NON-LINEAR TRANSIENT DYNAMIC SOIL-STRUCTURE INTERACTION WITH SPECIAL REFERENCE TO BLAST LOADING

Abstract

1.0 INTRODUCTION The area of soil-structure interaction has been a subject of wide research all over the world during the past about three decades. The interaction between the soil mass and the structure is influenced significantly, amongst the various parameters, by two major factors, viz., the nature of the applied load and the constitutive laws governing the behaviour of the structural material and the soil mass. Soil is a material which is essentially non-linear in nature. The review of literature suggests that most of the research work published on dynamic soil-structure interaction is limited to earthquake loading. However, the dynamic loads also include, apart from the earthquake loading, other forces such as impulsive, blast and impact. The literature related to dynamic soilstructure interaction involving these forces is extremely scanty. In the present study, some aspects of dynamic soil-structure interaction have been investigated under blast, impact and harmonic types of loads. The interaction effects due to these loads can be significant especially when the non-linearity of the ground is taken into account. 2.0 REVIEW OF EARLIER WORK 2.1 Blast Loads The blast loads have, in the past, become important service loads for certain categories of structures. However, very little work related to blast effects has been actually reported due to the fact that the categories of blast and impact loads are more important in strategic/defence applications and therefore the literature by and large remains classified. Special publications of USAARDEC, TM:5-1300-1969 and ARLCD-SP:84001-1986 provide the details of blast loads as applicable to various types of structures. Indian Standard code of practice, IS:4991-1968 also provides simplified guidelines for blast loading. Some of the recent studies include those by Singhal and Larson (1991) who have simulated the weapon blast pressures on flexible surfaces and presented an algorithm for prediction of these. Beshara (1994a, 1994b) has presented models for blast loading on above ground structures without considering soil-structure interaction effects for external blast, internal blast and ground shock and has discussed the provisions of various codes of practice on blast loads. Dharaneepathy et al. (1995) have studied the critical ground-zero distance for cylindrical towers for blast resistant design and recommended a value of 6 m/kg1'3 on the basis of their study. 2.2 Simulation of Boundaries In all the numerical studies involving dynamic effects for semi-infinite media, it becomes essential to impose artificial boundaries to enable the modelling. These artificial boundaries have to be essentially of transmitting type otherwise they may alter the response of the structureground system. Various models for boundary simulation have been presented. Simplest among them are the elementary boundaries at which either zero displacements are specified or zero surface tractions are enforced . Ghosh and Wilson (1969) have suggested that if the boundary is located at a distance of three to four times the radius of foundation in horizontal direction and two to three times in vertical direction, satisfactory results can be obtained. Lysmer and Kuhlemeyer (1969) have suggested the use of a single dashpot corresponding to each degree of freedom at nodes lying at the boundary, known as local boundary. In an another model, known as consistent boundary, spring-dashpot pairs are used at the boundary nodes. All the nodes lying at the boundary are fully coupled. Both spring and the dashpot have frequency dependent properties. To compute the properties of spring-dashpot system, discretised boundary-integral-equation procedure is used (Wolf, 1988). Boundary integral-equation technique is used primarily for frequency domain analysis. However, it has been used by Monalis and Beskose (1981,1983) to obtain the solution first in Laplace transform in domain using boundary integral-equation technique and then to obtain the solution in time domain using an inverse transformation. Some special techniques have also been proposed to simulate the non-reflecting boundaries which can be employed both for time domain as well as for frequency domain analysis. Cundal et al. (1974) have suggested a superposition boundary in which the boundary is split into two parts and then the system is solved twice, once with free boundary and then with fixed boundary. Averaging of the solutions is carried out after every three to four time steps. In another approach suggested by Liao and Wong (1984) for 1-D analysis, the boundary conditions at any time station are extrapolated from the values of displacements obtained at the previous time station. 3.0 PROBLEM IDENTIFICATION AND OBJECTIVES OF THE STUDY A critical review of literature suggests that: i) Most of the literature reported on dynamic soil-structure interaction has been found to be for earthquake loading only whereas for blast loading, the literature available is very meagre. ii) Most of the dynamic soil-structure interaction studies have been carried out in frequency domain in which only linear elastic behaviour of soil mass could be accounted for. However, it is well known that non-linearity of soil mass plays a significant role in deciding the behaviour of a structure-foundation system. Modelling of non-linear soil behaviour is possible only when dynamic analysis is carried out in time domain. Hi) Soil is essentially a semi-infinite media and has to be curtailed at a suitable distance from the structure for any finite element analysis. The effect of this curtailment has to be mitigated by using proper boundary simulation techniques. These techniques have been well established in frequency domain analysis. However, these are still being developed for time domain analysis. IV In view of the above facts, an attempt has been made in the present study to investigate dynamic soil-structure interaction phenomenon for blast, impact and harmonic loads in case of some structures of practical engineering importance using non-linear transient time domain analysis. As an integral part ofthe problem, the simulation of non-reflecting boundaries has been treated as a major issue. In view of the problem identified, the objectives of the work include - i) To establish proper guide lines for location of the elementary boundaries for proper boundary simulation, ii) To develop a transient transmitting boundary so as to simulate a non-reflecting boundary for use in any interaction analysis, iii) To develop a software code for non-linear transient dynamic analysis and iv) To study the behaviour of some structures of practical engineering importance like underground bunkers, pile foundations, industrial framed structures etc. 4.0 PRESENT STUDY 4.1 Boundary Simulation 4.1.1 Elementary boundaries In the present study, an attempt has been made to find the location of the soil boundary from the foundation such that the wave reflected from this boundary will have a negligible amplitude. To find this proper location, a parametric study for a circular foundation under impulse loading has been carried out by varying, i) the distance of the boundary from the foundation and ii) material damping of the soil mass. The results have been presented in the form