APPLICATION OF BOUNDARY ELEMENT ANALYSIS FOR MULTIPLE SEISMIC CRACKING IN CONCRETE GRAVITY DAMS

The previously developed two-dimensional boundary element procedure for analysing the propagation of a single discrete crack is extended to simultaneous multiple cracking in concrete gravity dams. A brief discussion of the generalized methodology is presented and the validity of the extended procedure is verified by performing a fracture analysis of the Fongman dam and comparing the predicted rupture process with the available experimental results. The fracture response of the Koyna dam is then studied extensively under the Koyna earthquake. Both single and multiple cracking models are employed to investigate the fracture process as well as final rupture in the dam. Similar final damage involving complete separation of the crest block of the dam is predicted, irrespective of whether single or multiple crack propagation models are employed. In relation to the phenomenon of hydrodynamic uplift pressure within propagating cracks, openings of the crack on the upstream face of the dam are examined in particular. The results indicate that this phenomenon is not expected to be significant during the crack development phase, and hence unlikely to affect the final rupture characteristics of dams undergoing strong earthquake excitation.     

A multifractal model of crack coalescence in rocks

Geometric characteristics of fractal sets of cracks are investigated from the standpoint of their coalescence. A 1D computer model, in which a realistic character of forms of crack sets is achieved through the inducing of sets with the use of the multiplicative cascade procedure, is considered. The investigation is aimed at the determination of conditions of coalescence of cracks organized as a superposition of fractal subsets of a unified set of cracks. The process of crack coalescence is investigated for three different values of the coalescence criterion. The geometric characteristics of the sets of cracks that are necessary for the transition of the crack coalescence process into an avalanche-like stage are estimated.     

Dynamic non-linear analysis of reinforced concrete shear wall by finite element method with explicit analytical procedure

A numerical procedure for a dynamic non-linear finite element analysis is proposed here to analyse three-dimensional reinforced concrete shear wall structures subjected to earthquake motions. A shear wall is modelled as a quasi-three dimensional structure which is composed of plane elements considering the in-plane stiffness of orthogonal flange panels. The proposed constitutive model is based on the non-linearity of reinforcement and concrete in which the tension stiffening in tension and the degradation of stiffness and strength in compression of concrete after cracking are considered. The acceleration-pulse method, which is a kind of explicit analytical procedure, is employed to solve the non-linear dynamic equations, where the dynamic equation can be solved without stiffness matrix and so the iterative procedure is not necessary for descending portion of stress–strain relationship caused by cracking and softening after compressive strength in concrete. The damping effect is considered by assuming equivalent viscous damping which can give good cyclic behaviours of inertia force vs. displacement relationships. This analytical method was applied to a test specimen of a reinforced concrete shear wall with a H-shaped section which was vibrated up to failure by using a large-scale shaking table with high -performance in Japan. The test was performed as one of the dynamic model tests for evaluation of seismic behaviour of nuclear reactor buildings. The calculations were performed sequentially from the elastic range to failure. The comparison with the test results shows that this approach has good accuracy. © 1997 by John Wiley & Sons Ltd     

Estimating the Impact of Vadose Zone Sources on Groundwater to Support Performance Assessment of Soil Vapor Extraction

