Viscous-spring Artificial Boundary Research Articles

Research on Seismic Input Method of Layered Ground Foundation

The seismic input of layered foundation is an essential part of seismic analysis of structure- foundation system. Most of the traditional seismic input methods only consider the first reflection process of seismic waves at the interface of different media, ignoring the subsequent reflection and refraction propagation process, which can not truly reflect the wave propagation process in the layered foundation. This paper proposes a new seismic input method for layered foundation, considering all reflected and refracted waves. Firstly, the viscous-spring artificial boundary model of the layered foundation is established, which can simulate the absorption of scattered waves and the elastic recovery capacity of semi-infinite foundation at the same time. Then, based on the wave mechanics theory, the equivalent nodal force calculation formula is derived to realize the vibration input of layered ground. Finally, the calculation results of the layered foundation and two-way surge tower engineering are verified. The results show that: compared to the traditional input method, the method proposed in this paper has a significant influence on the seismic response of layered foundation, and the method in this paper can better meet the accuracy requirements of engineering earthquake resistance, which provides an effective and practical calculation method for seismic analysis of layered foundation structure.

STUDY ON EARTHQUAKE DAMAGE MECHANISM OF AQUEDUCT STRUCTURE BASED ON DIFFERENT BOUNDARY

Numerically simulating an infinite domain foundation is an important method for solving structural dynamics problems. This paper introduces several artificial dynamic boundaries commonly used in the study of structural dynamics, and elaborates the theory and methods of the dynamic infinite element method boundary (IEMB) and viscous–spring artificial boundary (VSAB). The capacity of different boundary effects on seismic waves energy absorption is verified by establishing a layered half-space model. An irrigation aqueduct is taken as a research object. The IEMB, VSAB, and fixed boundary (FB) models are established and the Concrete Damaged Plasticity (CDP) constitutive is introduced, which is aimed at studying the dynamic failure mechanism and the rules of damage development to the aqueduct structure during the seismic duration. The results for the IEMB and VSAB show better energy absorption for the incident waves and a better simulation result for the damping effect of the far field foundation than that of the FB. Comparing the maximum displacement response rules of the three boundaries, it is seen that the maximum displacement response values of the VSAB and dynamic IEMB increased by 6%–48% and 9%–35%, respectively, over the FB. The calculation results of the VSAB are similar to that of the IEMB. The difference between the maximum acceleration response values is 2%–17% whereas the difference between the maximum displacement response values is 0.4%–19%. The IEMB studied in this paper provides a theoretical reference for large–scale building boundary treatment in structural dynamics calculations.

A scheme for switching boundary condition types in the integral static-dynamic analysis of soil-structures in Abaqus

Simulation of semi-infinite foundation is a key issue in the finite element analysis of dynamic soil-structure interactions. When the viscous-spring artificial boundary is used to simulate the radiation damping effect, the boundary condition types of the truncated foundation are different in the static and dynamic steps. It is needed to switch the displacement boundary to the traction boundary in the integral static-dynamic analysis. This paper proposes a scheme for steadily switching boundary condition types in the integral static-dynamic analysis of structures in Abaqus by means of the element birth and death technique. To verify the proposed scheme, a two-dimensional FE analysis of Pine Flat dam due to static and dynamic loads is carried out for wave motion problems of both internal and external sources. Results show that the proposed scheme can switch the boundary conditions steadily and improve the computational accuracy.

A generalized response spectrum method for seismic response analysis of underground structure combined with viscous-spring artificial boundary

Response spectrum analysis (RSA) has been applied to dynamic calculation of underground structure subjected to earthquake excitation. An analysis model composed of the underground structure and the surrounding soil was built to consider the soil-structure interaction (SSI). The seismic free field motion was enforced on the bottom boundary of the calculation model, namely the inertia force acts on the SSI model with fixed bottom to calculate the relative response of system. While the scattered waves propagating from the model into truncated infinite domain, namely the radiation damping effect of infinite domain, was not considered in the SSI model. In this paper, the viscous-spring artificial boundary (VSAB) is used at the bottom boundary of the SSI model to consider the radiation damping effect and to improve the calculation accuracy of the model. The damping of VSAB makes the SSI model being a non-classically damping system. The seismic free field is inputted as the nodal force at VSAB besides the inertia force on SSI model. A generalized response spectrum is defined as the peak value response of a single-degree-of-freedom (SDOF) system subjected to the additional nodal force. Subsequently, the complex modal RSA is generalized to calculate the seismic analysis model with VSAB. Finally, the rationality of the generalized RSA is indicated by applying it to the seismic analysis of a rectangular subway station structure and a circle tunnel in two typical sites.