of a guideline charit. To present the results in a generalised way, distance of the boundary has been non-dimensionalised with respect to the maximum wave length contained in the response spectrum. The chart can be used to find the location of the boundary for a specified level of maximum permissible error in the response. It has been observed that the percentage error approaches exponentially to zero with increase in radial distance of the boundary and damping ratio of the soil mass. 4.1.2 Transient transmitting boundary Extrapolation algorithm provides a promising solution to the boundary simulation problems. However, it has so far been established only for 1-D applications. An attempt has been made here to extend it for use in 2-D transient dynamic analysis problems. As the boundary conditions in this case change at every time step according to the extrapolated values, it has been termed as a transient transmitting boundary. The complete formulation has been presented for the proposed boundary. A detailed parametric analysis has been carried out to study the behaviour of the proposed boundary vis-a vis the elementary boundaries. It has been found that this boundary behaves not only in a much more reliable way in comparison to the elementary boundaries but the distance to this boundary from the structure, required to be modelled by conventional finite elements, also is drastically reduced for the same level of accuracy, resulting in significant computational saving. 4.2 Software Development A computer program for 2-D non-linear transient dynamic analysis in time domain using finite element method has been developed. The salient features of the program are being presented below. • Both linear elastic and elasto-plastic analyses with tension cut-off facility can be carried out in time domain using either explicit, implicit or explicit-implicit time marching scheme for any of the plane stress, plane strain or axi-symmetric conditions. Newmark's predictorcorrector scheme has been used for integration of equations of dynamic equilibrium. Elasto-plastic bar elements have been used to model the R.C.C. structures. VI • The program has the provision of considering blast loads due to either free air burst, air burst or surface burst. Blast loading recommended by Indian Standard Code of Practice, IS:4991-1968 and Special Publication of US Army, ARLCD-SP:84001-1986 have been considered. Program uses a unified approach for the application of blast loads on the structure instead of using the conventional surface to surface identification approach. • The complete formulation of transient transmitting boundary has been incorporated in the software and therefore non-reflecting boundaries can be represented in a more reliable way. A modified profile solver has been developed which can take into account non-zero prescribed displacements at the transient transmitting boundary. • The provision has been made in the program to carry out a linear or non-linear static analysis before the actual dynamic analysis starts so as to account for the initial stresses due to the static loads. • To support the main program, a pre-processor for mesh/data generation and graphical checking of the input data and a post processor for the graphical representation of the output data have also been developed. 4.3 Case Studies Using the non-linear transient analysis formulation and the software developed, a number of problems of practical engineering importance have been analysed. Abrief description of these is being presented below. 4.3.1 Analysis of buried arched bunker Aproblem of elasto-plastic analysis of a Buried Arched Shaped Bunker for blast loading has been chosen for analysis from published literature ( Stevens et al., 1983). The published results include the strain histories in reinforcing bars and velocities at various points in the arch. However, various material properties involved in the analysis were not reported. Therefore, Vll about 15 sets of material properties have been tried. It has been found that the peak strains in reinforcing bars occur at about the same time instant. However, the peak amplitude matches well in case of one particular data set only, which, of course, is logical also. 4.3.2 Analysis of single pile for impulse load A pile subjected to impulsive load (during pile driving) has been simulated numerically. Both elastic and elasto-plastic analyses have been carried out for three types of soil media viz., i) homogeneous medium dense sand, ii) homogeneous loose sand and iii) a layered media having top layer of loose sand underlain by a layer of medium dense sand. These cases have been analysed for the values of damping ratio, z = 5%, 10% and critical damping. The pile behaviour has been compared for all these cases. The pile behaviour has also been studied with respect to spread of yield zone and stresses in soil-pile system. Phor to canying out the above study, a similar problem from the published literature (Liao and Roesset, 1997) was solved and the results have been found to compare very well. 4.3.3 Analysis of block resonance test Block resonance test is one of the important tests during soil investigation for the sites where heavy machinery is to be installed. In the present study, an attempt has been made to simulate numerically the complete block resonance test. An elastic as well as elasto-plastic transient dynamic analysis has therefore been carried out for different operating frequencies and the block response has been compared with the actual field data presented by Prakash et al. (1973). A detailed parametric study has been carried out to investigate the influence of layered soil media and a buried intrusion of heavy material at a depth. It has been found that these parameters have considerable influence on the behaviour of the block. The study also demonstrates the potential of the software of simulating a block resonance test numerically for non-homogeneous soils. VIM 4.3.4 Analysis of RCC framed structure Framed structures may be subjected to blast loading mostly due to accidental explosions e.g. computer control building in case of oil refineries. The dynamic analysis of the structure may therefore be necessary to assess the level of vibrations. Here, a framed structure subjected to blast loading has been analysed for elastic and elasto-plastic conditions. 5.0 CONCLUSIONS i) A general purpose software code has been developed alongwith a pre-processor and a post-processor for non-linear transient dynamic analysis of structural systems subjected to blast loading. ii) An integrated approach has been presented to deal with different blast loads. iii) A guideline chart has been presented on the basis of parametric study to decide the location of the elementary boundary. iv) The work presents for the first time, formulation of a transient boundary for representation of 2-D semi-infinite media. This boundary has been found to work much better than the elementary boundaries. v) The non-linearity of the soil mass, especially the elasto-plastic behaviour, has been found to influence significantly the behaviour of the structure under blast and impact loading. vi) Analysis reveals that the block resonance test data, which is essential for the design of machine foundations, can be generated by carrying out the numerical experiments for both homogeneous and non-homogeneous soils. IX