Soil-structure-water interaction of intake-outlet towers allowed to uplift

A procedure that can be used for preliminary seismic analysis of intake-outlet towers including soil-structure-water interaction is developed. The formulation also considers the effect of partial soil-foundation separation, a phenomenon of considerable interest for the design of such systems that has not been addressed in the literature. The hydrodynamic pressure of the water is accounted for through added masses given in concise closed-form expressions for easy use in analysis and design. The nonlinear equations of motion, based on foundation-soil bond conditions, are solved numerically.The effects of soil-structure-water interaction are evaluated for a representative intake-outlet tower. Parametric studies are also conducted in the presence and absence of surrounding and contained water for typical cases of soil conditions and tower height-foundation width ratios. The results indicate that hydrodynamic effects are significant and cause an increase in deflections, moments and shears and a decrease in foundation rotation. The study shows that for short towers, foundation uplift is unlikely to occur. On the contrary for slender towers, uplift is more likely to appear, especially for foundations supported by stiff soil, causing significant decrease in moments and deflections.     

Rocking response of rigid blocks to earthquakes

This investigation deals with the rocking response of rigid blocks subjected to earthquake ground motion. A numerical procedure and computer program are developed to solve the non-linear equations of motion governing the rocking motion of rigid blocks on a rigid base subjected to horizontal and vertical ground motion. The response results presented show that the response of the block is very sensitive to small changes in its size and slenderness ratio and to the details of ground motion. Systematic trends are not apparent: The stability of a block subjected to a particular ground motion does not necessarily increase monotonically with increasing size or decreasing slenderness ratio. Overturning of a block by a ground motion of particular intensity does not imply that the block will necessarily overturn under the action of more intense ground motion. In contrast, systematic trends are observed when the problem is studied from a probabilistic point of view with the ground motion modelled as a random process. The probability of a block exceeding any response level, as well as the probability that a block overturns, increases with increase in ground motion intensity, increase in slenderness ratio of the block and decrease in its size. It is concluded that probabilistic estimates of the intensity of ground shaking may be obtained from its observed effects on monuments, minarets, tombstones and other similar objects provided suitable data in sufficient quantity is available, and the estimates are based on probabilistic analyses of the rocking response of rigid blocks, considering their non-linear dynamic behaviour.     

The interaction of elasticity and rocking in flexible structures allowed to uplift

Numerous structures uplift under the influence of strong ground motion. Although many researchers have investigated the effects of base uplift on very stiff (ideally rigid) structures, the rocking response of flexible structures has received less attention. Related practical analysis methods treat these structures with simplified ‘equivalent’ oscillators without directly addressing the interaction between elasticity and rocking. This paper addresses the fundamental dynamics of flexible rocking structures. The nonlinear equations of motion, derived using a Lagrangian formulation for large rotations, are presented for an idealized structural model. Particular attention is devoted to the transition between successive phases; a physically consistent classical impact framework is utilized alongside an energy approach. The fundamental dynamic properties of the flexible rocking system are compared with those of similar linear elastic oscillators and rigid rocking structures, revealing the distinct characteristics of flexible rocking structures. In particular, parametric analysis is performed to quantify the effect of elasticity on uplift, overturning instability, and harmonic response, from which an uplifted resonance emerges. The contribution of stability and strength to the collapse of flexible rocking structures is discussed. Copyright © 2012 John Wiley & Sons, Ltd.     

Inelastic displacement ratios for soil–structure systems allowed to uplift

The simultaneous effects of soil–structure interaction, foundation uplift and inelastic behavior of the superstructure on total displacement response of soil–structure systems are investigated. The superstructure is modeled as an equivalent single‐degree‐of‐freedom system with bilinear behavior mounted on a rigid foundation resting on distributed tensionless Winkler springs and dampers. It is well known that the behavior of soil–structure systems can be well described using a limited number of nondimensional parameters. Here, by introducing two new parameters, the concept is extended to inelastic soil–structure systems in which the foundation is allowed to uplift. An extensive parametric study is conducted for a wide range of the key parameters through nonlinear time history analyses. It is shown that while uplifting soil–structure systems experience excessive displacements, in comparison with systems that are not allowed to uplift, ductility demand in the superstructure generally decreases owing to foundation uplift. A new inelastic displacement ratio (IDR) is proposed in conjunction with a nonlinear static analysis of uplifting soil–structure systems. Simplified expressions are also provided to estimate the proposed IDR. Copyright © 2014 John Wiley & Sons, Ltd.     