On the Characteristics of Ground Motion and the Improvement of the Input Mode of Complex Layered Sites

It is a hot research topic to perform the dynamic interaction analysis between the engineering structure and the soil by using the time-domain method. This paper studies the seismic behaviour of the layered sites and the seismic response of the structures using the viscous-spring artificial boundary theory. The artificial boundary model of viscous-spring is initially based on homogeneous foundation. For the layered site (Foundation), the traditional homogeneous model or equivalent load input mode is not suitable, which may bring great error. By introducing the changes of coefficients and phases of reflection and transmission of seismic waves at the interface between layers, an improved method of equivalent load input mode of traditional viscous-spring artificial boundary model is proposed. This new wave model can simulate the propagation law of seismic wave in layered site more accurately, which is available for the seismic performance of engineering structure under the condition of large and complex layered site. At last, the simplified homogeneous model, the equivalent load input method and the improved layered model input method are used to study the seismic response of the engineering example. It is shown that the results calculated by the three methods are different, which shows that the homogeneous foundation model and the conventional equivalent load input method of seismic wave cannot simulate the seismic force accurately, whereas the improved wave input model can better reflect the characteristic of traveling wave in layered sites.

Effects of Oblique Incidence of SV Waves on Nonlinear Seismic Response of a Lined Arched Tunnel

The incident direction of earthquake motion is an important factor affecting the seismic response of underground structures. In this study, a three-dimensional (3D) oblique incidence method of SV waves is proposed and the effects of incident angles of SV waves on the seismic response of a lined arched tunnel are evaluated. Based on wave field decomposition principle and equivalent node force method and together with viscous-spring artificial boundary, the oblique incidence method of SV waves is implemented by transforming seismic wave field into the equivalent nodal forces acting on the artificial boundaries. By deriving the distance of the incident waves and the reflected wave on free surface to artificial boundaries, this method can comprehensively consider the phase difference of the seismic wave propagation and the influence of the damping effect of the rock medium on the seismic wave propagation. The method is programed into a dynamic finite element program and its effectiveness is examined by a numerical example. Consequently, the oblique incidence method is applied to evaluate the seismic behaviors of the tunnel. The numerical results reveal that (1) the oblique incidence of the seismic wave results in a larger seismic response; (2) the response amplitudes of the stress and displacement increase with the increase of incident angles and reaching the maximum in the case of 30° incident angle; (3) the damage extent increases with an increase in the incident angles, and the oblique incidence of the seismic wave is believed to increase the spatial difference of damage distribution.

Nonlinear Dynamic Response of a CC-RCC Combined Dam Structure under Oblique Incidence of Near-Fault Ground Motions

The velocity pulse contained in near-fault ground motions have a tremendous impact on dam safety. Previous studies have mainly focused on the response of dams under near-fault seismic records without considering the obliquely incident seismic waves. In this study, the structure–soil interaction (SSI) is taken into consideration, and the nonlinear behavior of a conventional concrete roller-compacted concrete (CC-RCC) gravity dam under near-fault pulse records and non-pulse records is investigated with consideration of the obliquely incident P waves. On the basis of the dam site conditions, three groups of near-fault pulse records are chosen, and three corresponding non-pulse records are fitted by their acceleration response spectra. Combining with the viscous-spring artificial boundary, the wave input method is proposed to transform the near-fault seismic records into the equivalent nodal forces at the boundary of the foundation. The concrete damaged plasticity model is used for the nonlinear analysis. The results show that the pulse ground motions are more destructive than the non-pulse motions. The nonlinear behavior of the dam varies with the incidence angle of P waves and generally reaches a maximum at 60° and 75°, the worst damage occurs at the interface between different materials of the dam, and the spatial variation of its damage is very obvious under near-fault seismic records with various incidence angles. Therefore, the effect of the angle of obliquely incident seismic waves and near-fault pulse effect should be considered comprehensively in the seismic analysis of dams.

