Estimation of shear wave velocity of earth dam materials using artificial blasting test

The objective of this study is to estimate the shear wave velocity of earth dam materials using the vibration generated from artificial blasting events, and to verify its applicability. In this study, near-field artificial blast testing and monitoring were carried out at the Seongdeok dam, Korea, as the first blasting tests to be carried out on an existing dam in Korea. Vibrations were induced by four different types of blasting, using various explosive charge weights and depths of blasting bore-holes. During the tests, acceleration time histories were measured at the rock outcrop adjacent to the point of the explosion, and at the crest of the dam. The fundamental frequency of the target dam was computed from the frequency analysis of measured acceleration histories. Numerical analyses were carried out, varying the shear modulus of the earth fill zone and using the acceleration histories measured at the rock outcrop as input ground motions. From a comparison between the fundamental frequencies calculated by numerical analyses and those of measured records, the shear wave velocities with depth, which are closely related to shear moduli, could be estimated. It is found that the effect of different blasting types on shear wave velocity estimation for the target dam materials is negligible, and that shear wave velocity can be consistently evaluated. Furthermore, by comparing the evaluated shear wave velocity with empirical formulae from previous research, the applicability of the method was verified. Therefore, in cases of mid-to-small earth dams, where the earthquake record is not available, the shear wave velocity of earth fill materials can be reasonably evaluated using blasting vibration records obtained at the site adjacent to the dam.     

汶川大地震中土坝破坏程度与坝体几何形状的关系分析

调查、搜集和研究了汶川地震中被评定为高危以上险情的147座小型水库土坝的地震破坏情况,给出了高危以上险情土坝的地震破坏程度划分为中等破坏、严重破坏和极严重破坏三个等级的原则和标准,以及土坝的地震破坏程度与地震烈度、土坝的宽高比、上游坡比、坝高的经验关系表,可发现:土坝的几何形状对其破坏程度起着重要的作用;对于6～8度地震烈度区,土坝的宽高比越小,或上游坡比越小,或坝体越高,则土坝的破坏程度越严重;对于9度以上地震烈度区,土坝通常发生极严重破坏。依据高危以上险情土坝的地震反应分析结果,给出了土坝地震破坏程度与土坝宽高比、坝高、土坝上游坡比及坝顶加速度放大系数、坝体最大动剪应力的经验关系曲线,发现在相同的地震烈度水平下,土坝的宽高比越小,或上游坡比越小,或坝高越大,且坝顶加速度放大系数越大或坝体最大动剪应力越大,则其地震破坏程度越严重;坝体最大动剪应力超过30kPa的土坝,通常发生严重或极严重破坏,坝体最大动剪应力大于100kPa的土坝,通常发生极严重破坏;土坝离发震断层越远,则其坝顶加速度放大系数越大。本文给出的高危以上险情土坝的地震破坏程度与坝体几何形状的经验关系,可为今后土坝抗震设计提供参考依据。     

汶川地震震损水库土坝动力反应与几何坝形的经验关系

在5·12汶川地震后的四川省水库土坝震害调查成果的基础上,选取汶川地震中受损的有完整资料的96座水库土坝为研究对象,应用等效线性模型对土坝进行了二维动力反应分析。选择3条有代表性的汶川地震实测记录,以三水准峰值加速度输入,得到土坝的动力反应（放大系数、最大动剪应力）与土坝几何形状（宽高比、上游坡比、坝高）间的经验关系。结果表明,土坝放大系数和最大动剪应力随着宽高比和上游坡比的增大而减小,随着坝高的增大而增大;输入波的频谱和峰值强度均对土坝动力反应与其几何形状的经验关系有重要影响。     

An investigation into the seismic behaviour of dams using dynamic centrifuge modelling

Dynamic response of dams is significantly influenced by foundation stiffness and dam-foundation interaction. This in turn, significantly effects the generation of hydrodynamic pressures on upstream face of a concrete dam due to inertia of reservoir water. This paper aims at investigating the dynamic response of dams on soil foundation using dynamic centrifuge modelling technique. From a series of centrifuge tests performed on model dams with varying stiffness and foundation conditions, significant co-relation was observed between the dynamic response of dams and the hydrodynamic pressures developed on their upstream faces. The vertical bearing pressures exerted by the concrete dam during shaking were measured using miniature earth pressure cells. These reveal the dynamic changes of earth pressures and changes in rocking behaviour of the concrete dam as the earthquake loading progresses. Pore water pressures were measured below the dam and in the free-field below the reservoir. Analysis of this data provides insights into the cyclic shear stresses and strains generated below concrete dams during earthquakes. In addition, the sliding and rocking movement of the dam and its settlement into the soil below are discussed.     