Soil vapor extraction (SVE) is a prevalent remediation remedy for volatile organic compound (VOC) contaminants in the vadose zone. To support selection of an appropriate condition at which SVE may be terminated for site closure or for transition to another remedy, an evaluation is needed to determine whether vadose zone VOC contamination has been diminished sufficiently to keep groundwater concentrations below threshold values. A conceptual model for this evaluation was developed for VOC fate and transport from a vadose zone source to groundwater when vapor‐phase diffusive transport is the dominant transport process. A numerical analysis showed that, for these conditions, the groundwater concentration is controlled by a limited set of parameters, including site‐specific dimensions, vadose zone properties, and source characteristics. On the basis of these findings, a procedure was then developed for estimating groundwater concentrations using results from the three‐dimensional multiphase transport simulations for a matrix of parameter value combinations and covering a range of potential site conditions. Interpolation and scaling processes are applied to estimate groundwater concentrations at compliance (monitoring) wells for specific site conditions of interest using the data from the simulation results. The interpolation and scaling methodology using these simulation results provides a far less computationally intensive alternative to site‐specific three‐dimensional multiphase site modeling, while still allowing for parameter sensitivity and uncertainty analyses. With iterative application, the approach can be used to consider the effect of a diminishing vadose zone source over time on future groundwater concentrations. This novel approach and related simulation results have been incorporated into a user‐friendly Microsoft® Excel®‐based spreadsheet tool entitled SVEET (Soil Vapor Extraction Endstate Tool), which has been made available to the public.     

Discrete‐like crack simulation by smeared crack‐based FEM for reinforced concrete

A numerical process that simulates crack propagation in reinforced concrete through post‐crack stress redistribution is presented. This process is developed within the context of the smeared crack approach. Continuity and orientation of the reinforcing bar components are automatically recognized in the pre‐processing stage. The process explicitly outputs crack widths by computing the bond slips along reinforcement, without imposing any additional nodes between the reinforcement and concrete. The process is incorporated with a finite element algorithm, and the validation is investigated through sample 3D static analyses of nine concrete specimens subjected to monotonic shear and flexure loads. These specimens contain relatively well‐distributed steel bars and fiber reinforced polymer (FRP) sheets of reinforcement ratio from 0.11 to 0.57%. The analyses predict the crack patterns and crack widths well, although some disagreements are found between the test and the analysis results. The proposed process outputs discrete, continuous in crack directions, and element boundary‐free crack patterns. Copyright © 2007 John Wiley & Sons, Ltd.     

An efficient three‐dimensional solid finite element dynamic analysis of reinforced concrete structures

Most of the finite element analyses of reinforced concrete structures are restricted to two‐dimensional elements. Three‐dimensional solid elements have rarely been used although nearly all reinforced concrete structures are under a triaxial stress state. In this work, a three‐dimensional solid element based on a smeared fixed crack model that has been used in the past mainly for monotonic static loading analysis is extended to cater for dynamic analysis. The only material parameter that needs to be input for this model is the uniaxial compressive strength of concrete. Steel bars are modelled as uniaxial elements and an embedded formulation allows them to have any orientation inside the concrete elements. The proposed strategy for loading or unloading renders a numerical procedure which is stable and efficient. The whole process is applied to two RC frames and compared against existing experiments in the literature. Results show that the proposed approach may adequately be used to predict the dynamic response of a structure. Copyright © 2005 John Wiley & Sons, Ltd.     

Fracture Toughness Evaluation Based on Tension-softening Model and its Application to Hydraulic Fracturing

This paper discusses the applicability of the tension-softening model in the determination of the fracture toughness of rocks, where the fracture toughness evaluated based on the tension-softening model is compared with the crack growth resistance deduced from laboratory-scale hydraulic fracturing tests. It is generally accepted that the fracture process is dominated by the growth of a fracture process zone for most types of rocks. In this study, the J-integral based technique is employed to determine the fracture toughness of Iidate granite on the basis of the tension-softening model, where compact tension specimens of different dimensions were tested in order to examine the specimen size effect on the measured fracture toughness. It was shown that the tension-softening relation deduced from the J-integral based technique allowed us to determine the specimen size independent fracture toughness K_c of Iidate granite. Laboratory-scale hydraulic fracturing tests were performed on cubic specimens (up to a 10 m sized specimen), where cyclic pressurization was conducted using a rubber-made straddle packer to observe the extent of the hydraulically induced crack. The experimental results of pressure and crack length were then used to construct the crack growth resistance curve based on the stress intensity factor K. The crack growth resistance obtained from the hydraulic fracturing tests was observed to initially increase and then level off, giving a constant K value for a long crack extension stage. The plateau K value in the crack growth resistance curve was found to be in reasonable agreement with the fracture toughness K_c deduced from the tension-softening relation. It was demonstrated that the tension-softening model provides a useful tool to determine the appropriate fracture toughness of rocks, which may be applicable for the analysis of the process of large-scale crack extension in rock masses.     

