Numerical simulation of the failure process of unreinforced masonry walls due to concentrated static and dynamic loading

Finite element analyses of brick masonry subjected to in-plane concentrated static and dynamic loads are carried out to study crack initiation and propagation during the failure process of unreinforced masonry walls. The numerical model is firstly validated by the experimental tests by using the same materials parameters and loading conditions. Then, the static and dynamic concentrated loads are applied to the mortar joints and brick, respectively, and numerical simulations are used to compare the fracture characteristics for these loads. In addition, a comparison of fracture mechanisms for the concentrated loads on the mortar joint and brick is also given. Finally, the effect of dynamic pressure (P_max) on the failure mechanism of brick masonry is considered.     

Damage,plasticity and failure of ceramics and cementitious composites subjected to multi-axial state of stress

Experimental data on mechanical behavior of ceramics and cementitious composites subjected to triaxial state of stress and verification of the theoretical model capable to describe deformability and fracture of brittle rock-like materials are presented in the paper. To check the validity of the theoretical model the stress–strain curves and stresses at material fracture determined experimentally for brick and mortar were compared with the theoretical predictions. The limit surface at material fracture obtained experimentally from triaxial tests was used in numerical analysis of masonry specimens subjected to compressive loading. These numerical results obtained by employing the Finite Element Method software package Mafem3D were compared with experimental data available in the literature. Fairly good agreement of numerical predictions with experimental results for masonry specimens was observed.     

Nonlinear parameter identification of models for masonry

This paper investigates the parameter estimation problem for brick masonry models. An identification procedure is proposed in which the uncertainties of known parameters and/or errors of measurements are its elements of distinction. The minimization process of the discrepancies between experimental data and theoretical measurements takes place by means of a first order iterative method. The identification procedure is applied to two different problems: the calibration of an interface model for brick–mortar joint in its functional form through monotonic experimental tests; to evaluate the unknown parameters of a continuum model for brick masonry walls in its non-holonomic form by means of in-plane cyclic shear–compression test of masonry panels. The general framework of the non-linear estimate methodology, the parameter identification problems and the numerical results are presented.     

Experimental investigations of the joint-mortar behaviour

An important failure mode of the masonry walls is the shearing process in joint mortar. In order to understand better this phenomenon, an experimental study is carried out on half brick couplet specimen. Load/Unload shear tests are performed to assess the type of the shear behaviour of the joint mortar. The cohesion and the internal friction angle are then derived from linear regression while assuming Mohr–Coulomb criterion. In particular, the influence of holes on the joint behaviour is studied by comparing results obtained with both solid and hollow bricks. In both cases, the experimental results show that there is not any stiffness degradation even in the softening regime. Actually, the shear modulus remains constant. Hence, the joint behaviour is considered to be elastoplastic, independently on the brick type. However, it seems that the presence of holes increases the stiffness but does not affect the internal friction angle of the joint mortar.     

Micromechanical models to guide the development of synthetic ‘brick and mortar’ composites

This paper describes a micromechanical analysis of the uniaxial response of composites comprising elastic platelets (bricks) bonded together with thin elastic perfectly plastic layers (mortar). The model yields closed-form results for the spatial variation of displacements in the bricks as a function of constituent properties, which can be used to calculate the effective properties of the composite, including elastic modulus, strength and work-to-failure. Regime maps are presented which indicate critical stresses for failure of the bricks and mortar as a function of constituent properties and brick architecture. The solution illustrates trade-offs between elastic modulus, strength and dissipated work that are a result of transitions between various failure mechanisms associated with brick rupture and rupture of the interfaces. Detailed scaling relationships are presented with the goal of providing material developers with a straightforward means to identify synthesis targets that balance competing mechanical behaviors and optimize material response. Ashby maps are presented to compare potential brick and mortar composites with existing materials, and identify future directions for material development.     

