Attenuation of vibration in rock by elastic replacement

Felix Kirzhner, Giora Rosenhouse, Yoram Zimmels

Technion, Israel Institute of Technology

Haifa, 32000, Israel

kfelix@techunix.technion.ac.ilљљ GioraRosenhouse@hotmail.com

 

Moving vehicles and trains are known to generate vibrations that have negative effects on people, noise sensitive devices, structures and buildings. In more extreme cases strong vibrations can crack buildings, damage machines and prevent production of precise devices. Hence, the vibration amplitudes should be restricted within the limits specified in standards, such as ANSI and DIN 4150. Vibrations that exceed standards limits call for protection measures in structures such as tunnels that serve vehicles and trains and laboratories that include vibration sensitive instruments. The use of isolation layers based on materials such as advanced polyurethane or rubber can reduce vibration amplitudes by more than 30 dB, but there is another possibility of using natural materials for that purpose. We mean that replacement of rock under the road by softer elastic material or crashed rock can be used for isolation purposes. In absence of lateral of "vibration bridges", the response of the elastic layer follows the concept of a mass-spring system, where the heavy rigid material over the elastic layer stands for the "mass", and the elastic layer represents the "spring". Otherwise, the isolation effect is due to impedance mismatch between the road and the elastic layer. In this work we consider design configurations for isolation against vibrations due to traffic in tunnels and machines over a rigid foundation, using ground replacement by an elastic layer. Foundations for machines can also be treated in the same way.

Foundations design is normally analyzed by applying ground properties in their natural state, where the ground over which the foundation is based may be too hard or non-uniform. In the first case it might transfer strong vibrations, and in the other case it can lead to differential settlements and even structural cracks and lack of stability. A possible way of controlling vibrations radiation caused by machines, vehicles and trains and isolating structural vibrations is also replacement of the original ground by layers of elastic media. The isolation of vibration amplitudes should be kept within the limits specified in standards, at the control points.

The paper investigates design configurations of such isolation and deflection controls by using computational simulations. The simulations are based here on the finite difference method, where the rock/soil model is elasto-plastic, using known data for the elastic layer rock and concrete. The excitation data is based on measured information. The "half space" ground is "cut" by using special vertical and horizontal boundary conditions. Finally, examples of solved practical cases are added to show the efficacy of the isolation by ground replacement by an elastic substitute.

Introduction

Vibrations transmitted through ground can reach vibration sensitive objects. Sources of man-made vibrations include surface and underground transportation by vehicles and trains, heavy industrial machinery and rock removing explosions in quarries. We distinguish between objects of different sensitivity to vibrations and regulations refer roughly to three main groups, namely, people, machines and structures. Of special interest are machines and devices that are extremely sensitive to vibrations.

There are different regulations that put limits on allowed levels of vibrations of humans, structures and machines [1,2,3] when the effect of ground-borne vibrations in buildings are caused by nearby subways or machines over foundations.

The transfer of vibrations through regular rock formations can lead to levels of vibration at the control points that exceed standards limits. Isolation of vibrations by replacement of hard rock by layers of soft soils can be considered one of the possible solutions that reduce lateral and vertical vibration velocities of the objects to be protected. Numerical models facilitate estimation of vibration amplitudes at the control points. The FLAC dynamic model, which is based on finite difference meshes, was chosen for simulation of ground vibrations due to transportation in tunnels, vibrating machines over rigid foundations earthquake waves etc. [4], where the approach to numerical dynamic analysis of soil-structure interaction was described by Cundall [5].