Brittle crack growth in rocks

Fracture phenomena in rocks are associated with mainly mode I crack growth, sometimes superposed by shear or torsion. The present paper contributes to a fracture mechanics analysis of mode I and mixed mode crack propagation, by presenting reliable fracture toughness data for some rocks which include the effect of induced crack propagation rate, and the influence of effective pressure, and by numerical calculations on fracture propagation in layered rock formations. Empirical relations between fracture toughness,K _Ic' and induced crack opening displacement rate, as well as effective pressure, are given. The observedK _Ic pressure relation supports a theoretical model which takes into account the existence of microcracks in the crack tip region. Finite element calculations of fracture propagation in layered rock formations demonstrate the important effect of mixed mode crack growth. The numerical approach is particularly applied to single crack growth in hydraulic fracturing and in three point bending tests on layered single edge crack specimens.     

一种基于3D复杂介质的弹性建模数值方法

储层中的裂隙会导致介质表现出各向异性.传统等效介质方法假定储层可以被等效成为横向各向同性介质,不适用于复杂裂缝储层的弹性等效建模和各向异性特征分析.本文在前人研究基础上,利用最小二乘方法开展3D复杂裂隙弹性等效数值模拟研究,并与常规等效介质理论方法进行比较,验证数值方法的精确性.数值方法不仅能有效避免Hudson理论和Eshelby-Cheng理论等解析方法在大裂隙密度条件下的参数估计误差,而且兼顾裂隙扰动作用对等效介质参数的影响.数值研究表明,数值方法能够较好地描述复杂裂缝介质的各向异性特征,为复杂裂缝储层地震波各向异性参数反演提供依据.     

模拟震源动力学破裂过程的数值方法研究

为模拟震源的动力学破裂过程,本文讨论一种求解剪切裂纹动力学扩展问题的有限差分法。在研究二维反平面破裂的基础上,我们把所用方法推广到三维问题。研究了许多简单震源模型,通过对比同一问题的解析解和其它数值解,对方法的正确性和计算精度进行了检验,结果表明我们的数值方法是可行的。最后,作为初步应用的例子,我们研究了非均匀断层的自发破裂问题。     

An analysis method for elastic waves propagation in material involving cracks

In this paper, a new model to treat the problem of elastic wave travelling in rock mass that embeds cracks is proposed, in which, instead of modelling the crack directly the mechanical effects of discontinuities are translated into the equivalent nodal forces on a numerical procedure. Thus the response is physically obtained as the superposition of the incident wave field and the scattering wave field produced by the radiation of the reflected waves from the crack surfaces. Finally, a numerical example is carried out and it shows that the results by the proposed method have a very good agreement with those of the exact ones.     

A Network Approach to Fracture: The Effect of Heterogeneity and Loading Conditions

—Fracture in a heterogeneous solid is simulated on a triangular network of bonds which figure the potential cracks of the medium. Heterogeneity is introduced by assuming a statistical strength distribution for the bonds. External stresses are applied to the network and the evolution of the bond population is analyzed when the stresses are increased. Bond-breaking is controlled by the crack-exten sion force which takes into account crack interactions by using an iterative procedure. Crack propaga tion leads to the coalescence of broken bonds crack clusters are formed. By using this kind of approach which combines fracture mechanics and network modelling, we are able to simulate the rupture of a rock specimen under various loading conditions without heavy computation. We discuss physical properties of the rupture process by examining the rupture stress and the geometric properties of the macroscopic fracture and their dependence on loading conditions and heterogeneity. Analysis of the geometric characteristics shows that the number of broken bonds can be fitted by a power law of the lattice size, the exponent depending on the loading conditions. Furthermore, an approximate computation of the mechanical response of the network demonstrates that the threshold secant modulus may be a more legitimate choice for a damage parameter in terms of system size independence.     