Study on Dynamic Structure-Soil-Structure Interaction of Three Adjacent Tall Buildings Subjected to Seismic Loading

The dynamic structure-soil-structure interaction (SSSI) involving three adjacent structures with pile-raft foundations arranged along the east-west direction in a viscoelastic half-space is numerically studied under earthquake excitation. The direction of earthquake excitation is perpendicular to the direction of the structural arrangement. In the simulation, the Davidenkov model of the soil skeleton curve is assumed for soil behavior, and the viscous-spring artificial boundary is adopted. In order to investigate the effects of SSSI, the clear distance between structures, structure types, structure heights, and the first natural periods of structures are considered, and a series of numerical simulations are conducted. The peak floor displacement and the peak inter-story shear force of structures are examined to determine the SSSI effects. Results show that SSSI effects change significantly with these factors. Furthermore, the structural seismic response could be increased or reduced as a result of SSSI, depending mainly on the structural characteristics, rather than the location of the structures. These results are significant for studying the effects of SSSI and the sustainable development of cities, especially for the seismic design of dense urban buildings.

Torsional and rocking response of the foundation induced by obliquely spatial incident S waves

The seismic response of a foundation with a viscous-spring artificial boundary induced by obliquely spatial incident shear (S) waves is investigated in this paper. The results obtained indicate that the torsional and rocking response of the foundation can be generated by obliquely spatial incident S waves. The magnitude of the torsional and rocking response of the foundation changes with a variation in the angle of the input S waves. Subsequently, a frame structure supported on a surface foundation is established to analyse the impact of the incident angles of seismic waves on the torsional and rocking response of the superstructure. Notably, the angle of incidence of the seismic waves has a significant effect on the amplitude of the torsional and rocking response of the superstructure. Thus, it is necessary to consider the angles of the incident seismic waves during the hazard assessment of the structures.

Impact of tensile strength and incident angles on a soil slope under earthquake SV-waves

The tensile strength and incident angles play important roles in seismically induced slope failures. In this paper, a new criterion for tension–shear coupling is proposed based on several sets of relevant lab data and is verified using the experimental data provided by previous researchers. This criterion can perfectly depict the tension region as well as the compression region in the entire stress space. Moreover, the tension–shear criterion was converted into an expression that could be directly used in a numerical method, and it was verified by a numerical example. In addition, the SV-waves were input using the equivalent nodal force method based on a viscous-spring artificial boundary. This process was implemented by the ABAQUS software, and two numerical examples were used to verify this method. Subsequently, based on the proposed new criterion and input method, the impacts of the strength criterion and incident angles on an analysis of seismically induced slope failures were studied. The results indicated that the evaluation of the tension–shear region is extremely important in the analysis of the seismically induced slope failures. The tensile strength of the seismically induced landslides was overestimated by the calculation of Mohr-Coulomb criterion owing to the ambiguous description of the tensile failure or the tension-shear failure, the assessment of the slope stability was thus not conservative. The incident angles of seismic waves affected the travel path and the directivity of slope seismic responses; the sliding displacement of the slope side near the epicenter rose with increasing angles of wave incidence, the critical slip surface deepened, and the hazard aggravated. Therefore, it is important to introduce both the tensile strength and incident angles when evaluating the stability of slopes subjected to seismic loads.

Shock Reduction Techniques for a Submarine Tunnel

Considering the effects of seepage and dynamic pressure, defining a rock mass as a saturated porous media, and using the finite element method, a dynamic fluid–structure interaction model of a subsea tunnel with a viscous spring artificial boundary is established. Adopting rubber and foam concrete as shock absorption layers and inputting both horizontal and vertical earthquake waves, the time history curves of the first principal stress at key points in the secondary lining structure are comparatively analyzed based on the presence and absence of shock absorption layers. The principal stress peaks are also analyzed. The damping effect of the shock absorption layer is studied. The results show that the peak and principal stresses at the main parts of the tunnel lining structure decrease after the shock absorption layer is established. Obvious decreases occur in the vault and inverted arch. A certain degree of peak stress reduction is also observed after the shock absorption layer is established. Establishing the shock absorption layer does not change the spectrum characteristics of the tunnel structure. Foam concrete shock absorption is recommended because the damping effect of foam concrete is more observable than that of rubber.

Seismic responses of an underground powerhouse structure subjected to oblique incidence SV and P waves

In this work, the impacts of seismic motion incident angles and the rock-structure interaction (RSI) on the seismic response of an underground powerhouse structure of a hydropower station are studied. Based on the viscous-spring artificial boundary condition, the input methods of oblique incidence SV and P waves are presented by transforming the seismic motion into equivalent nodal forces acting on the nodes of artificial boundaries. Based on the explicit central difference method, an explicit dynamic contact analysis method considering the bonding and damage characteristics of the contact face between the surrounding rock and the underground powerhouse structure is also proposed. Consequently, the proposed methods are implemented into an dynamic finite element program and applied to the seismic damage evolution process analysis for the concrete structure of an underground powerhouse, and the results reveal that (1) the stress and deformation response of the underground powerhouse structure caused by seismic excitations are clearly affected by the incident angle and its degree of damages reaches a maximum when the incident angle is 30°; (2) compared to the case of without the RSI, the damage distribution ranges and the damage coefficient of the underground powerhouse structure are much larger than that in the case of with the RSI; and (3) the contact state of the contact face plays a key role in the dynamic stability of the underground powerhouse structure, and a good contact state can help to reduce the dynamic damage of the underground structure.