Rocking instability of free-standing statues atop slender cantilevers under ground motion

This paper deals with the dynamic response of free-standing statues on the top surface of slender elastically supported cantilevers subjected to horizontal ground motion. Given that there is no link between the base of the statue and the top surface of the monolithic cantilever the statue is in equilibrium in the vertical direction under its own weight. Attention is focused on the determination of the minimum amplitude ground acceleration which leads to the rocking (overturning) instability of the statue whose mass and rotatory inertia are a priory known. It is assumed that the friction between the base of the statue and the top surface of the cantilever is sufficiently large to prevent sliding so that rocking prevails. After simulating the statue by a rigid block freely supported on the top surface of the elastically restrained monolithic cantilever, a theoretical dynamic analysis of the cantilever–rigid block system under horizontal ground motion is comprehensively presented. Two modes of overturning instability of the free standing rigid block are discussed: instability without or with impact. Criteria for overturning instability of the rigid block associated with the minimum amplitude ground acceleration which leads through the vanishing of the angular velocity to an escaped motion in the phase-plane portrait, are properly assessed.     

Rocking vibrations of rigid disk on saturated poroelastic medium

The dynamic response of a rigid disk on a saturated poroelastic half space and subjected to harmonic rocking excitation is studied. The mixed boundary-value problem for the case of relaxed contact condition between the disk and the poroelastic half space is reduced to a Fredholm integral equation of the second kind, which is solved numerically. The dynamic compliance coefficient for the rocking vibration of a rigid disk on a poroelastic half space is presented.     

Rocking instability of free-standing statues atop slender viscoelastic columns under ground motion

The highly complex rocking response of free-standing statues atop multi-drum columns underground excitation resulting in insuperable difficulties for obtaining reliable solution is reexamined analytically. This is achieved after simulating the columns by monolithic viscoelastic cantilevers having structural damping, based on experiments, equivalent to the energy dissipation due to impact and sliding of multi-drum columns. Subsequently, the conditions of rocking (overturning) instability of free-standing rigid blocks (representing the statues) after their uplift from the top surface of the laterally vibrating cantilevers, are established, including overturning with or without impact. Attention focuses on the minimum amplitude ground acceleration which leads to an escaped motion through the vanishing of the angular velocity and acceleration. Maximization of such a minimum amplitude (implying stabilization) of the rigid block is obtained by seeking the optimum combination of values of the slenderness ratio of the column and its height. Analytically derived results based on linearised analyses are in excellent agreement with those obtained via nonlinear numerical analyses.     

Rocking vibrations of a rigid circular foundation on poroelastic half-space to elastic waves

A study is carefully conducted for the rocking response of a rigid circular foundation resting on a poroelastic half-space when subjected to seismic waves under the framework of Biot’s theory. The free-field waves, rigid-body scattering field waves and radiation scattering field waves are introduced to consider the complex behavior of the soil owing to the scattering phenomena caused by the existence of the foundation. The contact surface between the soil and the foundation is supposed to be perfectly bonded and fully permeable. Combining with the divided wave fields, two sets of dual integral equations elaborating the mixed boundary-value conditions are established, and then reduced to Fredholm integral equations. Therefore, with a semi-analytical method, the expressions of the rocking displacements are obtained. The numerical results of the rocking vibration of the foundation for incident P, SV and Rayleigh waves are presented. The influences of certain parameters, such as the permeability of the soil, the incident angle, Poisson’s ratio and the mass of the foundation, on the rocking vibration of the foundation are explored and studied. Different reactions are found when the foundation is excited by different waves.     

Seismic response of slender rigid structures with foundation uplifting

The rocking of rigid structures uplifting from their support under strong earthquake shaking is investigated. The structure is resting on the surface of either a rigid base or a linearly elastic continuum. A large-displacement approach is adopted to extract the governing equations of motion allowing for a rigorous calculation of the nonlinear response even under near-overturning conditions. Directivity-affected near-fault ground motions, idealized as Ricker wavelets or trigonometric pulses, are used as excitation. The conditions under which uplifting leads to large angles of rotation and eventually to overturning are investigated. A profoundly nonlinear rocking behavior is revealed for both rigid and elastic soil conditions. This geometrically nonlinear response is further amplified by unfavorable sequences of long-duration pulses in the excitation. Moreover, through the overturning response of a toppled tombstone, it is concluded that the practice of estimating ground accelerations from overturning observations is rather misleading and meaningless.     

Rocking vibrations of a rigid embedded foundation in a poroelastic soil layer

An approximate analytical method is presented for the dynamic response of a rigid cylindrical foundation embedded in a poroelastic soil layer under the excitation of a time-harmonic rocking moment. The soil underlying the foundation base is represented by a single-layered poroelastic soil based on rigid bedrock while the soil along the side of the foundation is modeled as an independent poroelastic stratum composed of a series of infinitesimally thin layers. The accuracy of the present solution is verified by comparisons with existing solutions obtained from other researchers. Numerical results for the rocking dynamic impedance and dynamic response factor are presented to demonstrate the influence of nondimensional frequency of excitation, poroelastic soil layer thickness, depth ratio of the foundation and internal friction of the poroelastic soil.     

