Influence of the soil–structure interaction on the fundamental period of buildings

This paper includes an investigation of the influence of the soil–structure interaction (SSI) on the fundamental period of buildings. The behaviour of both the soil and the structure is assumed to be elastic. The soil‐foundation system is modelled using translational and rotational discrete springs. Analysis is first conducted for one‐storey buildings. It shows that the influence of the SSI on the fundamental frequency of building depends on the soil–structure relative rigidity K_ss. Analysis is then extended for multi‐storey buildings. It allows the generalization of the soil–structure relative rigidity K_s to such complex structures. Charts are proposed for taking into account the influence of the SSI in the calculation of the fundamental frequency of a wide range of buildings. Copyright © 2007 John Wiley & Sons, Ltd.     

Non-linear dynamic earth dam–foundation interaction using a BE–FE method

A general, rigorous, coupled Boundary Element–Finite Element (BE–FE) formulation is presented for non-linear seismic soil–structure interaction in two dimensions. The BE–FE method is applied to investigate the inelastic response of earth dams to transient SV waves. The dam body, consisting of heterogeneous materials modelled with a simple non-linear hysteretic model, is discretized with finite elements, whereas the elastic half-space is discretized with boundary elements. The study focuses on the combined effects of the material non-linearity and foundation flexibility. The results show the significant effect of the foundation flexibility in reducing the response through radiation of energy. For excitations with peak ground accelerations from 0·2gto 0·6g, the crest acceleration amplification ranges from 2·5 to 1·4 and seems to be comparable with field observations and results from other studies. Deamplification increasing with strain is reported at the lower part of the dam. The method is computationally powerful and can be used for efficient non-linear analysis of complex soil–structure systems. The efficiency of the BE–FE method allows further improvements with incorporation of a more advanced constitutive model and consideration of the generation and dissipation of pore-water pressures during the earthquake. © 1998 John Wiley & Sons, Ltd.     

Vertical response of single piles: transient analysis by time-domain BEM

The transient dynamic response of single piles in a layered half-space under a time-dependent vertical force is analyzed by an FEM-BEM coupling approach. The pile is modeled by FEM and the layered half-space is modeled by a general cylindrical coordinates time-domain BEM. Only one-dimensional discretization is necessary on the boundaries of the three-dimensional layered half-space by virtue of the Fourier theory, while the pile shaft can be discretized as a one-dimensional elastic beam. The compatibility and equilibrium conditions between pile shaft and soil layers are employed to assemble respective equations into one. Fairly good agreement between two unknown solutions and the current approach is found. Parametric studies reveal the influences of several dimensionless factors, such as E_p/E_s, l/r₀, _p/_s and ν_s. The effect of soil layering and the support condition of the pile tip is also reported by numerical examples.     

Two-dimensional scattering of in-plane body waves due to a discontinuity in bedrock

The direct boundary integral equation technique is used to study in-plane surface amplification of in-plane seismic body waves for the case of an inhomogeneity in a bedrock half-space. In the studied soil configuration, a soil layer rests on a rock half-space which includes a rock inclusion. The rock inclusion considered is a semi-infinite horizontal rock layer in which its upper boundary borders the soil layer. Materials in the soil–rock configuration are considered viscoelastic except for the section of the rock half-space below the level of the rock inclusion which is considered elastic. A parametric study is performed to determine controlling factors for surface displacement due to in-plane body waves. The study investigates varying the stiffness and the thickness of the rock inclusion for a range of frequencies and wave incidence angles. Anti-plane waves for this type of soil-rock configuration have been addressed in a previous article by Heymsfield (Earthquake Engng. Struct. Dyn. 28 : 841–855 (1999)). Copyright © 1999 John Wiley & Sons, Ltd.     