Dynamic responses and damage forms analysis of underground large scale frame structures under oblique SV seismic waves

This paper mainly focuses on distinctive dynamic responses of the underground large scale frame structure (ULSFS) under obliquely asynchronous seismic inputs of the near-fault ground motion. To achieve the arbitrarily oblique input of seismic waves, the ground motions are transformed into equivalent forces adding on the 3-D viscous-spring artificial boundary nodes based on the theory of wave propagation. The ULSFS with great scales along two horizontal directions are proposed according to a well-designed underground market under construction. The dynamic responses of the ULSFS under different oblique incident angles of seismic waves are compared. The failure mechanisms of the ULSFS are explored by the tensile damage of floor slabs and walls, and stresses and strains of frame columns. The results demonstrate that dynamic responses of the ULSFS with two horizontal great scales would be sensitive to oblique incident angles of the seismic input; and the ULSFS is more likely to be compression-shear failure under the combination of the asynchronous horizontal and vertical seismic waves.

Comparative numerical analysis on dynamic effects of underground large scale frame structures under seismic waves

In this paper, dynamic effects of the underground large scale frame structure (ULSFS) with large scales along both two horizontal directions are investigated by 3-D numerical analyses. To guarantee the accuracy of seismic inputs, seismic waves are transformed into equivalent forces adding on the truncated boundary nodes based on the viscous-spring artificial boundary. 3-D finite element models of 4-span, 8-span, and 20-span underground frame structures with surrounding foundation are proposed to simulate small, middle and large scale underground structures. For a comprehensive study of results, another two analyses of the ULSFS are proposed to evaluate the two dynamic effects of structures: structural inertial effects on inner structures, and effects of structural vibration on the whole soil-structure system, respectively. Furthermore, several soil conditions are employed to study influences of the relative stiffness between the structure and soil on the two mentioned dynamic effects of the ULSFS. The results demonstrate that dynamic effects of the ULSFS are much more significant compared with small scale underground structures which make the structural deformations and internal forces to be larger; and dynamic effects of the ULSFS would decrease with increasing elastic moduli of surrounding soils due to great soil constraints.

The Research of Influence of Above Building on Tunnel Dynamic Response

Based on finite element software ABAQUS, by using equivalent viscous-spring artificial boundary element combine wave motion input, a series of two-dimensional plane strain models of above building-soil-tunnel were built to study the influence of above building on tunnel dynamic response. The dynamic nonlinear effects of soils are considered by using equivalent linear method. Three seismic input with different spectrum characteristics were used here as input motion. Results show that the influence of above building is negligible. The dimension of above building, spacing between structures and the buried depth of tunnel are the important factors of the interaction system, in contrast, the stiffness of above building have small influence degree.

Impact of incident angles of earthquake shear (S) waves on 3-D non-linear seismic responses of long lined tunnels

The incident direction of earthquake waves has significance on the seismic responses of long lined tunnels. In this study, based on the equivalent node force method and together with the viscous-spring artificial boundary, the 3-D input method of SV and SH-waves with arbitrary incident angles is studied firstly. The input method is introduced within the framework of ABAQUS software and is verified by two numerical examples. Consequently, the proposed input method is employed to investigate the impact of the incident angles of SV and SH-waves on the seismic responses of a long lined tunnel. The numerical results indicate that the non-linear seismic responses of long lined tunnels are highly affected by the incident angles of S-waves. As the incident directions of SV and SH-waves being not perpendicular to the tunnel longitude, non-uniform motions appear along the tunnel longitude, as well as the longitudinal internal forces. The plastic deformation and strain components along the tunnel cross-section are also influenced by the incident angles of SV and SH-waves. It is thus important to include the incident angles of earthquake waves in mapping the seismic risk of tunnels.

