The mechanical behaviour of synthetic sandstone with varying brittle cement content

The purpose of this work was to investigate the influence of cement on the mechanical behaviour of granular rocks. Following the technique described in den Brok et al. [den Brok, S. W. J., David, C. and Bernabé, Y., Preparation of synthetic sandstones with variable cementation for studying the physical properties of granular rocks. C. R. Acad. Sci., 1997, 325, 487–492], two blocks of synthetic sandstones with different cement content were prepared for mechanical testing under hydrostatic and triaxial conditions. The results of the mechanical tests show that the behaviour of the synthetic rocks compares well with that of natural sandstones. Increasing the amount of cement from 3 to 5% in volume had important consequences on the mechanical properties: the critical pressure, strength and elastic moduli were significantly increased and the brittle-to-ductile transition was shifted towards higher pressures. We compared our results to the models of Zhang et al. [Zhang, J., Wong, T. -F. and Davis, D. M., Micromechanics of pressure-induced grain crushing in porous rocks. J. Geophys. Res., 1990, 95, 341–352] and Wong et al. [Wong, T. -F., David, C. and Zhu, W., The transition from brittle faulting to cataclastic flow in porous sandstones: Mechanical deformation. J. Geophys. Res., 1997, 102, 3009–3025]. We conclude that Zhang et al.'s microstructural parameter φD (i.e. the product of porosity φ by grain size D) appeared to be a scaling parameter for both the failure envelopes and the critical pressure as defined in these models. Intuitively, the contact length L is expected to play a crucial role in the mechanical properties of granular materials. Accordingly, we made a statistical analysis of this microstructural parameter in our synthetic materials and in a suite of natural sandstones. A positive correlation with Young's modulus and a negative correlation with porosity were found. This last result gives a physical background for the use of parameter (φD) in theoretical models. We want to emphasize that working on synthetic sandstones allows for a better control of the structural parameters (grain size, sorting, cement content, etc.) which appear to be so important for the mechanical properties of granular rocks.     

Buckling of elastic cylindrical shells considering the effect of localized axisymmetric imperfections

The effect of localized axisymmetric initial imperfections on the critical load of elastic cylindrical shells subjected to axial compression is studied through analytical modeling. Some classical results regarding sensitivity of shell buckling strength with respect to distributed defects having axisymmetric or asymmetric forms are recalled. Special emphasis is placed after that on the more severe case of localized defects satisfying axial symmetry by displaying an analytical solution to the Von Kármán–Donnell shell equations under specific boundary conditions. The obtained results show that the critical load varies very much with the geometrical parameters of the localized defect. These variations are not monotonic in general. They indicate, however, a clear reduction of the shell critical load for some defects recognized as the most hazardous isolated ones. Reduction of the critical load is found to reach a level which is up to two times lower than that predicted by general distributed defects.     

Greenways for recreation and maintenance of landscape quality: five case studies in Portugal

The use of the concept of greenway can be identified in Portugal throughout the 20th century as a planning and design tool. Several examples, such as the ‘Improvement Plans for Lisbon’ by Ressano Garcia (1901), the continuum naturale concept [Cabral, F.C., 1980. O Continuum Naturale e a Conservação da Natureza. Conservação da Natureza. Serviço de Estudos do Ambiente, Lisbon; Andresen, T., 2001. Francisco Caldeira Cabral. Landscape Design Trust, Surrey, UK, 213 pp.], the Green Plan for Lisbon [Telles, G.R., et al., 1997. Plano Verde de Lisboa. Ed. Colibri, Lisboa, 197 pp.], deal with the subjects of implementing vegetation corridors, pedestrian networks and landscape quality. These examples establish Portuguese planning and design tradition within the international greenway movement first identified by Fabos [Fabos, J.Gy., 1991. From Park to Greenways into the 21st Century. In: Proceedings from Selected Educational Sessions, ASLA Annual Meeting, Kansas City, Missouri]. Though several projects have been developed at the planning level, there is a need to analyze the applicability of such a concept at the regional, municipal and local level. We must consider the characteristics of Portugal's cultural landscape, recognition by other professions dealing with planning and involvement by politicians. By analyzing five case studies, this paper shows the significance of the greenway as a planning and design strategy, which coincides, with the current objectives of political and planning authorities at the municipal level. It also proves that it is possible to reconcile political objectives and urban development while safeguarding landscape quality and providing new opportunities for public recreation and education. Greenway planning and design is now undoubtedly a subject of growing significance in Portugal.     