Hydraulic properties of concentrated flow of a bank gully in the dry‐hot valley region of southwest China

To quantify spatiotemporal variation in hydraulic properties of bank gully concentrated flow, a series of scour experiments were run under water discharge rates ranging from 30 to 120 l min^?1. Concentrated flows were found to be turbulent and supercritical in the upstream catchment area and downstream gully beds. As discharge increased, values of the soil erosion rate, Reynolds number (Re), shear stress, stream power, and flow energy consumption (ΔE) increased while values of the Froude number (Fr) and the Darcy–Weisbach friction factor (resistance f ) did not. With the exception of gully headcut collapse under discharge rates of 60, 90, and 120 l min^?1, a declining power function trend (P < 0.05) in the soil erosion rate developed in the upstream catchment area, headcuts, and downstream gully beds. However, increasing trends were observed in temporal variations of hydraulic properties for downstream gully beds and the upstream catchment area. Despite significant differences in temporal variation between the soil erosion rate and hydraulic property values, relative steady state conditions of the soil erosion rate and ΔE were attained following an initial period of adjustment in the upstream catchment area, headcuts, and downstream gully beds under different discharge rates. A logarithmic growth of flow energy consumption per unit soil loss (ΔE_u) was observed in bank gullies and the upstream catchment area as the experiment progressed, further illustrating the actual reason behind the discrepancy in temporal variation between soil erosion rates and ΔE. Results demonstrate that ΔE can be used to estimate headcut erosion soil loss, but further quantitative studies are required to quantify coupling effects between hydraulic properties and vertical variation in soil mechanical properties on temporal variation for bank gully soil erosion rates. Copyright © 2015 John Wiley & Sons, Ltd.     

Two-dimensional scattering of SH waves in a soil layer underlain with a sloping bedrock

A two-dimensional analysis is applied to examine the effect that a sloping bedrock half-space has on the amplification of an anti-plane shear wave. The direct boundary integral equation method is used for the two-dimensional analysis. The particular soil–rock configuration investigated includes a homogeneous soil layer underlain by a sloping rock half-space. The rock half-space dips for a horizontal distance L and then becomes horizontal so that the overlying soil layer has a thickness H that remains constant from this point to infinity. The materials in the soil–rock configuration are considered viscoelastic except in the rock half-space below soil layer thickness H, which is considered elastic. This limitation in damping is due to the correction used for the truncation of the half-space boundary. Four cases are used to study the relationship between rock slope and surface displacement, vertical, 1:2, 1:4, 1:8. Surface displacements are determined for each of these cases for half-space incidence angles of 90, 75, and 60°. To allow for applicability to a wide range of problems, results are determined as a function of dimensionless parameters. In addition, solutions from a one-dimensional analysis are compared with the results of the two-dimensional analysis to establish limits outside of which a one-dimensional analysis suffices.     

Bridge–embankment interaction under transverse ground excitation

Seismic performance and dynamic response of bridge–embankments during strong or moderate ground excitations are investigated through finite element (FE) modelling and detailed dynamic analysis. Previous research studies have established that bridge–embankments exhibit increasingly flexible performance under high‐shear deformation levels and that soil displacements at bridge abutment supports may be significant particularly in the transverse direction. The 2D equation of motion is solved for the embankment, in order to evaluate the dynamic characteristics and to describe explicitly the seismic performance and dynamic response under transverse excitations accounting for soil nonlinearities, soil–structure interaction and imposed boundary conditions (BCs). Using the proposed model, equivalent elastic analysis was performed so as to evaluate the dynamic response of approach embankments while accounting for soil–structure interaction. The analytical procedures were applied in the case of a well‐documented bridge with monolithic supports (Painter Street Overcrossing, PSO) which had been instrumented and embankment participation was identified from its response records after the 1971 San Fernando earthquake. The dynamic characteristics and dynamic response of the PSO embankments were evaluated for alternative BCs accounting for soil–structure interaction. Explicit expressions for the evaluation of the critical embankment length L_c are provided in order to quantify soil contribution to the overall bridge system under strong intensity ground excitations. The dynamic response of the entire bridge system (deck–abutments–embankments) was also evaluated through simplified models that considered soil–structure interaction. Results obtained from this analysis are correlated with those of detailed 3D FE models and field data with good agreement. Copyright © 2007 John Wiley & Sons, Ltd.     

