etd@IISc Collection:
http://hdl.handle.net/2005/33
2014-07-18T00:55:52ZBehaviour Of FRP Strengthened Masonry In Compression And Shear
http://hdl.handle.net/2005/2292
Title: Behaviour Of FRP Strengthened Masonry In Compression And Shear
Authors: Pavan, G S
Abstract: Masonry structures constitute a significant portion of building stock worldwide. Seismic performance of unreinforced masonry has been far from satisfactory. Masonry is purported to be a major source of hazard during earthquakes by reconnaissance surveys conducted aftermath of an earthquake. Reasons for the poor performance of masonry structures are more than one namely lack of deformational capacity, poor tensile strength & lack of earthquake resistance features coupled with poor quality control and large variation in strength of materials employed. Fibre Reinforced Plastic (FRP) composites have emerged as an efficient strengthening technique for reinforced concrete structures over the past two decades. Present thesis is focused towards analysing the behaviour of Fibre Reinforced Plastic (FRP) strengthened masonry under axial compression and in-plane shear loading. Determination of in-planes hear resistance of large masonry panels requires tremendous effort in terms of cost, labour and time. Masonry assemblages like prisms and triplets that represent the state of stress present in masonry walls and masonry in-fills when under the action of in-planes hear forces present an alternative option for research and analysis purposes. Hence, present research is focused towards analysing the performance of FRP strengthened masonry assemblages and unreinforced masonry assemblages.
Chapter1 provides a brief review on the behaviour of masonry shear walls and masonry in-fills under the action of in-plane shear forces in addition to the performance of masonry structures during past earthquakes. Review of available literature on FRP confinement of masonry prisms with bed joints inclined from 00 to 900 to the loading axis under axial compression, analytical models available for FRP confined concrete, shear strength of masonry triplets attached with FRP is presented.
Chapter 2 primarily focuses on determining the various properties of the materials involved in this research investigation. Test procedure and results of the tests conducted to determine the mechanical and related properties of the materials involved are presented. Elastic properties and stress-strain response of burnt clay brick, mortar and FRP laminates are presented.
Studies conducted on behaviour of GFRP confined masonry prisms under monotonic axial compression are included in Chapter 3. The study comprised of testing masonry prisms, both unconfined and FRP confined masonry prisms under axial compression. Stretcher bond and English bond prisms, with bed joints normal and parallel to loading axis are included in this study. Two grades of GFRP,360g/m2 and 600 g/m2 are employed to confine masonry prisms. The experimental program involved masonry prism types that accounted for variations in masonry bonding pattern, bed joint inclination to the loading axis and grade of GFRP. Review of the available analytical models predicting compressive strength of FRP confined masonry prism is presented. Available models for FRP confinement of masonry are re-calibrated using the present experimental data generating new coefficients for the already existing model to develop new expression for predicting the compressive strength of FRP confined prisms. In addition to the prism types mentioned earlier, behaviour of unconfined and GFRP confined stretcher bond prisms with bed joints inclined at 300, 450 & 600 to the loading axis are further investigated.
Chapter 4 primarily deals with the shear strength and deformational capacity of masonry triplets that represent joint shear failure in masonry. An experimental program involving masonry triplets attached with different types of FRP(GFRP and CFRP), grade of FRP, percentage area covered by FRP and reinforcement pattern is executed. This exercise determined the influence of these parameters over the enhancement achieved in terms of shear strength and ultimate displacement. Results of tests conducted on stretcher bond prisms presented in chapter 3 and results of tests on shear triplets presented in this chapter are combined to study the interaction between shear and normal stresses acting along the masonry bed joint at different angles of inclination.
The thesis culminated with chapter 5 as concluding remarks highlighting the salient
Information pertaining to the behaviour of FRP strengthened masonry under axial compression and in-plane shear loading obtained as an outcome of the research conducted as a part of this thesis.2014-04-07T18:30:00ZNumerical Methods For Solving The Eigenvalue Problem Involved In The Karhunen-Loeve Decomposition
http://hdl.handle.net/2005/2308
Title: Numerical Methods For Solving The Eigenvalue Problem Involved In The Karhunen-Loeve Decomposition
Authors: Choudhary, Shalu
Abstract: In structural analysis and design it is important to consider the effects of uncertainties in loading and material properties in a rational way. Uncertainty in material properties such as heterogeneity in elastic and mass properties can be modeled as a random field. For computational purpose, it is essential to discretize and represent the random field. For a field with known second order statistics, such a representation can be achieved by Karhunen-Lo`eve (KL) expansion. Accordingly, the random field is represented in a truncated series expansion using a few eigenvalues and associated eigenfunctions of the covariance function, and corresponding random coefficients.