不同时期水库地震活动主要影响因素讨论以三峡库区微震活动为例

结合微震活动的流体作用强度检测及孔隙压扩散模拟,讨论了三峡库区不同时期微震活动的主要影响因素。以2008年9月蓄水季为界划分前、后期,前期流体渗透导致的孔隙压力增加,使裂隙或断层面强度降低,是库区微震活动的主要影响因素,这一时期微震频次及ETAS模型参数μ值有起伏地缓慢增大,与库水位加卸载过程关系不明显; 后期由于流体渗透引起的孔隙压力变化趋于零,在新的流体平衡条件下,库水位加卸载过程所导致的裂隙或断层面上的应力变化,成为库区微震活动的主要影响因素,这一时期微震频次及μ值显示出与水位变化明显的关联特征。库区小震震源深度的时间变化支持上述观点。在此基础上,进一步讨论了水库“诱发”和水库“触发”地震的力学差异,认为前者主要缘于流体渗透导致的裂隙或断层面强度的“主动”降低,后者则主要与库水加卸载所导致的裂隙或断层面上应力增强有关。进一步推论认为,流体对小地震“诱发”、“触发”皆可能发生,但中强地震缘于流体“诱发”的可能性非常小,对水库区发生的中强地震,流体仅可能对处于临界状态的断层系统起到“触发”作用。     

THREE-DIMENSIONAL INTERPRETATION OF GRAVITY DATA FROM SEDIMENTARY BASINS USING AN EXPONENTIAL DENSITY-DEPTH FUNCTION*

In mapping the topography of the basement of deep sedimentary basins by gravity modelling, the accuracy can be improved by incorporating an exponential increase in density with depth. For calculating the gravity effect of a three-dimensional (3D) structure with such an exponential density-depth relation a frequency-domain forward algorithm based on series expansion is presented, the numerical evaluation of which can be performed efficiently by fast Fourier transform. The algorithm can be applied in a recursive procedure to give the inverse solution in terms of basement relief. The inversion procedure is satisfactorily tested on a 2D synthetic example and a 3D field example of gravity data from the western margin of the Pannonian Basin in eastern Austria, where up to 2.2 km of Tertiary sediments overlie an igneous or metamorphic basement. The results are confirmed by basement intersections in several wells.     

Non-stationary frequency response function

Using the Duhamel’s integral concept, a non-stationary frequency response function (complete-FRF) for the dynamic response of a single degree of freedom system initially at rest has been developed. Although the procedure is devised to be applied in the frequency domain, this new function is time dependent and can be employed to calculate the transient response of a system in a forced vibration case. The method has been successfully checked with two different cases of loading in the time domain which have either analytical solution or accurate numerical solution using Newmark’s algorithm. The method has been compared with the solution obtained from the commonly used steady frequency response function, and a detailed analysis of the four parameters that appear in the complete-FRF function: time, damping ratio, natural period and input frequency is presented. Finally, the proposed non-steady FRF has been applied to the calculation of an elastic displacement response spectrum to confirm the great influence of the natural period of the system and the frequency content of the solicitation in frequency-domain spectral analysis.     

Cohesive Crack Analysis of Toughness Increase Due to Confining Pressure

Apparent fracture toughness in Mode I of microcracking materials such as rocks under confining pressure is analyzed based on a cohesive crack model. In rocks, the apparent fracture toughness for crack propagation varies with the confining pressure. This study provides analytical solutions for the apparent fracture toughness using a cohesive crack model, which is a model for the fracture process zone. The problem analyzed in this study is a fluid-driven fracture of a two-dimensional crack with a cohesive zone under confining pressure. The size of the cohesive zone is assumed to be negligibly small in comparison to the crack length. The analyses are performed for two types of cohesive stress distribution, namely the constant cohesive stress (Dugdale model) and the linearly decreasing cohesive stress. Furthermore, the problem for a more general cohesive stress distribution is analyzed based on the fracture energy concept. The analytical solutions are confirmed by comparing them with the results of numerical computations performed using the body force method. The analytical solution suggests a substantial increase in the apparent fracture toughness due to increased confining pressures, even if the size of the fracture process zone is small.     