Hydrochemical variations during flood pulses in the south‐west China peak cluster karst: impacts of CaCO3–H2O–CO2 interactions

High‐resolution measurements of rainfall, water level, pH, conductivity, temperature and carbonate chemistry parameters of groundwater at two adjacent locations within the peak cluster karst of the Guilin Karst Experimental Site in Guangxi Province, China, were made with different types of multiparameter sonde. The data were stored using data loggers recording with 2 min or 15 min resolution. Waters from a large, perennial spring represent the exit for the aquifer's conduit flow, and a nearby well measures water in the conduit‐adjacent, fractured media. During flood pulses, the pH of the conduit flow water rises as the conductivity falls. In contrast, and at the same time, the pH of groundwater in the fractures drops, as conductivity rises. As Ca²⁺ and HCO₃^? were the dominant (>90%) ions, we developed linear relationships (both r² > 0·91) between conductivity and those ions, respectively, and in turn calculated variations in the calcite saturation index (SI_C) and CO₂ partial pressure (P) of water during flood pulses. Results indicate that the P of fracture water during flood periods is higher than that at lower flows, and its SI_C is lower. Simultaneously, P of conduit water during the flood period is lower than that at lower flows, and its SI_C also is lower. From these results we conclude that at least two key processes are controlling hydrochemical variations during flood periods: (i) dilution by precipitation and (ii) water–rock–gas interactions. To explain hydrochemical variations in the fracture water, the water–rock–gas interactions may be more important. For example, during flood periods, soil gas with high CO₂ concentrations dissolves in water and enters the fracture system, the water, which in turn has become more highly undersaturated, dissolves more limestone, and the conductivity increases. Dilution of rainfall is more important in controlling hydrochemical variations of conduit water, because rainfall with higher pH (in this area apparently owing to interaction with limestone dust in the lower atmosphere) and low conductivity travels through the conduit system rapidly. These results illustrate that to understand the hydrochemical variations in karst systems, considering only water–rock interactions is not sufficient, and the variable effects of CO₂ on the system should be evaluated. Consideration of water–rock–gas interactions is thus a must in understanding variations in karst hydrochemistry. Copyright © 2004 John Wiley & Sons, Ltd.     

Transient response of single piles under horizontal excitations

The general time-domain boundary element in cylindrical co-ordinates developed for the study of wave propagation in a layered half-space is extended to the response analysis of single piles under horizontal transient excitations. The pile is treated as a beam, and therefore, only the bending stiffness has to be considered in the analysis. As required by the non-axisymmetric nature of the problem, the soil is modelled by boundary (cylindrical) elements with the vertical, radial and tangential displacements as well as their corresponding tractions as independent variables. The characteristic matrices for the two different types of element can be formed in the usual manner, and they are combined to form the equation of motion for the whole system by virtue of compatibility and equilibrium conditions along the pile-soil interface. The transient responses of a pile under Heaviside loads are found to converge to the static values. Parametric studies are carried out to reveal the influences of pile-soil stiffness ratio (E_p/E_s) and soil layering.     

Dynamic interaction analysis of a circular cylindrical shell of finite length in a half-space

A study on the transient response of a circular cylindrical shell of finite length embedded in a homogeneous, isotropic and linear elastic half-space is presented. The soil-structure system is subjected to suddenly applied explosion waves. The numerical method employed is a combination of the time domain semi-analytical boundary element method used for the semi-infinite soil medium and the finite strip method used for the circular cylindrical shell. The two methods are combined through equilibrium and compatibility conditions at the soil-structure interface. The dynamic responses at the interface between the soil medium and the structure for every time step are obtained. Numerical examples are presented in detail to demonstrate the use and versatility of the proposed method. The following parameters are found to affect the response: (1) the slenderness ratio of the length over the diameter of the shell, L/D; (2) the relative wall thickness, h/a; (3) the relative stiffness ratio between the shell and the medium, E_s/E_m; and (4) the incidence angle of the explosion wave, α.     

南北地震带两次典型强震周边自然电场变化及机理探讨

根据场源不同可将地电场E分为大地电场E_T和自然电场E_SP。空间S_q电流系和固体潮一般被认为是大地电场E_T的起源;自然电场E_SP源于地下介质的物理化学作用,其局部性变化相对稳定。2013年南北地震带相继发生了芦山M_S7.0地震（30.3°N,103.0°E）和岷县、漳县M_S6.6地震（34.5°N,104.2°E）。两次地震周边约400 km范围内的地电场台站（成都、汉王）数据表明震前自然电场E_SP出现明显的小幅度突跳或大幅度跃变,同时在时间上具有准同步性,其他地电场台站也有类似变化。基于大地电场岩体裂隙水（电荷）渗流（移动）模型,对两次地震周边自然电场E_SP的变异机理进行探讨,尝试解析其物理过程。     