The adsorption of bovine serum albumin by activated sludge

The rapid removal, from suspension, of between 2–% of bovine serum albumin (BSA) by BSA acclimated activated sludge was attributed to adsorption. The extent of adsorption varied with the substrate to biomass (s/b) ratio. The concentration of BSA adsorped was influenced by both the concentration of BSA and the concentration of activated sludge. The experimental data did not conform to the calssical adsorption equations of Langmuir (J. Am. chem. Soc.40, 1361–1403, 918) or Freundlich (Colloid and Capillary Chemistry, Methuen, London, 1926) but to a newly developed equation, the activated sludge adsorption equation (ASAE). This new equation was tested and proven by experimental data and by data obtained independently by Banerji et al. (J. Wat. Pollut. Control Fed.40, 161–173, 1968) who investigated starch removal by activated sludge. Following the development of the ASAE, it was found possible to express both the concentration of BSA adsorbed per unit weight activated sludge (m) and the concentration of BSA in equilibrium per unit weight activated sludge (C/b) as a function of the concentration of BSA added to the system per unit weight adsorbent (C_t). Thus adsorption could be expressed as a function of the substrate to biomass (s/b) ratio.     

Multiple support seismic excitation of the Evripos bridge based on free-field and on-structure recordings

The 395 m long Evripos bridge in central Greece connects the island of Evia to the mainland. An accelerometer array of 43 triaxial sensors has been monitoring both the free-field excitation and the response of the superstructure in a series of seismic events since 1994. This paper focuses on the characteristics of the spatially variable earthquake ground motions (SVEGMs) recorded during two seismic events (1999 and 2013) and the corresponding bridge response. A model updating is performed to match the numerically predicted with the measured bridge response. Then, the nature of the recorded ground motions is studied and the incoherency patterns of the seismic waves are compared with empirical or semi-empirical models. It is observed that the loss of coherency at the site is isotropic. It is also documented, for the first time based on actual free-field and on-structure recordings, that the asynchronous excitation of a bridge excited higher modes of vibration while suppressing the oscillation on its fundamental frequency. The latter is in line with analytical predictions and is believed to be a key finding in understanding the nature of SVEGM and predicting its potential impact on the seismic response of bridges.     

Extracting the bulk effective parameters of a metamaterial via the scattering from a single planar array of particles

In this paper we present a method for retrieving the effective parameters of a metamaterial composed of a regular rectangular orthorhombic lattice of linear biaxially anisotropic particles suspended in free space. By assuming the point–dipole interaction approximation, equations are derived which extract the electric and magnetic polarizabilities of the individual particles given the measured or simulated scattering parameters of a single planar array of particles. These results are in turn substituted into the Clausius–Mossotti equations to find the bulk effective permittivity and effective permeability. To demonstrate our approach, the extraction method is applied to a metamaterial consisting of a cubic arrangement of magnetodielectric spheres using the scattering parameters obtained by simulating the structure with Ansoft HFSS. Our results show good agreement with a known analytical solution at frequencies in which the Clausius–Mossotti approximation is valid.     

Elastic wave velocities and permeability evolution during compaction of Bleurswiller sandstone

Field observations and laboratory experiments have recently documented the formation of compaction bands in porous sandstones [Mollema and Antonellini, Tectonophysics 1996;267:209–28; Olsson and Holcomb, Geophys Res Lett 2000;27:3537–40; Bésuelle, J Geophys Res 2001;106:13435–42; Klein et al., Phys Chem Earth 2001;26:21–5]. It has been observed experimentally [Wong et al., J Geophys Res 2001;28:2521–4; Baud et al., J Geophys Res 2003, submitted; Fortin et al., 2003, Abstract EGS-AGU Nice] that under axisymmetric compression, compaction bands develop sub-perpendicular to the main compressive stress which is predicted theoretically in the framework of strain localization theory [Bésuelle, J Geophys Res 2001;106:13435–42; Issen and Rudnicki, J Geophys Res 2000;105:21529–36]. Volumetric strain, fluid transport and elastic properties are intimately coupled to one another, for they all depend on a few intrinsic parameters such as the porosity, the crack density, and the matrix and fluid elastic properties. On the one hand, Scott et al. [Rock Mech Min Sci Geomech 1993;30:763–9] showed that elastic wave velocities were clearly affected during the deformation of porous sandstones. On the other hand, Zhu and Wong [J Geophys Res 1997;102:3027–41] showed that the relation between the evolution of permeability and volumetric strain during compaction of sandstones was not straightforward. In this study, we present for the first time the simultaneous evolution of volumetric strain, elastic wave velocities and permeability for a set of deformation experiments of Bleurswiller sandstone. We show that, although very coherent to one another, those three sets are not systematically correlated. Indeed, inelastic compaction, whether it is distributed or localized, is accompanied by a drastic decrease of elastic wave velocities due to grain crushing, a decrease of permeability and porosity due to pore collapse. Using simple statistical physics concepts based on the study of Kachanov [Adv Appl Mech 1993;30:259–445] and Guéguen and Dienes [Math Geol 1989;21:1–13], we try to understand and address the issue of coupling/decoupling between volumetric strain (mainly sensitive to equant porosity variations), elastic properties (mainly sensitive to crack density) and permeability (theoretically sensitive to both) during the formation of compaction bands. Finally, we show that the mineral composition of a sandstone is a key parameter controlling the effective pressure at which the onset of pore collapse P^* takes place.     