Constitutive relations for a growing masonry with setting mortar

A model is proposed for averaging a periodic block structure, namely, a growing brick masonry body with setting interlayers of bonding mortar. The brick (block) material is assumed to be elastic, and the setting mortar is described by the model of an inhomogeneously aging viscoelastic medium. The obtained system of constitutive relations describes an anisotropic inhomogeneously aging viscoelastic medium and contains a small parameter that is the ratio of the hardening interlayer thickness to the brick thickness. Also presented is an example of solving the problem of erecting a brickwork (wall) deviating from the vertical in the gravity field.     

Closed-form expressions for the macroscopic flexural rigidity coefficients of periodic brickwork

Approximate expressions for the macroscopic out-of-plane elastic coefficients of brick masonry with a regular pattern are derived in closed form using a homogenization approach for periodic media. Following an approach similar to the Method of Cells for fiber reinforced composites, a (piecewise-)differentiable expression depending on very a limited number of degrees of freedom and fulfilling suitable periodicity conditions is proposed for the microscopic transverse displacement field over any Representative Volume Element (RVE). Some of the equilibrium conditions at the interfaces between bricks and mortar joints are also fulfilled. By averaging the moment and curvature fields over the RVE, the macroscopic bending stiffness coefficients can be explicitly obtained. Using the FE solution of a masonry panel subjected to elementary load conditions as a benchmark, the proposed approach is found to accurately match the numerically obtained stiffness coefficients, for masonry elements of different geometry and different mechanical properties. In several instances, the proposed expressions agree with the numerical predictions better than other analytical expressions available in the literature.     

Derivation of a model of imperfect interface with finite strains and damage by asymptotic techniques: an application to masonry structures

The proposed study aims to derive an imperfect interface model which couples finite strain and damaging. The governing equations are obtained via an asymptotic approach within the finite strain theory. Theoretical findings have been numerically validated within an original application to brick/mortar interfaces in masonry walls in shear loading conditions.     

多孔砖砌体抗剪强度原位检测的试验研究

多孔砖砌体因具有节约土地能源资源,砌筑效率高,保温隔热和透气性能好等特点,目前已逐步成为砌体结构房屋的主要墙体材料。本文通过多孔砖砌体与标准试件抗剪强度的对比试验研究及试验结果的有限元分析,提出了多孔砖砌体抗剪强度原位双砖双剪的检测方法及其抗剪强度的计算公式。该方法可为多孔砖砌体结构房屋的可靠性评定、房屋建设、事故分析以及抗震加固等提供最基本的技术数据,为多孔砖砌体的应用与推广奠定了基础,并为砌体现场检测技术标准的补充修订提供了依据。     

A one dimensional analysis of convective drying of porous materials

A one-dimensional finite element analysis has been carried out to study temperature and moisture variation of porous materials during convective drying. The predicted results for brick and mortar with constant transport properties agree with available experimental data. Henderson’s modified equation has been used to obtain the desorption data for the materials.     

Kinematic FE limit analysis homogenization model for masonry walls reinforced with continuous FRP grids

A homogenization model for periodic masonry structures reinforced with continuous FRP grids is presented. Starting from the observation that a continuous grid preserves the periodicity of the internal masonry layer, rigid-plastic homogenization is applied directly on a multi-layer heterogeneous representative element of volume (REV) constituted by bricks, finite thickness mortar joints and external FRP grids. In particular, reinforced masonry homogenized failure surfaces are obtained by means of a compatible identification procedure, where each brick is supposed interacting with its six neighbors by means of finite thickness mortar joints and the FRP grid is applied on the external surfaces of the REV. In the framework of the kinematic theorem of limit analysis, a simple constrained minimization problem is obtained on the unit cell, suitable to estimate – with a very limited computational effort – reinforced masonry homogenized failure surfaces.A FE strategy is adopted at a cell level, modeling joints and bricks with six-noded wedge shaped elements and the FRP grid through rigid infinitely resistant truss elements connected node by node with bricks and mortar. A possible jump of velocities is assumed at the interfaces between contiguous wedge and truss elements, where plastic dissipation occurs. For mortar and bricks interfaces, a frictional behavior with possible limited tensile and compressive strength is assumed, whereas for FRP bars some formulas available in the literature are adopted to reproduce the delamination of the truss from the support.Two meaningful structural examples are considered to show the capabilities of the procedure proposed, namely a reinforced masonry deep beam (0°/90° continuous reinforcement) and a masonry beam in simple flexion for which experimental data are available. Good agreement is found between present model and alternative numerical approaches.     