Axisymmetric soil–structure interaction by global–local finite elements

A version of the global–local finite element method is presented for studying dynamic steady-state soil–structure interaction wherein the soil medium extends to infinity. Herein, only axisymmetric behaviour is considered. In this approach, conventional finite elements are used to model the structure and some portion of the surrounding soil medium considered to be homogeneous and isotropic. A complete set of outgoing waves in the form of spherical harmonics for the entire space is used to represent the behaviour in the half-space beyond the finite element mesh and these are termed the global functions. Full traction and displacement continuity is enforced at the finite element mesh interface with the outer region. On the free surface of the half-space in the outer field, traction-free surface conditions are enforced by demanding that a sequence of integrals of the weighted-average tractions must vanish. Numerical examples are presented for the response of different shaped foundations, resting on the free surface or at various submerged levels, due to a normal seismic plane compressional wave. Plots of differential scattering cross-sections show the angular distribution of the energy (its directional nature) of the scattered field.     

Evaporation of perennial semi‐arid woodland in southeastern Australia is adapted for irregular but common dry periods

Measurements of water vapour flux from semi‐arid perennial woodland (mallee) were made for 3 years using eddy covariance instrumentation. There have been no previous long‐term, detailed measures of water use in this ecosystem. Latent energy flux (LE) on a half hourly basis was the measure of the combined soil and plant evaporation, ‘evapotranspiration’ (E_LE) of the site. Aggregation over 3 years of the site measured rain (1136 mm) and the estimated evaporation (794 mm) suggests that 342 mm or 30% of rain had moved into or past the root zone of the vegetation. Above average rainfall during 2011 and the first quarter of 2012 (633 mm, 15 months) would likely have been the period during which significant groundwater recharge occurred. At times immediately after rainfall, E_LE rates were the same or exceeded estimates of potential E calculated from a suitably parameterized Penman–Monteith (E_PMo) equation. Apparent free water E from plant interception and soil evaporation was about 2.3 mm and lasted for 1.3 days following rainfall in summer, while in autumn, E was 5.1 mm that lasted over 5.4 days. The leaf area index (LAI) needed to adjust a wind function calibrated Penman equation (E_PMe) to match the E_LE values could be back calculated to generate seasonal change in LAI from 0.12 to 0.46 and compared well with normalized difference vegetation index; r = 0.38 and p = 0.0213* and LAI calculated from digital cover photography. The apparently conservative response of perennial vegetation evaporation to available water in these semi‐arid environments reinforces the conclusion that these ecosystems use this mechanism to survive the reasonably common dry periods. Plant response to soil water availability is primarily through gradual changes in leaf area. Copyright © 2015 John Wiley & Sons, Ltd.     

Continuous measurement of whole‐tree water balance for studying urban tree transpiration

Street and garden trees in urban areas are often exposed to advection of strong vapour pressure deficit (VPD) air that can raise the whole‐tree transpiration rate (E_T), known as the oasis effect. However, urban trees tend to have small soil volume compared with natural conditions, and so they are believed to strongly regulate stomata. E_T characteristics of such urban trees have not been well understood because of a lack of reliable measurement methods. Therefore, we propose a novel weighing lysimeter method and investigate the whole‐tree water balance of an isolated container‐grown Zelkova serrata to examine (a) which biotic and abiotic factors determine E_T and (b) which spatial and temporal information is needed to predict E_T under urban conditions. Whole‐tree water balance and environmental conditions were measured from 2010 to 2012. Although leaf area substantially increased in the study period, daily E_T did not vary much. E_T increased with VPD almost linearly in 2010 but showed saturation in 2011 and 2012. Root water uptake lagged E_T by 40 min in 2012. These results suggest that the small planter box interfered with root growth and that hydraulic supply capacities did not increase sufficiently to support leaf area increase. From analysis of water balance, we believe that neglecting soil drought effects on street trees without irrigation in Japan will overestimate E_T over 4–5 sunny days at the longest. This is unlike previous studies of forest.     