The eigenvalues and eigenfunctions of the covariance kernel are obtained by solving a second order Fredholm integral equation. A closed-form solution for the integral equation, especially for arbitrary domains, may not always be available. Therefore an approximate solution is sought. While finding an approximate solution, it is important to consider both accuracy of the solution and the cost of computing the solution. This work is focused on exploring a few numerical methods for estimating the solution of this integral equation. Three different methods:(i)using finite element bases(Method1),(ii) mid-point approximation(Method2), and(iii)by the Nystr¨om method(Method3), are implemented and numerically studied. The methods and results are compared in terms of accuracy, computational cost, and difficulty of implementation. In the first method an eigenfunction is first represented in a linear combination of a set of finite element bases. The resulting error in the integral equation is then minimized in the Galerkinsense, which results in a generalized matrix eigenvalue problem. In the second method, the domain is partitioned into a finite number of subdomains. The covariance function is discretized by approximating its value over each subdomain locally, and thereby the integral equation is transformed to a matrix eigenvalue problem. In the third method the Fredholm integral equation is approximated by a quadrature rule, which also results in a matrix eigenvalue problem. The methods and results are compared in terms of accuracy, computational cost, and difficulty of implementation.
The first part of the numerical study involves comparing these three methods. This numerical study is first done in one dimensional domain. Then for study in two dimensions a simple rectangular domain(referred toasDomain1)is taken with an uncertain material property modeled as a Gaussian random field. For the chosen covariance model and domain, the analytical solutions are known, which allows verifying the accuracy of the numerical solutions. There by these three numerical methods are studied and are compared for a chosen target accuracy and different correlation lengths of the random field. It was observed that Method 2 and Method 3 are much faster than the Method 1. On the other hand, for Method 2 and 3, additional cost for discretizing the domain into nodes should be considered whereas for a mechanics-related problem, Method 1 can use the available finite element mesh used for solving the mechanics problem.
The second part of the work focuses on studying on the effect of the geometry of the model on realizations of the random field. The objective of the study is to see the possibility of generating the random field for a complicated domain from the KL expansion for a simpler domain. For this purpose, two KL decompositions are obtained: one on the Domain1, and another on the same rectangular domain modified with a rectangular hole (referredtoasDomain2) inside it. The random process is generated and realizations are compared. It was observed from the studies that probability density functions at the nodes on both the domains, that is, on Domain 1 and Domain 2, are similar. This observation leads to a possibility that a complicated domain can be replaced by a corresponding simpler domain, thereby reducing the computational cost.2014-05-04T18:30:00ZStudies On Characterization Of Self Compacting Concrete : Microstructure, Fracture And Fatigue
http://hdl.handle.net/2005/2237
Title: Studies On Characterization Of Self Compacting Concrete : Microstructure, Fracture And Fatigue
Authors: Hemalatha, T
Abstract: Evolution of concrete is continuously taking place to meet the ever-growing demands of the construction industry. Self compacting concrete (SCC) has emerged as a result of this demand to overcome the scarcity of labour. SCC is widely replacing normal vibrated concrete (NVC) these days owing to its advantages such as homogeneity of the mix, filling ability even in heavily congested reinforcement, smooth finish, reduction in construction time etc.
The ingredients used for SCC is the same as that of the NVC. But the proportioning of ingredients to achieve self compactability alters the microstructure of SCC which in turn affects the mechanical and fracture properties. Moreover, the mineral admixtures such as fly ash and silica fume when used for improving the workability of SCC help in the development of the microstructural skeleton. In this study, three SCC mixes SCC1- made with only cement, SCC2 - with fly ash in addition to cement and SCC3 - with fly ash and silica fume in addition to cement for achieving normal, medium and high strength SCC respectively are cast. The microstructural changes in SCC with and without mineral admixtures over a period of time are studied using different techniques such as scanning electron microscopy (SEM), energy dispersive spectrometer (EDS) and X-ray diffraction (XRD).
The modification of mechanical properties at microstructural level brings difference in the behavior at macro level. Hence in this study, the mechanical properties at microstructural are obtained by using microindentation test and are scaled up to the macro level to predict the influence of micromechanical properties on macro response. The fracture properties of SCC is considered to be the interest of this study and is carried out with the help of advanced techniques such as acoustic emission (AE) and digital image correlation (DIC).
From the various studies carried out, it is inferred that the mixes with mineral admixtures behave in a more brittle manner when compared to mix having no mineral admixture. It is also observed that class ‘F’ fly ash hydrates at a slow pace and the strength gain is observed after 28 days and even beyond 90 days. Hence, it is concluded that it is appropriate to consider the strength at 90 days instead of 28 days for a SCC mix with class ‘F’ fly ash. Silica fume on the other hand is observed to result in a more rapid gain in strength and this can partially offset the delay in strength gain due to fly ash.2013-09-10T18:30:00ZA 3D Lattice Model For Fracture Of Concrete : A Multiscale Approach
http://hdl.handle.net/2005/2236
Title: A 3D Lattice Model For Fracture Of Concrete : A Multiscale Approach
Authors: Mungule, Mahesh Parshuram
Abstract: It is quite well known that fracture behavior of concrete is complex and is influenced by several factors. Apart from material properties, geometric parameters influence fracture behavior and one notable phenomenon is size effect. The existence of the size effect in concrete is well known and various attempts to model the behavior is
well documented in literature. However the approach by Bazant to describe the size
effect behavior in concrete has received considerable attention. The major advantage
of developing the size effect law for concrete is the ability to describe the fracture behavior (namely failure strength) of large size structures inaccessible to laboratory testing. The prediction of size effect is done on the basis of laboratory testing of small size geometrically similar structures. In all the models developed earlier heterogeneity of concrete has not been quantitatively simulated. Hence, the complete description considering heterogeneity in concrete is attempted using the lattice model to understand size effect behavior in concrete.