Flexural–torsional buckling of thin-walled composite box beams

Buckling of an axially loaded thin-walled laminated composite is studied. A general analytical model applicable to the flexural, torsional and flexural–torsional buckling of a thin-walled composite box beam subjected to axial load is developed. This model is based on the classical lamination theory, and accounts for the coupling of flexural and torsional modes for arbitrary laminate stacking sequence configuration, i.e. unsymmetric as well as symmetric, and various boundary conditions. A displacement-based one-dimensional finite element model is developed to predict critical loads and corresponding buckling modes for a thin-walled composite bar. Governing buckling equations are derived from the principle of the stationary value of total potential energy. Numerical results are obtained for axially loaded thin-walled composites addressing the effects of fiber angle, anisotropy and boundary conditions on the critical buckling loads and mode shapes of the composites.     

Finite element reliability analysis of bridge girders considering moment–shear interaction

Reliability analysis is necessary in bridge design to determine which parameters have the most significant influence on the structural response to applied loadings. To support finite element reliability applications, analytical response sensitivities are derived with respect to uncertain material properties, girder dimensions, reinforcing details, and moving loads by the direct differentiation method (DDM). The resulting expressions have been implemented in the general finite element framework OpenSees which is well suited to the moving load analysis of bridges. Numerical examples verify the DDM response sensitivity equations are correct, then a first-order reliability analysis shows the effect uncertain parameters have on the interaction of negative moment and shear force near the supports of a continuous reinforced concrete bridge girder. A unique contribution is the treatment of moment–shear interaction using Lamé curves with foci calculated from MCFT equations. In addition, the analysis demonstrates non-seismic bridge engineering applications that have been developed in the OpenSees framework.     

Influence of load-non-uniformity and eccentricity on the stability and load carrying capacity of orthotropic tubular columns of regular hexagonal cross-section

The paper contains an analysis of the influence of non-uniformity and eccentricity of compressive loads on global and local buckling, on interactive buckling, and on the load-carrying capacity of thin-walled columns. Isotropic and orthotropic tubular columns of regular hexagonal cross-section have been examined. Equilibrium equations for the first and the second order non-linear approximation have been solved using the asymptotic Byskov–Hutchinson method. Numerical calculations have been performed for numerous different loading modes of isotropic columns and also for several loading modes of orthotropic columns. The results are presented in diagrams with some conclusions.     

The compressive post-local bucking behaviour of thin plates using a semi-energy finite strip approach

A geometrically non-linear finite strip for the post-local-buckling analysis of geometrically perfect thin-walled prismatic structures under uniform end shortening is developed in this paper. The formulation of the aforementioned finite strip is based on the concept of the semi-energy approach. In this method, the out-of-plane displacement of the finite strip is the only displacement which is postulated by a deflected form. The postulated deflected form is substituted into von Kármán’s compatibility equation which is solved exactly to obtain the corresponding forms of the mid-plane stresses and displacements. The solution of von Kármán’s compatibility equation and the postulated out-of-plane deflected form are then used to evaluate the potential energy of the related finite strip. Finally, by invoking the principle of minimum potential energy, the equilibrium equations of the finite strip are derived. The developed finite strip is then applied to analyse the post-local-buckling behaviour of thin flat plates. The results are discussed in detail and compared with those available from published works, wherever possible. This has provided confidence in the validity and capability of the developed finite strip in handling the post-local-buckling problem of plate structures.     