A one‐dimensional model for simulating armouring and erosion on hillslopes: 2. Long term erosion and armouring predictions for two contrasting mine spoils

This paper investigates the dynamics of soil armouring as a result of fluvial erosion for a non‐cohesive sandy gravel spoil from the Ranger Mine, Australia, and a cohesive silt loam spoil from the Northparkes Mine, Australia, using a model for hillslope soil armouring. These long term predictions concentrate on the temporal and spatial changes of the spoil grading and erosion over 100–200 years for the flat cap regions (1–2%) and steep batter edges (10–30%) typically encountered on waste rock dumps. The existence of a significant rock fragment fraction in the Ranger spoil means that it armours readily, while Northparkes does not. For Ranger the waste rock showed reductions in (1) cumulative erosion of up to 81% from that obtained by extrapolating the initial erosion rate out 100 years and (2) the erosion/year by more than 10‐fold. For Northparkes reductions were less marked, with the maximum reduction in erosion/year being 37% after 200 years. For Ranger the reductions were greatest and fastest for intermediate gradient hillslopes. For the steepest hillslopes the armouring decreased because the flow shear stresses were large enough to mobilize all material in the armour layer. Model uncertainty was assessed with probabilistic confidence limits demonstrating that these erodibility reductions were statistically significant. A commonly used hillslope erosion model (sediment flux = β₁ discharge m₁ slope n₁) was fitted to these predictions. The erodibility, β₁, and m₁ decreased with time, which was consistent with our physical intuition about armouring. At Ranger the parameter m₁ asymptoted to 1·5–1·6 while at Northparkes it asymptoted to 1·2–1·3. At Ranger transient spatial trends in armouring led to a short term (50–200 years in the future) reduction in n₁, to below zero under certain circumstances, recovering to an asymptote of about 0·5–1. At Northparkes n₁ asymptoted to about 0·6, with no negative transients predicted. The m₁ and n₁ parameters predicted for Ranger were shown to be consistent with field data from a 10‐year‐old armoured hillslope and consistent with published relationships between erodibility and rock content for natural hillslopes. Copyright © 2007 John Wiley & Sons, Ltd.     

Dissolved Organic Carbon in Seepage Water – Production and Transformation during Soil Passage

Dissolved organic carbon (DOC) in seepage water can combine with organic pollutants, with Al and heavy metal ions and transport them through the soil profile with a potential to contaminate groundwater. We studied the production of DOC in aerobic decomposition experiments at 8 °C and moisture close to field capacity in soils from two sites with different microbial activities (spodic dystric Cambisols with moder (SLB) and mor‐moder (SLS) layers) using ¹³C‐depleted plants of differing decomposability (Epilobium angustifolium and Calamagrostis epigeios). Additionally, we investigated the DOC transformation during soil passage in decomposition experiments and in the field for the sites SLB and SLS. For SLS, decomposition of Epilobium resulted in a cumulative CO₂ production of 14% of the added C within 128 days. Priming effects were negligible. CO₂ production for the experiments using Calamagrostis was less with 11% for SLB and 10% for SLS. Cumulative DOC production was markedly high in the Epilobium decomposition experiment, being 25 g m^–2, out of which 11 g m^–2 were Epilobium‐derived (2% of the added C). For the Calamagrostis experiments, cumulative productions of DOC and Calamagrostis‐derived DOC (0.1% of the added C for SLS and SLB) were much less. During the soil passage, much of the DOC was removed by sorption or decomposition processes. Field studies at SLS and SLB using ¹³C natural abundance showed that ¹³C distribution of soil organic matter increased with depth, probably mainly due to a discrimination of C isotopes by decomposing microorganisms. DOC, however, showed a depletion of ¹³C from –28γ PDB to –29γ (SLB at 40 cm) or –28 to –30γ (SLS at 20 cm) with depth, owing to preferential decomposition of ¹³C‐enriched substances or preferential adsorption. This study indicates that DOC production is strongly affected by litter composition and that significant changes in DOC composition may occur during its passage through a soil depth of 40 cm.     