Controlled overturning of unanchored rigid bodies

Typical small hospital and laboratory equipment and general supplies cannot be anchored to resist earthquake motions. In order to protect these non‐structural components, a common procedure is to provide barriers to restrain overturning of objects on shelves and other furniture. In many cases this option is not available, especially for hospital equipment, because of other functional requirements. This work presents an alternative approach. The method proposed here does not avoid overturning, but controls the direction of overturning by providing an inclination to the support base so that the overturning occurs in a preferential direction towards a safe area. For example, objects on shelves, could overturn towards the inside or a wall, and equipment on tables could overturn away from the edge. In both cases this would not only reduce the damage to the particular items, but reduce the amount of debris on the floor. In order to determine the proper inclination of the base, specific rigid bodies are analytically evaluated for bi‐directional excitation obtained from 314 earthquake records, in approximately 7500 cases. For each case, several inclination angles are evaluated. Finally, a parametric curve is adjusted to the data, given a relation between angle of inclination and percentage of controlled overturning cases. In all cases a 7° angle gives more than 98% confidence of controlled overturning. The design expressions were later compared with experimental results obtained on a six‐degree‐of‐freedom shake table; confirming the analytical expressions. Copyright © 2006 John Wiley & Sons, Ltd.     

Criteria for initiation of motion of rigid bodies to base excitation

It is known that when an unanchored rigid body is placed on a horizontal base which oscillates horizontally, it may undergo one of four modes of motion: rest, slide, slide–rock and rock. Initiation of a rigid body into these modes depends on the slenderness ratio of the body, the coefficient of friction between the body and the base and the acceleration of the base. In this study, the coefficient of friction and the base acceleration are considered random. For specific probability distributions of the coefficient of friction and the peak base acceleration, and for various values of the mean and standard deviation of the two random variables, the probabilities of occurrence of these modes of motion are obtained for a body of given slenderness ratio. It is shown that randomness of the coefficient of friction and base peak acceleration should not be ignored. Copyright © 2005 John Wiley & Sons, Ltd.     

Rocking bodies with arbitrary interface defects: Analytical development and experimental verification

The rocking response of a rigid, freestanding block in two dimensions typically assumes perfect contact at the base of the block with instantaneous impacts at two distinct, symmetric rocking points. This paper extends the classical two‐dimensional rocking model to account for an arbitrary number of rocking points at the base representing geometric interface defects. The equations of motion of this modified rocking system are derived and presented in general terms. Energy dissipation is modeled assuming instantaneous point impacts, yielding a discrete angular velocity adjustment. Whereas this factor is always less than unity in the classical model, it is possible for this factor to exceed unity in the presented model, yielding a finite increase in the angular velocity at impact and a markedly different rotational response than the classical model predicts. The derived model and the classical model are numerically integrated and compared to the results of recent shake table tests. These comparisons show that the new model significantly enhances agreement in both peak angular displacement and motion decay. The equations of motion and the energy dissipation of the presented model are further investigated parametrically considering the size of the defect, the number of rocking points, and the aspect ratio and size of the block.     

Experimental assessment of contact forces on a rigid base following footing uplift

A number of investigations in the recent decades have shown that footing uplift can reduce the seismic loading on a structure. Guidelines to design a structure with seismic uplift capability have been proposed. However, these studies mainly focus on the structural response and neglect the impact forces on the footing from re‐contact between the footing and the supporting medium. A small number of computational studies of the induced forces on the footing have been performed. This paper presents the results of free vibrations and shake table tests on a single degree‐of‐freedom model of a bridge pier with footing uplift on a rigid base. Two support conditions are considered, that is, footing fixed to the base and footing free to uplift on a rigid base. Load cells were placed at the interface of the footing and rigid base to measure the contact forces during structural vibration. The footing responses of both flexible and rigid structures due to free vibration are compared. The results show that the flexibility of the structure has significant effects on footing uplift duration and amplitude and reduces the contact force, in some cases very significantly. The flexible structure was also subjected to harmonic base excitations. It is found that varying the characteristics of the excitation changes the uplift amplitude but does not affect the contact force significantly. Copyright © 2017 John Wiley & Sons, Ltd.     