Probability density evolution method for seismic liquefaction performance analysis of earth dam

To investigate the seismic liquefaction performance of earth dams under earthquake loading, we present a new methodology for evaluating the seismic response of earth dams based on a performance‐based approach and a stochastic vibration method. This study assesses an earthfill dam located in a high‐intensity seismic region of eastern China. The seismic design levels and corresponding performance indexes are selected according to performance‐based criteria and dam seismic codes. Then, nonlinear constitutive models are used to derive an array of deterministic seismic responses of the earth dam by dynamic time series analysis based on a finite element model. Based on these responses, the stochastic seismic responses and dynamic reliability of the earth dam are obtained using the probability density evolution method. Finally, the seismic performance of the earth dam is assessed by the performance‐based and reliability criteria. Our results demonstrate the accuracy of the seismic response analysis of earth dams using the random vibration method. This new method of dynamic performance analysis of earth dams demonstrates that performance‐based criteria and reliability evaluation can provide more objective indices for decision‐making rather than using deterministic seismic acceleration time series as is the current normal practice. Copyright © 2016 John Wiley & Sons, Ltd.     

Two-dimensional dynamic analysis of concrete gravity and embankment dams including hydrodynamic effects

An analysis procedure in the frequency domain is developed for determining the earthquake response of two-dimensional concrete gravity and embankment dams including hydrodynamic effects; responses of the elastic dams and compressible water are assumed linear. The dam and fluid domain are treated as substructures and modelled with finite elements. The only geometric restriction is that an infinite fluid domain must maintain a constant depth beyond some point in the upstream direction. For such an infinite uniform region, a finite element discretization over the depth is combined with a continuum representation in the upstream direction. The fluid domain model approximately accounts for interaction between the fluid and underlying foundation medium through a damping boundary condition applied along the reservoir bottom, while the dam foundation is assumed rigid. Several examples are presented to demonstrate the accuracy of the fluid domain model and to illustrate dam responses obtained from the analysis procedure.     

Hydrodynamic pressures and response of gravity dams to vertical earthquake component

Hydrodynamic pressures and structural response of concrete gravity dams, including dam-reservoir interaction, due to the vertical component of earthquake ground motions are investigated. The response of the dam is approximated by the deformations in the fundamental mode of vibration, and the effects of deformability of bed rock on hydrodynamic pressures are recognized in the analysis. Expressions for the complex frequency response functions for the dam displacement, dam acceleration and lateral hydrodynamic force are derived. These results along with the Fast Fourier Transform algorithm are utilized to compute the time-history of responses of dams of 100, 300 and 600 ft height, with full reservoir, for different values of elastic modulus of mass concrete: 3.0, 3.5, 4.0, 4.5 and 5.0 million psi, to the vertical component of El Centro, 1940, and Taft, 1952, ground motions. It is concluded that the hydrodynamic forces caused by vertical ground motion are affected substantially by damreservoir interaction and depend strongly on the modulus of elasticity of the dam. The dam response to the vertical component of ground motion is compared with that due to the horizontal component. It is concluded that because the vertical component of ground motion causes significant hydrodynamic forces in the horizontal direction on a vertical upstream face, responses to the vertical component of ground motion are of special importance in analysis of concrete gravity dams subjected to earthquakes.     