EFFECTIVE OPTIMAL STRUCTURAL CONTROL OF SOIL–STRUCTURE INTERACTION SYSTEMS

A methodology is developed in this paper to include soil–structure interaction effects in optimal structural control, General Multi-Degree-Of-Freedom (MDOF) structural models are considered. The SSI transfer functions for ground motion and control force in the physical space are presented first, followed by a methodology for using system identification techniques to find an equivalent fixed-base model of an MDOF SSI system. An iterative technique is applied to combine these methods for the determination of optimal control gains. The control effectiveness of considering soil–structure interaction is investigated for the controlled SSI system. It is found that the control algorithm considering SSI effects is more effective than the corresponding control algorithm assuming a fixed-base system model. In addition, the advantage of applying this methodology is observed to be more prominent in the cases where the SSI effects are more significant. © 1997 by John Wiley & Sons, Ltd.     

Step–pool evolution in the Rio Cordon,northeastern Italy

The principle that formative events, punctuated by periods of evolution, recovery or temporary periods of steady‐state conditions, control the development of the step–pool morphology, has been applied to the evolution of the Rio Cordon stream bed. The Rio Cordon is a small catchment (5 km²) within the Dolomites wherein hydraulic parameters of floods and the coarse bedload are recorded. Detailed field surveys of the step–pool structures carried out before and after the September 1994 and October 1998 floods have served to illustrate the control on step–pool changes by these floods. Floods were grouped into two categories. The first includes ‘ordinary’ events which are characterized by peak discharges with a return time of one to five years (1·8–5·15 m³ s^?1) and by an hourly bedload rate not exceeding 20 m³ h^?1. The second refers to ‘exceptional’ events with a return time of 30–50 years. A flood of this latter type occurred on 14 September 1994, with a peak discharge of 10·4 m³ s^?1 and average hourly bedload rate of 324 m³ h^?1. Step–pool features were characterized primarily by a steepness parameter c = (H/L_s)/S. The evolution of the steepness parameter was measured in the field from 1992 to 1998. The results indicate that maximum resistance conditions are gradually reached at the end of a series of ordinary flood events. During this period, bed armouring dominate the sediment transport response. However, following an extraordinary flood and unlimited sediment supply conditions, the steepness factor can suddenly decrease as a result of sediment trapped in the pools and a lengthening of step spacing. The analogy of step spacing with antidune wavelength and the main destruction and transformation mechanism of the steps are also discussed. Copyright © 2001 John Wiley & Sons, Ltd.     

Dynamic 3-D soil–railway track interaction by BEM–FEM

A study on the dynamic response of a railway track is presented via a 3-D formulation based on the frequency domain Boundary Element Method (BEM) and the Finite Element Method (FEM). The railway track consists of a group of surface, massive, rigid footings resting on a viscoelastic half-space and connected by an overlaying rail structure. The BEM, employing the full-space fundamental solutions and quadrilateral elements, is used for the simulation of the elastic half-space while the FEM is used to model the rigid footings and the rail superstructure. The loading function consists of a set of externally applied, harmonic or transient loads. Frequency as well as transient, by way of FFT, results are presented for various modes of vibration. Various numerical studies assess the through-the-soil interaction of the adjacent footings, the influence of soil damping, the effect of the overlaying structure on the frequency content of the system, and the effective simulation of an infinitely long railway track by a truncated one.     

The effects of Soil–Structure Interaction on a reinforced concrete viaduct

This paper presents a numerical strategy to model a three‐pier viaduct made of prestressed concrete. The viaduct was tested pseudodynamically in ELSA laboratory (JRC Ispra, Italy). During the experimental campaign, only the three piers were tested, whereas the behaviour of the deck was simulated using the finite element method. The first part of the paper presents a numerical model of the viaduct based on the Timoshenko multifibre beam elements and non‐linear constitutive laws. Comparisons with the experimental results show the good performance of the approach. In the second part, a parametric study is carried out showing the influence of Soil–Structure Interaction (SSI). Various types of soils are considered using a recently developed macro‐element representing a rigid shallow foundation. The macro‐element is suitable for dynamic (seismic) loadings and it takes into account the plasticity of the soil, the uplift of the foundation, P?θ effects and the radiative damping. Finally, the numerical results are compared with the ones coming from a classical engineering approach using linear elastic springs at the base of the piers. This comparison shows that SSI is a complex phenomenon inducing displacements and internal forces in the structure that are difficult to predict with the linear approach. Based on the results obtained in this paper, it seems now possible to use this approach to investigate numerically the behaviour of a wider variety of configurations. Copyright © 2010 John Wiley & Sons, Ltd.