Fracture toughness study for a brittle rock subjected to mixed mode I/II loading

A semi-disk specimen containing an angled edge crack has been used in the past for conducting fracture tests on a brittle rock named Johnstone [Fracture testing of a soft rock with semi-circular specimens under three-point bending. Part 2—mixed mode. Int J Rock Mech Min Sci Geomech Abstr 1994b;31(3):199–212]. The test specimen is appropriate for investigating brittle fracture when the rock samples are subjected to the combined effects of tension and shear along the crack line. However, the experimental results reported in Lim, Johnston, Choi, Boland [Fracture testing of a soft rock with semi-circular specimens under three-point bending. Part 2—mixed mode. Int J Rock Mech Min Sci Geomech Abstr 1994b;31(3):199–212.] are inconsistent with all of the well-known theoretical criteria available for predicting mixed mode brittle fracture. In this paper, a modified criterion is used to provide accurate predictions for the reported experimental results. The modified criterion makes use of a three-parameter model (based on K_I, K_II and T) for describing the crack tip stresses. It is shown that the non-singular stress term T has a significant role when the rock fracture tests are conducted on the semi-disk specimens.     

The precision of abundance estimates of plankton from composite samples

Nine parallel composite plankton samples were taken to investigate the precision of abundance estimates from such samples. Equations describing the variance as a function of the number of counted individuals, the number of samples in the composite sample and the parameter c (Cassie R. M., Oceanogr. Mar. Biol.1, 223–252, 1963) were developed. Comparisons with literature data showed the equations to be reasonable approximations.     

半离散法分析薄壁柱的畸变屈曲

采用广义梁理论(GBT)的耦合差分方程解决了半离散法分析薄壁柱的畸变屈曲问题。作者近期发表的两篇文章对类似GBT的新型半离散分析方法进行了阐述。对横截面进行离散分析,寻找沿梁变化的解析解。采用新方法,利用齐次和非齐次方程建立确定梁全部变形的一般GBT方程并求解,从而使GBT的(复杂)变形方程变形为可降阶的微分方程。提出的半离散方法在广义梁理论(GBT)基础上增加了用于柱的失稳分析和失稳形态识别的几何刚度因素。通过势能的变化并在梁理论中引入约束条件,对初始应力下建立的GBT齐次微分方程进行修正,以分析其变形特性。对简支梁梁端施加横向位移和轴力,建立GBT初始应力方程,通过该方程寻求失稳的解决方法。根据已知的边界条件,利用三角函数关系式和求解特征值的方法求解这些可降阶的微分方程,使得屈曲形态和相关特征值与分叉荷载因素相符。因此,无需通过模态分解,可由耦合的GBT方程直接求得屈曲形态的解析解。通过实例分析了柱的整体失稳、屈曲变形和局部纵弯失稳,以及如何将新方法用于描述特征曲线和弹性屈曲曲线。将该方法的分析结果与ABAQUS、GBTUL和CUFSM软件的分析结果进行对比,验证了该方法的正确性。     

Distortional buckling modes of semi-discretized thin-walled columns

This paper presents distorting buckling solutions for semi-discretized thin-walled columns using the coupled differential equations of a generalized beam theory (GBT). In two related papers recently published by the authors a novel semi-discretization approach to GBT has been presented. The cross section is discretized and analytical solutions are sought for the variation along the beam. With this new approach the general GBT equations for identification of a full set of deformation modes corresponding to both homogeneous and non-homogenous equations are formulated and solved. Thereby giving the (complex) deformation modes of GBT which decouple the state space equations corresponding to the reduced order differential equations.In this paper the developed semi-discretization approach to generalized beam theory (GBT) is extended to include the geometrical stiffness terms, which are needed for column buckling analysis and identification of buckling modes. The extension is based on an initial stress approach by addition of the related potential energy terms. The potential energy of a single deformation mode is formulated based on a discretization of the cross section. Through variations in the potential energy and the introduction of the constraints related to beam theory this leads to a modified set of coupled homogeneous differential equations of GBT with initial stress for identification of distortional displacement modes. In this paper we seek instability solutions using these GBT initial stress equations for simply supported columns with constrained transverse displacements at the end sections and a constant axial initial stress. Based on the known boundary conditions the reduced order differential equations are solved by using the trigonometric solution functions and solving the related eigenvalue problem. This gives the buckling mode shapes and the associated eigenvalues corresponding to the bifurcation load factors. Thus the buckling modes are found directly by the analytical solution of the coupled GBT-equations without modal decomposition. Illustrative examples showing global column buckling, distortional buckling and local buckling are given and it is shown how the novel approach may be used to develop signature curves and elastic buckling curves. In order to assess the accuracy of the method some of the results are compared to results found using the commercial FE program Abaqus as well as the conventional GBT and FSM methods using the software packages GBTUL and CUFSM.     