The effect of travelling seismic waves on the dynamic response of earth dams

A theoretical investigation of the dynamic response of earth dams to the travelling seismic waves is presented. The earth dam is simplified as a truncated two-dimensional elastic wedge. The dam body consists of an isotropical linear viscoelastic material with homogeneous elastic modulus and density. The seismic waves travel along the longitudinal direction of the earth dam. The numerical calculations show the following. (i) For the longitudinal mode of vibration, the greater the ratio (H/L) of the height to the lenght of the complete wedge, the more the natural transverse period of vibrational of the two-dimensional wedge is less than that of the one-dimensional wedge. Especially for the first two natural transverse period, this influence is large. The decrease of the ratio of the natural transverse period for a two-dimensional wedge to that for a one-dimensional wedge with the ratio H/L is rapid for the higher than for the lower longitudinal modes. (ii) Comparing with the one-dimensional wedge, the natural transverse periods for the two-dimensional case in the complete wedge are lower, and they will increase as the coefficient of truncation, h/H increases. (iii) When the frequency of forced vibration is less than the natural transverse frequency for one-dimensional wedge, the amplification is less for a two-dimensional wedge than for a one-dimensional wedge. (iv) When the phase difference of ground motion at both ends of the dam equals π, the amplification for a two-dimensional wedge is less than that for a one-dimensional wedge, but when the phase difference equals nπ, (n > 1), the situation is reversed. (v) As the coefficient of truncation, h/H, increases, the displacement model partecipations decrease monotically. (vi) In general, the displacement caused by an earthquake is greater for a one-dimensional wedge than for a two-dimensional wedge when considering the seismic waves travelling, but the acceleration response of a two-dimensional wedge with long length of dam to travelling seismic waves with long dominant period is greater than that of a one-dimensional wedge. When the length of the dam is short enough, the response of a two-dimensional wedge without considering the influence of travelling seismic waves always gives the greatest value.     

Seismic shear strains and seismic coefficients in dams and embankments

In a previous publication¹ dealing with the lateral seismic response of dams and embankments the authors developed an inhomogeneous shear beam (SB) model in which the modulus increases as a power m of the depth, with m ranging from 0.35 to 0.90 and depending on material and geometric parameters. Reference 1 studied primarily the free vibration characteristics and the distribution of peak seismic displacements in earth dams. This paper focuses on seismic shear strains and stresses, and on seismic coefficients. Both steady-state and transient vibrations are considered and the effects of inhomogeneity are graphically illustrated. A comprehensive comparative study is undertaken using five dam cross-sections, each excited by four recorded accelerograms. It is found that plane-strain finite-element analyses yield distributions of peak values of seismic shear strains which, in general, are in good accord with the results of a ‘consistent’ inhomogeneous SB model. The limitations of the developed model are also elucidated and possible ways of overcoming them are suggested.     

Seismic response of earth dam with varying depth of liquefiable foundation layer

Earthquake induced liquefaction continues to be a major threat to many engineered structures around the world. Analysis of liquefaction becomes particularly difficult for two-dimensional (and 3D) problems such as dam/foundation systems. Predominantly, analyses for such systems are performed utilizing some type of finite element or finite difference procedure. Verification or validation of the analyses relies on very limited field performance data with reduced knowledge of the full scope of system conditions or loading conditions.Research reported in this paper represents a portion of ongoing work to obtain a database of information useful for numerical model calibration and to gain a better understanding of the complex dynamics of liquefying foundations under earth dams. Specifically, a highly instrumented model of an earth dam with clay core founded on a liquefiable foundation subjected to earthquake loading is being studied. Properties of the liquefiable foundation are varied to determine the related effects on the overlying earth dam. In this paper, results from three centrifuge physical models will be presented. The models are identical, with the exception of the location (depth) of a liquefiable layer in the foundation, and are subjected to the same dynamic excitation. Results and discussion related to the significance of the liquefiable layer location within the foundation and damage to the earth dam are presented.     

土石坝地震响应的非线性剪切条模型与对比分析

对一维剪切条计算模型进行改进,提出了土石坝非线性地震反应的简化计算方法。首先将坝体沿坝高离散为一系列的具有不同剪切刚度与阻尼比等参数特性的层状体系,建立了各层的振动控制方程及其边值条件,进而采用数学物理方程方法进行了求解,确定了体系的振动特性,并根据振型叠加原理和Duhamel积分确定了坝体地震反应的线弹性解。采用等价线性化方法考虑坝料的动力非线性性质,通过对线弹性地震响应的反复迭代计算,使得各层土的模量和阻尼比与其相应的剪应变水平相协调,确定出与非线性坝体系统相等效的线性解答,并将所得到的地震响应作为非线性地震响应的近似解。最后,以均质坝和心墙坝作为算例进行了具体的数值计算,将所得结果与有限元数值解进行对比分析,论证了所提方法的适用性和合理性。     

Decoupling approximation to the evaluation of earthquake-induced plastic slip in earth dams

