated in this study. First, the paper gives the equation of motion in terms of the displacements for the homogeneous isotropic viscoelastic medium in the frequency domain. Then, the governing equations can be reduced to two Helmholtz equations and the displacement of the viscoelastic medium can be expressed via the potentials. By applying the double Fourier transform with respect to the horizontal coordinates, the general solution for the potentials of the visoelastic medium in the frequency wavenumber domain can be derived.

Three-Dimensional Modeling and Simulation of a Falling Electronic Device

This article focuses on a realistic mathematical model for multiple impacts of a rigid body to a viscoelastic ground and its comparison to theoretic results. The methodology is used to study impact on an electronic device. When an electronic device drops to the floor at an uneven level, the rapid successions of impact sequence are important for their shock response to internal structure of the devices. A three-dimensional, continuous contact, computational impact model has been developed to simulate a sequence of multiple impacts of a falling rigid body with the ground. The model simulates the impact procedure explicitly and thus is capable of providing detailed information regarding impact load, impact contact surface, and the status of the body during the impact. For the purposes of model verification, we demonstrate the numerical simulation of a falling rod problem, in which the numerical results are in good agreement with the analytic solutions based on discrete contact dynamics impact models. It is indicated by the numerical experiments that simultaneous impacts occurred to multiple locations of the body and that subsequent impacts might be larger than initial ones due to different angles of impact. The differential equation-based computational model is shown to be realistic and efficient in simulating impact sequence and laid a foundation for detailed finite element analysis of the interior impact response of an electronic device.

Stress Reduction Coefficient and Amplification Factor for Seismic Response of Ground

Incorporating the increase of shear modulus with depth (z) by using a depth exponent p , the response of linear visco-elastic ground under steady state harmonic vibration was examined. The soil mass lying above the rigid base was discretized into a large number of horizontal layers. For a given vertical thickness ( Hr ) of the upper ground material in the first mode of resonance, it was noted that the resonant frequency ( fr ) as well as the values of amplification factor ( Mf ) and the stress reduction coefficient ( Cd ) at a given z∕ Hr can be computed as a function of p and D , where D is the damping ratio of the material. An increase in D leads to (1) an increase in Cd ; (2) a very little increase in fr ; and (3) a decrease in Mf . On the other hand, an increase in p causes: (1) an increase in fr ; (2) a marginal increase in Mf ; and (3) a decrease in Cd . It was evident that the values of Mf and Cd at a given depth will be affected significantly by changes in the chosen thickness of the soil deposit ...

Effect of variability of soil physical properties on clutter and false alarms in land mine detection

The effects of variability of the ground on land mine detection and false alarm rates are analyzed within the framework of a viscoelastic‐layered model of the ground. A matrix technique was used to describe sound interaction with layered viscoelastic ground. The resonance method in combination with a global search method is used to estimate a set of parameters for a three‐layered viscoelastic ground model. Results of the estimation show good agreement between computed and experimental data. The effect of a finite size of sound source on the acoustic‐to‐seismic transfer function is discussed. The effect of variability of ground properties on the acoustic‐to‐seismic transfer function (admittance function) is analyzed. Analysis is performed on the plane of parameters of the layered ground in a wide frequency range for all angles of incidence. It is revealed that small variations in the shear speed in the top layer of ground will not cause variation in the acoustic‐to‐seismic transfer function at low frequencies but may cause strong variation at high frequencies. Results of outdoor measurements of the acoustic‐to‐seismic transfer function are presented, and a correlation between the high magnitude of the acoustic‐to‐seismic transfer function in certain frequency ranges and moisture content on the surface is revealed. A simple model explaining the correlation between moisture content in the upper layer, the acoustic‐to‐seismic transfer function, and ground properties is suggested.

移動点加振源からの波動入射を受ける複数の構造物周辺の地表面振動

This paper deals with a simulation method of the ground vibration around multiple structures resting on a visco-elastic ground excited by waves radiated from a moving source. Based on 2.5-D analysis, the simulation method consists of two methods. The one is for obtaining the driving force of structures due to the moving source in the frequency domain and the other is for calculating the ground vibration caused by the vibration of structures excited by the driving force. The ground vibration is obtained as the sum of the vibration due to the moving source in the free wave field and the vibration due to waves radiated from structures in the scattered wave field in the frequency domain and it is transformed into the time domain. The effect of the movement of excitation on the vertical ground vibration is evaluated by observing time series of the vibration.

Ice flow and isostasy of the north polar cap of Mars

The flow of the north polar cap of Mars, which is assumed to consist mainly of H 2O ice, is investigated with the three-dimensional ice-sheet model SICOPOLIS. We consider a simplified topography and a climatic forcing varying between the present state and warmer, more humid conditions in the past with an obliquity cycle of 1.3 million earth years (yr). Furthermore, SICOPOLIS is coupled with the three-layer viscoelastic ground model displace to simulate the isostatic response of the underlying lithosphere/mantle system. Likely ice-flow velocities at present are a few mm/yr, along with surface accumulation/ablation rates of the order of 0.1 mm water equiv./yr and basal temperatures more than 50°C below pressure melting. Thicknesses of the rheological lithosphere of 50– 400 km are consistent with geothermal heat fluxes of 15– 36 mW m −2 , with some evidence for values of ca. 80– 120 km and 20– 30 mW m −2 , respectively. For an Earth-like upper-mantle viscosity of O(10 21 Pa s ) , relaxation times of the lithosphere/mantle system are much shorter than significant load changes, so that the mantle behaves as an inviscid fluid. The poor correlation between the computed and measured free-air gravity signal indicates that it is determined by mass anomalies of a different origin.

Three-Dimensional Ground Motion Simulations for Large Earthquakes on the San Andreas Fault with Dynamic and Observational Constraints

I have simulated 0–0.5 Hz viscoelastic ground motion in Los Angeles from M 7.5 earthquakes on the San Andreas fault using a fourth-order staggered-grid finite-difference method. Two scenarios are considered: (a) a southeast propagating and (b) a northwest propagating rupture along a 170-km long stretch of the fault near Los Angeles in a 3D velocity model. The scenarios use variable slip and rise time distributions inferred from the kinematic inversion results for the 1992 M 7.3 Landers, California, earthquake. The spatially variable static slip distribution used in this study, unlike that modeled in a recent study,1 is in agreement with constraints provided by rupture dynamics. I find peak ground velocities for (a) and (b) of 49 cm/s and 67 cm/s, respectively, near the fault. The near-fault peak motions for scenario (a) are smaller compared to previous estimates from 3D modeling for both rough and smooth faults.1,2 The lower near-fault peak motions are in closer agreements with constraints from precarious rocks located near the fault. Peak velocities in Los Angeles are about 30% larger for (b) 45 cm/s compared to those for (a) 35 cm/s.