基于分离式建模的砖石古塔动力性能与响应分析

为研究砖石古塔的动力特性及地震响应机制,以渭南慧照寺塔为对象,采用块体-灰浆分区离散方法,分别建立刚性地基条件与考虑地基-结构相互作用条件下古塔的数值模型,计算比较了塔体的动力特性;并分别按9度小震、中震和大震输入El-Centro波、Taft波和兰州人工波,计算了结构的位移和加速度反应,与相互作用系统进行比较。结果表明,考虑土-结构相互作用后,古塔结构的一阶自振频率降低5.7%,二阶频率降低45%;El-Centro波和Taft波作用下,位移和加速度响应显著增大,大震作用时,与不考虑土-结构相互作用对比,主拉应力峰值显著增加,古塔从灰浆开裂发展为砖与灰浆同时开裂;兰州人工波作用下,考虑土-结构相互作用后,主拉应力和结构开裂变形反而降低。研究结果可为古塔抗震计算与性能评估提供参考。     

A nonlinear homogenization procedure for periodic masonry

The present paper deals with the problem of the determination of the in-plane behavior of masonry material. The masonry is considered as a composite material composed by a regular distribution of blocks connected by horizontal and vertical mortar joints. The overall constitutive relationships of the regular masonry are derived by a rational micromechanical and homogenization procedure. Linear elastic constitutive relationship is considered for the blocks, while a new special nonlinear constitutive law is proposed for the mortar joints. In particular, a mortar constitutive law, which accounts for the coupling of the damage and friction phenomena occurring during the loading history, is proposed; the developed model is based on an original micromechanical analysis of the damage process of the mortar joint. Then, an effective nonlinear homogenization procedure, representing the main novelty of the paper, is proposed; it is based on the transformation field analysis, using the technique of the superposition of the effects and the finite element method. The presented methodology is implemented in a numerical code. Finally, numerical applications are performed in order to assess the performances of the proposed procedure in reproducing the mechanical behavior of masonry material.     

爆炸载荷下仿贝壳结构的动态响应

贝壳珍珠层是一种具有高强度和高韧性的天然材料,这种优异的性能主要来源于多尺度、多层级的“砖泥”结构。本文受贝壳特殊结构的启发,构建了仿贝壳砖泥结构的有限元模型,并进行了爆炸实验。通过实验发现:在爆炸冲量为0.047 N·s时,试件发生灾难性破坏,使得中心处发生掉落,且伴随着试件夹持端的剪切破坏,与数值模拟结果具有良好的一致性。在实验基础上,对仿贝壳砖泥结构在爆炸载荷下的动态响应进行了数值模拟。研究发现,在爆炸载荷下仿贝壳砖泥结构会产生五种不同的破坏模式,包括:Ⅰ,结构整体无损伤;Ⅱ,结构前表面无明显破坏,后表面发生破坏;Ⅲ,结构发生掉落型贯穿破坏,夹持端无剪切破坏;Ⅳ,结构发生小块掉落型贯穿破坏,夹持端发生剪切破坏;Ⅴ,结构发生大块掉落型贯穿破坏,夹持端发生剪切破坏。并且给出了不同破坏模式的临界阈值,单层砖泥结构的破坏阈值为0.019 N·s,五层砖泥结构的破坏阈值为0.047 N·s,当冲量超过破坏阈值时,试件发生灾难性破坏。研究分析了堆叠层数对仿生结构的力学响应,在同一冲量下,随着层数的增加,结构的破坏模式发生改变,由贯穿型破坏逐渐变为仅发生一定塑性变形。随着层数增加,结构的损伤阈值增加。最后提出仿贝壳砖泥结构的增韧机理主要有裂纹偏转和微裂纹。     