Towards a simple dynamic process conceptualization in rainfall–runoff models using multi‐criteria calibration and tracers in temperate,upland catchments

Empirically based understanding of streamflow generation dynamics in a montane headwater catchment formed the basis for the development of simple, low‐parameterized, rainfall–runoff models. This study was based in the Girnock catchment in the Cairngorm Mountains of Scotland, where runoff generation is dominated by overland flow from peaty soils in valley bottom areas that are characterized by dynamic expansion and contraction of saturation zones. A stepwise procedure was used to select the level of model complexity that could be supported by field data. This facilitated the assessment of the way the dynamic process representation improved model performance. Model performance was evaluated using a multi‐criteria calibration procedure which applied a time series of hydrochemical tracers as an additional objective function. Flow simulations comparing a static against the dynamic saturation area model (SAM) substantially improved several evaluation criteria. Multi‐criteria evaluation using ensembles of performance measures provided a much more comprehensive assessment of the model performance than single efficiency statistics, which alone, could be misleading. Simulation of conservative source area tracers (Gran alkalinity) as part of the calibration procedure showed that a simple two‐storage model is the minimum complexity needed to capture the dominant processes governing catchment response. Additionally, calibration was improved by the integration of tracers into the flow model, which constrained model uncertainty and improved the hydrodynamics of simulations in a way that plausibly captured the contribution of different source areas to streamflow. This approach contributes to the quest for low‐parameter models that can achieve process‐based simulation of hydrological response. Copyright © 2009 John Wiley & Sons, Ltd.     

An innovative methodology for seismic retrofitting of existing RC buildings by metal shear panels

In the present paper, the seismic upgrading of existing reinforced concrete (RC) structures by means of steel and pure aluminium shear panels is examined. After a preliminary experimental evaluation of the performance of the bare RC structure, a design approach based on the capacity spectrum method has been developed according to the procedure provided in the ATC 40 American guidelines. First, the geometrical configuration of the applied shear panels has been defined according to simplified analytical relationships, while appropriate steel members have been designed to allow the insertion of shear panels in the existing RC structure. Then, complex finite element models have been implemented in order to check the reliability of the proposed design procedure. Also, a numerical evaluation of the global response of the upgraded structure has been processed aiming at evaluating the interaction between the RC structure and the metal devices. Finally, the effectiveness of the applied shear panels has been proven by means of full‐scale experimental tests, which confirmed the significant improvement of the RC structure performance, in terms of strength, stiffness and deformation capacity. Copyright © 2008 John Wiley & Sons, Ltd.     

Slow Crack Propagation and Slip Correlations

— The propagation of an interfacial crack through a weak plane of a transparent Plexiglas block is studied experimentally. The toughness is controlled artificially by a sand blasting procedure, and fluctuates locally in space like uncorrelated random noise. The block is fractured in mode I at low speed (10^?7?10^?4 m/s). The crack front is observed optically with a microscope and a high resolution digital camera. During the propagation, the front is pinned by micro-regions of high toughness and becomes rough. Roughness of the crack front is analyzed in terms of self-affinity. The in-plane roughness exponent is shown to be 0.63±0.05. Experimental results are compared to a numerical model. The model reproduces the self-affine behavior of the crack front, i.e., long-range correlations of the roughness. Analogies between mode I and mode III are presented in order to discuss implications of the experimental results for creeping faults. Accordingly, correlations of the slip pattern are shown to exist over scales substantially larger than the asperity sizes.