The version of the program FLAC that was applied here is a code based on a two-dimensional explicit finite-difference algorithm for dynamic modeling. This program has two main schemes: (a) Quiet boundaries (non-reflecting) and (b) Free Field boundaries. In the first scheme the modeling of problems of geo-mechanics involves media, which are better represented as unbounded in the range of the analysis. Deep underground excavations are normally assumed as being surrounded by an infinite medium, while ground surface, structures over and near-surface buried structures are assumed to lie within and over a half-space. In the second scheme, the seismic analysis of surface structures (such as dams) requires discretisation of the region of the material adjacent to the foundation. The seismic input is normally represented by plane waves propagating upwards through the underlying material. The boundary conditions along the sides of the domain must allow for a free-field motion, which takes place in absence of the structure. Example of application of FLAC is given in [6]. FLAC uses a dynamic algorithm for solution of two general classes of mechanical problems: quasi-static and dynamic. In this work FLAC is combined with physical argumentation, to show how replacement of rock with softer material helps to achieve isolation against vibration.

Summary and conclusions

The present work has dealt with the effect of isolation against vibrations generated by rigid roads in tunnels and by machines over a foundation laid over ground. The isolation is achieved by replacing a layer of rock under the road or foundation by elastic layer of soft soil. Using simple models, it is shown that the impedance mismatch between the layers is the main reason for decrease of the vibration amplitude. Isolation of the sides of the road by elastic soil prevents lateral leakage of vibrational energy. The lateral isolation is considerably more effective when the elastic replacement has a sufficiently low modulus of elasticity. The combined vertical and lateral isolation can to be modeled as a mass-spring-damper system. This model involves a strong dependence on frequency, which is in contrast to the layer model in the absence of lateral isolation.

A finite-difference model was used to predict particle velocities in layered soil media. The calculations by FLAC show the efficacy of using an elastic replacement layer under the road in tunnels and under machine foundation.

This work shows that from the practical point of view a variety of elastic soils can serve as efficient protective replacements. Numerical analysis can give an indication about the expected improvement for each type of soil. Durable elastic materials that can withstand prolonged loads with little or no change in their elastic properties should be preferred.

 

References

1.          R.V.Whitman. Personal Communications with Prof. R.V. Whitman, MIT, Cambridge, Mass., 1967, USA.

2.          R.L.Eshleman. Vibration Standards. In Shock and Vibration Handbook, C.M. Harris and Crede, C.E., eds., 2^nd ed., McGraw-Hill, NY, 1976, Ch. 19.

3.          H.Backmann, W.Ammann. Vibrations in Structures (Induced by Man \ands Machines). Int. Assoc. for Bridge and Structural Engng, IABSE - AIPC - IVBH, 1987, Zuerich, 69.

4.          Itasca Consulting Group, FLAC - Fast Lagrangian Analysis of Continua. Version 3.4. ITASCA Consulting Group, INC, Minneapolis, 1996, Minnesota.

5.          P.A.Cundal. Explicit finite difference methods in geomechanics. Proc Numerical Methods in Engineering, EF Conference on Numerical Methods in Geomechanics, Blacksburg, Virginia, June Vol. 1, 1976, 132-150.

6.          F.Kirzhner, G.Rosenhouse. Numerical analysis of tunnel dynamic response to earth motions, Tunneling and Underground Space Technology, 15, 3, 2000, 249-258.

7.          L.E.Kinsler, A.R.Frey. Fundamentals of Acoustics, 2^nd ed. John Wiley & Sons, Inc., 1962, 524 p.

8.          F.Kirzhner, G.Rosenhouse, Y.Zimmels. Environmental protection against underground propagation of vibration by elastic barriers, Proc. NARMS-TAC 2002, Mining and Tunneling Innovation and Opportunity Conference, Hammah et al. (eds), University of Toronto, 2002, pp. 727.

9.          J.F.Wiss. Damage Effect of Pile Driving Vibration. Highway Research Report, No.155, 1967.

10.      R.J.Steffens. Some Aspects of Structural Vibration. In Proc. Of Symp. Vibration in Civil Engineering, London, 1966.

11.      G.Rosenhouse, F.Kirzhner, Y.Zimmles. The effect of ground replacement on control of underground vibrations and differential settlements of structures, Computational Methods in Contact Mechanics, WIT Press, C.A. Brebbia (ed.), Southampton, 2003, pp.3-13.