Non-linear micropolar and classical continua for anisotropic discontinuous materials

Non-linear Cosserat and Cauchy anisotropic continua equivalent to masonry-like materials, like brick/block masonry, jointed rocks, granular materials or matrix/particle composites, are presented.An integral procedure of equivalence in terms of mechanical power has been adopted to identify the effective elastic moduli of the two continuous models starting from a Lagrangian system of interacting rigid elements. Non-linear constitutive functions for the interactions in the Lagrangian system are defined in order to take into account both the low capability to carry tension and the friction at the interfaces between elements. The non-linear problem is solved through a finite element procedure based on the iterative adjustment of the continuum constitutive tensor due to the occurrence of some limit situation involving the contact actions of the discrete model.Differences between the classical and the micropolar model are investigated with the aid of numerical analyses carried out on masonry walls made of blocks of different size. The capability of the micropolar continuum to discern, unlike the classical continuum, the behaviour of systems made of elements of different size is pointed out. It is also shown that for anisotropic materials, even in the elastic case, the micropolar solution in general does not tend to the classical solution when the size of the elements vanishes.     

Compatible model for herringbone bond masonry: Linear elastic homogenization,failure surfaces and structural implementation

A simplified kinematic procedure at a cell level is proposed to obtain in-plane elastic moduli and macroscopic masonry strength domains in the case of herringbone masonry. The model is constituted by two central bricks interacting with their neighbors by means of either elastic or rigid-plastic interfaces with friction, representing mortar joints. The herringbone pattern is geometrically described and the internal law of composition of the periodic cell is defined.A sub-class of possible elementary deformations is a-priori chosen to describe joints cracking under in-plane loads. Suitable internal macroscopic actions are applied on the Representative Element of Volume (REV) and the power expended within the 3D bricks assemblage is equated to that expended in the macroscopic 2D Cauchy continuum. The elastic and limit analysis problem at a cell level are solved by means of a quadratic and linear programming approach, respectively.To assess elastic results, a standard FEM homogenization is also performed and a sensitivity analysis regarding two different orientations of the pattern, the thickness of the mortar joints and the ratio between block and mortar Young moduli is conducted. In this way, the reliability of the numerical model is critically evaluated under service loads.When dealing with the limit analysis approach, several computations are performed investigating the role played by (1) the direction of the load with respect to herringbone bond orientation, (2) masonry texture and (3) mechanical properties adopted for joints.At a structural level, a FE homogenized limit analysis is performed on a masonry dome built in herringbone bond. In order to assess limit analysis results, additional non-linear FE analyses are performed, including a full 3D numerical expensive heterogeneous approach and models where masonry is substituted with an equivalent macroscopic material with orthotropic behavior and possible softening. Reliable predictions of collapse loads and failure mechanisms are obtained, meaning that the approach proposed may be used by practitioners for a fast evaluation of the effectiveness of herringbone bond orientation.     

Residual fracture energy of cement paste, mortar and concrete subject to high temperature

Quantifying high temperature damage is an issue that can hardly be dealt with experimentally because of the complexity of the loading control, of temperature and of moisture. The experimental investigation was carried out. The measurement of the mechanical characteristics (fracture energy, tensile strength, elastic modulus and thermal damage parameter) of five cementitious materials, cement paste, mortar, ordinary concrete and two HPC concretes were performed by three-point bending tests after heating/cooling cycles at 120, 250 and 400 °C. The tests showed that the cementitious materials behave almost identical when the fracture energy G_f is considered as a function of maximum temperature. The thermal damage due to heating from 120 to 400 °C increases the fracture energy by 50% with the reference tests at room temperature. A more tortuous crack surface is one reasonable explanation for the significant increase in G_f. It is demonstrated that the temperature exposure makes all cementitious materials tested significantly more ductile and less resistant.