Newmark's sliding block analysis for evaluating earthquake-induced permanent displacements of earth dams and slopes did not consider the effects of elastic dynamic response. Makdisi and Seed extended the analysis to include such effects, using the simpfying assumption that the computation of dynamic response and plastic slip can be decoupled. This paper examines the error introduced by this assumption, using three idealized lumped-mass models for a dam. Both sinusoidal and synthetic earthquake motions are employed. When the predominant frequency of the input motion lies in the proximity of the fundamental frequency of the dam, the slip based upon the decoupling assumption exceeds the exact value. This error decreases as the threshold acceleration required to initiate slip and the damping in the soil increase. For practical application, the error should seldom exceed 20 per cent.     

Elasto-plastic earthquake shear-response of one-dimensional earth dam models

A simplified analysis procedure for the non-linear hysteretic earthquake-response of earth dams is presented. The dam is modelled as a one-dimensional hysteretic shear-wedge subjected to base excitation. The hysteretic stress-strain behaviour of the dam materials is modelled by using elasto-plastic constitutive equations based on multi-surface kinematic plasticity theory. The method is based on a Galerkin formulation of the equations of motion in which the solution is expanded using eigenmodes of the linearized problem defined over the spatial domain occupied by the dam. The technique is applied to analyse the non-linear dynamic response of an earth dam subject to two very different input ground motions. The following investigations are presented: (i) comparison between the results obtained using two soil models depicting different nonlinear properties, (ii) comparison between the results of the one-mode and the multi-mode solution expansions, (iii) comparison with the results obtained through an elaborate finite element representation of the dam, and finally, (iv) comparison with the results obtained through the Makdisi-Seed¹¹ iterative procedure for earth dam analysis. The comparisons show that the proposed technique can be used to determine adequately the transient earthquake response of long earth dams. Furthermore, the efficiency and low computational cost make the technique very attractive; it can easily and systematically be extended to two- and three-dimensional calculations of earth dam response.     

Estimation of shear moduli and damping factors of earth dam materials

Abdel-Ghaffar and Scott developed a procedure for extracting the shear moduli and damping factors of soils based upon strong motion records from earth dams. It is a very efficient procedure for earth dams that exhibited predominantly first mode response along the upstream-downstream direction. In their approach, they employed digital band-pass filters on the crest and abutment acceleration records, and constructed the hysteresis loops of soils by treating these filtered records as the input-output to a non-linear SDOF structure. In the process an important superposition assumption was implicitly introduced. This study looked into the implications of this linear superposition assumption on presumed nonlinear systems. Specifically, numerical simulations were conducted in finding out whether or not such a procedure is capable of extracting a known input dynamic behaviour of soils. It was found that the hysteresis loops were generally distorted, and to minimize errors only those loops of larger strain amplitudes should be used. Simple guidelines were suggested accordingly. Applications to real records from two dams were carried out following the proposed guidelines. Results of such applications were explored.     

Shear moduli of volcanic soils

The shear modulus of soils is one of the important parameters in small strain level geotechnical problems (i.e. the study of earthquake effects and soil–structure interaction). In this paper, the shear moduli of crushable volcanic soils at small strain level were investigated in bender element and cyclic undrained triaxial tests. Comparison of results shows that the shear moduli from bender element tests agree well with those determined in cyclic triaxial tests. The influence of particle breakage, effective confining pressure, consolidation time, void ratio and fines content on the shear modulus are also discussed. In the present study, empirical equations for evaluating the shear modulus of granular materials with particle breakage are proposed based on the test results.     

Lateral response of dams in semi-elliptical rigid canyons

An analytical closed-form solution is developed for the lateral response of earth and rockfill dams built in semi-elliptical canyons. The dam is idealized as a linearly hysteretic elastic body deforming only in shear, whereas the canyon is assumed to be rigid. The solution for the dam response is given in terms of prolate spheroidal radial and angular functions of the first kind and zero order. Results are presented for natural frequencies, modal displacement shapes, participation factors, and response to transient and steady-state harmonic base excitation for various dam length-to-height ratios. Comparisons are made of the effects of the length-to-height ratio and the canyon shape on the response of dams built in semi-elliptical and rectangular canyons. A subsequent study (Dakoulas, P. & Hsu, C.H., Response of earth dams in semi-elliptical flexible canyons to oblique SH waves, Report, Rice University, Houston, Texas, 1993) extends this model to a semi-elliptical canyon consisting of flexible elastic rock, subjected to obliquely incident harmonic SH waves.     