Non-linear seismic responses of tunnels within normal fault ground under obliquely incident P waves

The faults play an important role in inducing tremendous potential threat to the stability capability of embedded tunnels in strong earthquake events. Based on the finite element method with the viscous-spring artificial boundary, the earthquake motions of oblique incidence can be transformed into the equivalent nodal forces acting on the truncated boundary of finite element model. In the present work, the formulas of equivalent nodal forces for the 2-D plane P waves with arbitrary incident angles are deduced and implemented into the commercial software ABAQUS. The accuracy of the formulas and the implementation are demonstrated by the numerical examples of a 2-D semi-infinite space and an circular lined tunnel in half-space subjected to obliquely incident P waves. The proposed numerical method is employed to investigate the non-linear responses of the tunnels within surface normal fault ground under obliquely incident P waves. The numerical results indicate that the tunnels buried in the hanging wall, in the foot wall and across the fault, suffer different failure patterns. The tunnels across the fault suffer the most serious plastic damage, followed by that within the hanging wall. Moreover, the seismic responses of the tunnels across the fault and within the hanging wall increase with the inclination degree of the incident P waves, as well as opposite relationship for tunnels within the foot wall.

Seismic response analysis of GRPS embankment under oblique incident P wave

In order to investigate the seismic performance of geosynthetic reinforced and pile supported (GRPS) embankment under seismic loads, an input method for three-dimensional oblique incidence of P wave was proposed. This method is based on the explicit finite element method while considering the viscous-spring artificial boundary (VSAB) condition. Using the proposed method, a numerical study was conducted, and the influence of oblique incidence on the seismic response of GRPS embankment under the oblique incident P waves was analyzed. The results indicate that in comparison with vertical incidence, the oblique incidence can significantly increase the displacement, velocity and acceleration of key locations in the GRPS embankment. The existence of geosynthetics can alleviate the impact of seismic load on the response of the embankment to a certain degree. Moreover, the number of reinforcement layers and modulus of geogrid also greatly influence the seismic performance of GRPS embankment.

Influence of construction interfaces on dynamic characteristics of roller compacted concrete dams

To study the influence of construction interfaces on dynamic characteristics of roller compacted concrete dams (RCCDs), mechanical properties of construction interfaces are firstly analyzed. Then, the viscous-spring artificial boundary (VSAB) is adopted to simulate the radiation damping of their infinite foundations, and based on the Marc software, a simplified seismic motion input method is presented by the equivalent nodal loads. Finally, based on the practical engineering of a RCC gravity dam, effects of radiation damping and construction interfaces on the dynamic characteristics of dams are investigated in detail. Analysis results show that dynamic response of the RCC gravity dam significantly reduces about 25% when the radiation damping of infinite foundation is considered. Hot interfaces and the normal cold interfaces have little influence on the dynamic response of the RCC gravity dam. However, nonlinear fracture along the cold interfaces at the dam heel will occur under the designed earthquake if the cold interfaces are combined poorly. Therefore, to avoid the fractures along the construction interfaces under the potential super earthquakes, combination quality of the RCC layers should be significantly ensured.

Damage evolution of tunnel portal during the longitudinal propagation of Rayleigh waves

Rayleigh waves significantly compromise the safety of tunnel portals. This paper establishes a three-dimensional numerical model, with a plastic-damage model for the concrete lining structure, to analyze the damage evolution of the tunnel portal during the longitudinal propagation of Rayleigh waves. To generate the wave field, a Rayleigh wave input method based on viscous-spring artificial boundary is developed. The submodeling technique is employed to overcome difficulties introduced by contradictions between element size, model scale and affordable computational cost. The simulation results, including the deformation of pavement at the entrance and the crack pattern of the tunnel lining, correspond well with the field observation of the Longxi Tunnel during the Wenchuan Earthquake. This paper proposes that the opening width of predominant circumferential cracks and a dimensionless damage index based on the internal damage variable can be used to quantitatively estimate the damage extent of the lining structure. The result of damage assessment shows that all damage is limited within a certain scope of the tunnel portal and that the extent of each crack decreases with its increasing distance from the entrance. The extent of damage may also be induced through earthquake loading with a relatively lower amplitude. Therefore, the cyclic and accumulative effect of successive earthquake loading over time, rather than simply, the effect of loading with a maximum amplitude, can determine the final damage state of lining structure. Although incapable of preventing the appearance of hairline cracks, the strengthening effect of reinforcement remarkably reduces the maximum width of crack openings and the overall damage extent of the lining structure. Moreover, the presence of reinforcing steels prevents micro-cracks from expanding to wider crack, which is essential to keep the tunnel lining waterproof and mechanically stabilized. The simulation methodology introduced in this paper could also potentially reliably predict the damage process of the tunnel lining and the extent of damage under the effect of complicated earthquake loading, aside from the Rayleigh wave.