In the present study, a detailed description of the heterogeneity in concrete is at-
tempted by 3D lattice structure. Analytical treatment to gain insights to fracture
behavior is difficult and hence a numerical approach capable of handling the het-
erogeneous nature of the material is adopted. A parametric study is performed to
understand the influence of various model parameters like mesh size, failure criterion,
softening model. The conventional size effect studies for 2D geometrically similar
structures are performed and a comparison is done with experimentally observed
behavior. The variation of fracture process zone with respect to structure size is
observed as the reason for size effect. The influence of variation in properties of ag-
gregate, matrix and interface are studied to explain the deviation in pre-peak and
post-peak response. A statistical study is performed to establish the size dependence
of linear regression parameters (Bf ‘t and D0) which are used in Bazant size effect law.
An analytical framework is also proposed to substantiate the above results. Size effect
in concrete is generally attributed to the effect of depth viz. the dimension in the
plane of loads. However although the effect of thickness viz. a dimension in a plane
perpendicular to that of the loads is not considered in concrete. The same is quite
well known in fracture of metals. Therefore the variation in grading of aggregates
along with the influence of thickness on fracture behavior is analysed. To understand
the thickness effect a comparison of 2D and 3D geometrically similar structures is
performed to understand the effect of thickness on fracture parameters.
Heterogeneity is a matter of scale. A material may be homogeneous at a coarser scale while at a finer scale it is heterogeneous. Hence only way to capture the effect of the behavior at micro level on the behavior at meso level particularly in a heterogeneous material like concrete is by a multi-scale modelling. The best numerical tool for multiscale model of a heterogeneous material is lattice model. The heterogeneous
nature of concrete is not just due to the presence of aggregates but is evident right
from the granular characteristics of cement. The hydration of cement grain leads to
the development of products with varying mechanical and chemical properties. As
the micro-crack initiation and development of thermal cracking is observed at the
micron level, understanding of hydration behavior in concrete can be thought of as
a pre-requisite for complete understanding of fracture behavior. The properties of
matrix and interface observed during hydration modelling can also be used as an
input for fracture predictions at upper scale models (eg. mesoscale). This can also be used to study the coupling of scales to understand the multi-scale fracture behavior in concrete. A numerical model is hence developed to study the hydration of concrete.
Due to the existence of complex mechanisms governing the hydration behavior in con-
crete and the large number of parameters affecting its rate, the hydration of a grain
is assumed to proceed in isolation. A single particle hydration model is developed to
study the hydration of isolated grain. A shrinking core model usually used to describe
the burning of coal is adopted as a base model for analytically describing the hydra-
tion behavior. The shrinkage core model in literature is modified to be applicable to
hydration of cement matrix. The effect of particle diameter as well as changing water
concentration is incorporated into the model whereas the influence of reduction in
pore sizes as well as the effect due to embedding of particles and the constraint due
to hydration of neighbouring particles is accounted using correction factor. The effect
of temperature on rate of hydration is considered to be independent of the physical
and chemical aspects of grain. Hence a temperature function developed using Arrhe-
nius equation and activation energy is incorporated separately. The porous nature of
reaction products affects the diffusivity leading to the development of tortuous path
for flow of water through the hydrated portion. Knowing the tortuosity it is possible to obtain the diffusivity which in turn can be used as an input to the lattice model.
An algorithm is developed to determine the tortuosity in diffusion of water through
the reaction products. The tortuosity depends on the distribution of pores in the
hydrated system. This requires the use of simulation technique to generate the initial
position of voids. A simulation technique is also required to generate the initial con-
figuration of hydrating cement system. In order to generate the initial configurations
of such systems a numerical technique to generate a large scale assembly of particles
is proposed.
In the present work, parameters of Bazant's size effect law Bf’t and D0 are shown
to depend on structure size and heterogeneity. The span to thickness ratio of the structure increases fracture energy and also substantially influences the response of structure. The variation in failure load occurring due to the heterogeneous nature of the material is shown to follow a normal distribution. The fracture behavior of a material is seen to be influenced strongly by the variation in the strength of matrix and interface. The model proposed to describe the hydration process of cement can be used to determine the properties of matrix and interface. The degree of hydration as well as the embedded centre plane area can be adopted as a measure of strength of matrix and interface. The understanding of the hydration process and the wall effect around the aggregate surface can possibly improve our ability to predict the strength of interface. The material strength of the interface is certainly a necessary input to the lattice model. Infact experimental determination of interface strength is a lot more complicated than the present numerical approach. The only weakness of the present numerical approach is the assumption regarding certain empirical constants which of course may be improved further. Understanding of material behavior can be further improved if a molecular dynamics approach is adopted to describe the hydration behavior of cement. The approach via molecular dynamics is suggested as a problem for future research.2013-09-09T18:30:00Z