2011年M_W9.0东日本大地震动力学破裂过程的数值模拟

力学上,地震可以看作在应力场作用下由于断层带介质的突然损伤或软化导致的断层带失稳事件.本文基于这个地震动力学模型,利用一种可以模拟断层大位错的有限元方法,研究了2011年MW9.0东日本大地震(Tohoku-Oki)的动力学破裂过程.比较了无障碍体和具有不同刚度障碍体的断层带模型产生的断层位移、位错和应力降.主要结果表明,障碍体的存在并不明显地改变障碍体区域的初始构造应力场.对有障碍体情形,准静态结果显示断层上盘最大逆冲位移和最大剪切位错分别为51m和58m,均发生在海底表面海沟处,与无障碍体的结果(最大剪切位错约55m)相比差别不大;下盘最大倾向位移(-10m)并不与上盘最大值出现在同一位置,而是在障碍体处.障碍体处剪应力降(约11 MPa)大于周围非障碍体区域.障碍体处正应力降的最大值约为3 MPa.模拟结果似乎不支持海山是导致本次地震异乎寻常大位错的原因,而倾向于断层带剪切刚度在地震过程中极度损伤或软化.     

Earthquake analysis of gravity dams including hydrodynamic interaction

A general procedure for analysis of the response of gravity dams, including hydrodynamic interaction and compressibility of water, to the transverse horizontal and vertical components of earthquake ground motion is presented. The problem is reduced to one in two dimensions considering the transverse vibration of a monolith of a dam, and the material behaviour is assumed to be linearly elastic The complete system is considered as composed of two substructures—the dam, represented as a finite element system, and the reservoir, as a continuum of infinite length in the upstream direction governed by the wave equation. The structural displacements of the dam (including effects of water) are expressed as a linear combination of the modes of vibration of the dam with the reservoir empty. The effectiveness of this analytical formulation lies in its being able to produce excellent results by considering only the first few modes. The complex frequency response for the modal displacements are obtained first. The responses to arbitrary ground motion are subsequently obtained with the aid of the Fast Fourier Transform algorithm An example analysis is presented to illustrate results obtained from this method. It is concluded that the method is very effective and efficient and is capable of producing results to any desired degree of accuracy by including the necessary number of modes of vibration of the dam.     

Seismic behaviors of earth-core and concrete-faced rock-fill dams by dynamic centrifuge tests

The investigation on the seismic behavior of dams becomes crucial but is limited to lack of experimental or field data. This paper aims to experimentally simulate two major dam types of earth-core rock-fill dam and concrete-faced rock-fill dam by dynamic centrifuge tests to investigate the seismic response of the dam. A series of staged centrifuge tests was performed by applying real earthquake records from 0.05 to 0.5g. The distributions of amplification ratio differed depending on the magnitude of earthquake loading and the zoning condition. The amplification ratio at the crest increased in the bedrock acceleration that exceeds 0.3g and strongly influenced by the loosening behavior of the upper part. The residual settlements and horizontal displacement at the dam crest were small. Shallow surface sliding was dominant failure. The maximum tensile stress on the face slab by dynamic loading occurred at a height of around 4/5 near the upstream water level. Finally, two-dimensional numerical simulations were performed in an effort to simulate the centrifuge models. The centrifuge tests and numerical analysis obtained mostly comparable results, thus confirming that centrifuge modeling reasonably simulates the seismic behavior of dams.     

高土石坝振动台模型试验理论、技术与应用

对土石坝振动台模型试验理论和技术进行系统阐述,提出基于原型和模型坝料静、动力特性试验的模型相似设计方法和不同强度地震动递进输入(白噪声微振-设计地震-校核地震-破坏试验)的振动试验方法。基于1g大型振动台和ng超重力离心机振动台设备性能现状,结合高土石坝的结构特点和动力试验相似模拟要求,对土石坝振动台模型试验的优势及局限进行深入讨论。结合已有的工程实践,对土石坝振动台模型试验在工程中的应用进行总结,并以某实际高面板堆石坝为例研究面板坝生命周期内经历多次地震情况下结构动力特性的演化规律。