Motions of rigid bodies and criteria for overturning by earthquake excitations

This investigation deals with motions of rigid bodies on a rigid floor subjected to earthquake excitations, and criteria for overturning of the bodies. In order to study any motions of a body in a plane, the motions are classified into six types, i.e. (1) rest, (2) slide, (3) rotation, (4) slide rotation, (5) translation jump and (6) rotation jump. Then, the following are studied: the equations of motion, transitions of motion, and motions after impact between the body and the floor. One of the features of this investigation is the introduction of the tangent restitution coefficient which enables us to estimate the magnitude of the tangent impulse at the instant of impact. A computer program was developed to simulate the motions of bodies subjected to horizontal and vertical ground motions, numerically solving the non-linear equations of motion. Several types of simulation were carried out and the following conclusions were found. The coefficient of friction must be greater than the breadth—height-ratio in order for the body to rock. The motions after impact from translation jump are greatly influenced by the normal and tangent restitution coefficients. As criteria for overturning of bodies, at least two factors must be taken into account: the horizontal acceleration and the velocity of the floor. Then it is possible to estimate the motions of the floor from the overturning of bodies in a more reliable manner than before.     

Non‐linear response analyses of rectangular rigid bodies subjected to horizontal and vertical ground motion

This investigation deals with non‐linear seismic responses of free‐standing rectangular rigid bodies on horizontally and vertically accelerating rigid foundations. The responses are classified into two initial responses and four subsequent responses, accordingly the equations of motion governing the liftoff, slip and liftoff–slip interaction motions and boundary conditions corresponding to commencement and termination of the motions are defined. The time histories of responses presented herein show that the body is sensitive to small changes in the friction coefficient and slenderness, and to the wave properties and intensity of ground motions. Systematic trends are observed: the bodies on the low‐grip foundation avoid overturning while they are allowed to slip regardless of details of ground motions; the long period earthquakes tend to make the body overturn and slip largely. In contrast, the timing when liftoff and slip commences and terminates and their directions do not directly correspond with intensity of ground motions. Moreover, the vertical ground motion adds irregularities on the responses, since it excites or damps the responses. It is concluded that governing equations of motion and boundary conditions in view of discontinuous non‐linear systems are necessary to analyse actual motions of the rectangular rigid bodies subjected to horizontal and vertical ground motion. Copyright © 2002 John Wiley & Sons, Ltd.     

地震动作用下刚体扭转效应的振动台模拟试验

2008年汶川地震中江油市太白公园曲径桥上的石雕发生转动破坏现象,本文对这一转动现象进行了振动台模拟试验。模拟试验结果表明:① 在振动台三向加载1.5倍的汶川地震江油台记录的平动加速度后,模型的转动情况与实际观测的石雕转动情况比较一致;② 石雕的转动与石雕的非对称性、地震动输入角度和地震动的竖向作用有关;③ 加载竖向地震动作用后,石雕模型会发生摇摆现象,说明竖向地震动是造成模型扭转现象的重要原因,这也说明在分析相似震害现象时竖向地震动作用不可忽视。      

Land uplift due to subsurface fluid injection

The subsurface injection of fluid (water, gas, vapour) occurs worldwide for a variety of purposes, e.g. to enhance oil production (EOR), store gas in depleted gas/oil fields, recharge overdrafted aquifer systems (ASR), and mitigate anthropogenic land subsidence. Irrespective of the injection target, some areas have experienced an observed land uplift ranging from a few millimetres to tens of centimetres over a time period of a few months to several years depending on the quantity and spatial distribution of the fluid used, pore pressure increase, geological setting (depth, thickness, and area extent), and hydro-geomechanical properties of the injected formation. The present paper reviews the fundamental geomechanical processes that govern land upheaval due to fluid injection in the subsurface and presents a survey of some interesting examples of anthropogenic uplift measured in the past by the traditional levelling technique and in recent times with the aid of satellite technology. The examples addressed include Long Beach, Santa Clara Valley, and Santa Ana basin, California; Las Vegas Valley, Nevada; Cold Lake and other similar sites, Canada; Tokyo and Osaka, Japan; Taipei, Taiwan; Krechba, Algeria; Upper Palatinate, Germany; Chioggia and Ravenna, Italy.     

Rocking response of flexible circular foundations on layered media

The analysis of the response of a flexible circular foundation on layered media due to an arbitrarily distributed vertical loading is presented. The analysis is based on the ‘ring method’ approach, i.e. discretization of the foundation in a set of concentric rings. The arbitrarily distributed loading is expanded in the circumferential direction in a Fourier series. The influence coefficient matrix of soil for each element of the series is evaluated utilizing the stiffness matrix approach. The stiffness matrix of the foundation is obtained from the finite difference energy method approach. Numerical examples illustrate the influence of several soil-foundation parameters on the rocking response of a foundation. Results are presented in terms of displacement and soil reaction distributions and impedance functions point to significantly different responses of flexible and rigid foundations.