A theoretical solution for analysis of tunnels below groundwater considering the hydraulic–mechanical coupling

An analytical solution for the analysis of tunnels below groundwater table in plane strain axisymmetric condition is presented. Seepage body force and secondary permeability of the rock mass due to the mechanical–hydraulic coupling are taken into account. The strain-softening behavior model and Hoek–Brown empirical strength criterion for the rock mass are used in the analysis. As the derived analytical equations do not have closed form solutions, a computer program has been prepared for solving the corresponding equations numerically and examining the analysis. It is shown that the tunnel stability depends on the seepage and the pore water pressure particularly in the case of high pore pressure gradient.     

Interactive buckling and load carrying capacity of thin-walled beam–columns with intermediate stiffeners

The design of thin-walled beam–columns must take into account the overall instability and the instability of component plates in the form of local buckling. This investigation is concerned with interactive buckling of thin-walled beam–columns with central intermediate stiffeners under axial compression and a constant bending moment. The columns are assumed to be simply supported at their ends. The asymptotic expansion established by Byskov and Hutchinson (AIAA J. 15 (1977) 941) is employed in the numerical calculations performed by means of the transition matrix method and Godunov’s orthogonalisation. Instead of the finite strip method, the exact transition matrix method is used in this case. The most important advantage of this method is that it enables us to describe a complete range of behaviour of thin-walled structures from all global (flexural, flexural-torsional, lateral, distortional and their combinations) to local stability. In the presented method for lower bound estimation of the load carrying capacity of structures, it is postulated that the reduced local critical load should be determined taking into account the global pre-critical bending within the first order non-linear approximation to the theory of the interactive buckling of the structure. The paper’s aim is to expand the study of the equilibrium path in the post-buckling behaviour of imperfect structures with regard to the second order non-linear approximation. In the solution obtained, the transformation of buckling modes with an increase of the load up to the ultimate load, the effect of cross-sectional distortions and the shear lag phenomenon are included. The calculations are carried out for a few beam–columns. The results are compared to those obtained from the design code and to the data reported by other authors.The results discussed in the present study represent the most important results obtained by the authors in earlier investigations devoted to central intermediate stiffeners (Int. J. Solid Struct. 32 (1995) 1501; Eng. Trans. 43 (1995) 383; Int. J. Solid Struct. 37 (2000) 3323; Int. J. Solid Struct. 33 (1996) 315; Thin Wall. Struct. 39 (2001) 649; Arch. Mech. Eng. XLVIII (2001) 29).     

The tolerance averaging model of dynamic stability of thin plates with one-directional periodic structure

A dynamic stability of thin plates with one-directional periodic structure is investigated. An averaged non-asymptotic approach, called the tolerance averaging, is applied to derive governing equations of these plates. Obtained tolerance model equations of the Kirchhoff-type plate take into account the effect of the period lengths on the overall plate behaviour [Jędrysiak J. Dispersive models of thin periodic plates. Theory and applications. Sci. Bul. Łódź Tech. Univ., No. 872, series. Sci Trans 289, Łódź, 2001 [in Polish]]. It is shown that this effect plays a crucial role in some special cases of a dynamic stability of such plates.     

Numerical simulation model of vibration responses of rectangular plates embedded with piezoelectric actuators

A numerical simulation model for random large amplitude vibration control of composite plate using piezoelectric material is presented. The H_∞ control design is employed to suppress the large amplitude vibrations of composites plates under random loading. The numerical simulation model is developed and based on the finite element method. The finite element governing equation includes fully coupled structural and electrical nodal degrees of freedom, and consider the von Karman large amplitude vibration. The modal reduction method using the structural modes is adopted to reduce the finite element equations into a set of modal equations with fewer degrees of freedom. The modal equations are then employed for controller design and time domain simulation. In the simulations without control, the value of the linear mode to the nonlinear deflection is quantified; and the minimum number of linear modes needed for accurate model is obtained. In the simulations with control, it is shown that the truncated modes, which are neglected in the control design, deteriorate the controller performance. Generally, the vibration reduction level is not monotonically increasing with the size of the piezoelectric actuator. The optimal piezoelectric actuator size depends on the excitation level. For higher excitation level, optimal actuator size is larger. The H_∞ controller based on the linear finite element formulation gives better vibration reduction for small amplitude vibration, but it still gives reasonable performance for large amplitude vibration provided that the piezoelectric actuator is big and powerful enough.