Abstract
Blasts and explosions occur in many activities that are either man-made or nature induced. The effect of the blasts could have a residual or devastating effect on the buildings at some distance within the vicinity of the explosion. In this investigation, an analytical solution for the time response of a rigid foundation subjected to a distant blast is considered. The medium is considered to be an elastic half-space. A formal solution to the wave propagations on the medium is obtained by the integral transform method. To achieve numerical results for this case, an effective numerical technique has been developed for calculation of the integrals represented in the inversion of the transformed relations. Time functions for the vertical and radial displacements of the surface of the elastic half-space due to a distant blast load are determined. Mathematical procedures for determination of the dynamic response of the surface of an elastic half-space subjected to the blast along with numerical results for displacements of a rigid foundation are provided.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Abbreviations
- F 0 :
-
Amplitude of the applied blast force
- ω :
-
Angular frequency of the applied force
- G :
-
Shear modulus of the medium
- r :
-
Radial distance from the blast
- u 1 + iu 2 :
-
Complex nondimensional radial displacement function
- v 1 + iv 2 :
-
Complex nondimensional vertical displacement function
- u :
-
Radial displacement at any point on the surface
- v :
-
Vertical displacement at any point on the surface
- ∇2 :
-
Laplace operator for Cartesian coordinates
- u(t):
-
Displacement of the massless foundation along x-axis
- v(t):
-
Displacement of the massless foundation along y-axis
- w(t):
-
Displacement of the massless foundation along z-axis
- t :
-
Time
- θ :
-
Angle of radial blast w.r.t. x-axis
- E :
-
Young’s modulus
- Ï… :
-
Poisson ratio
- ε :
-
Linear strain direction
- φ x :
-
Elastic rotation of the massless foundation about x-axis
- φ y :
-
Elastic rotation of the massless foundation about y-axis
- φ z :
-
Elastic rotation of the massless foundation about z-axis
References
Aggarwal HR, Ablow CM (1967) Solution to a class of three-dimensional pulse propagation problems in an elastic half-space. Int J Eng Sci 5:663–679
Apsel RJ (1979) Dynamic Green's functions for layered media and applications to boundary value problems. Ph.D. Dissertation, University of California, San Diego, USA
Banerjee PK, Mamoon SM (1990) A fundamental solution due to a periodic point force in the interior of an elastic half-space. Int J Earthquake Eng Struct Dyn 19:91–105
Barkan DD (1962) Dynamics of bases and foundations. McGraw-Hill, New York
Chao CC (1960) Dynamical response of an elastic half-space to tangential surface loadings. J Appl Mech ASME 27:559–567
Davies TG, Banerjee PK (1983) Elastodynamic Green's function for half-space. Report GT/1983/1, Department of Civil Engineering, State University of New York at Buffalo, USA
Elorduy J, Nieto JA, Szekely EM (1967) Dynamic response of bases of arbitrary shape subjected to periodic vertical loading. Proceeding international symposium on wave propagation and dynamic properties of earth materials, Albuquerque, University of New Mexico, 105–123
Hamidzadeh HR (1978) Dynamics of rigid foundations on the surface of an elastic half-space. Ph.D. Dissertation, University of London, England
Hamidzadeh HR (1986) Surface vibration of an elastic half-space. Proc SECTAM XIII 2:637–642
Holzlohner U (1980) Vibrations of the elastic half-space due to vertical surface loads. Int J Earthq Eng Struct Dyn 8:405–441
Housner GW, Castellani A (1969) Discussion of "Comparison of footing vibration tests with theory. By F.E. Richart, Jr. and R.V. Whitman, J. SMFD, ASCE, 95:360–364
Jones R (1958) In-situ measurement of the dynamic properties of soil by vibration method. Geotechnique 8(1):1–21
Ke L, Wang Y, Zhang Z (2005) Propagation of love waves in an inhomogeneous fluid saturated porous layered half-space with properties varying exponentially. J Eng Mech 131:1322–3128
Kobori T, Suzuki T (1970) Foundation vibrations on a viscoelastic multilayered medium. Proceeding third Japan earthquake engineering symposium Tokyo, 493–499
Lawrence FV Jr (1965) Ultrasonic shear wave velocities in sand and clay. Rep. R65-05., WES, Department of Civil Engineering Massachusetts Institute of Technology Cambridge, Mass
Nautiyal CM (1972) Seismic wave propagation in a layer over a half space. Massachusetts Institute of Technology
Pekeris CL (1955a) The seismic buried pulse. Proc Natl Acad Sci U S A 41:629–639
Pekeris CL (1955b) The seismic surface pulse. Proc Natl Acad Sci U S A 41:469–480
Peplow AT, Jones CJC, Petyt M (1999) Surface vibration propagation over a layered elastic half-space with an inclusion. Appl Acoust 56(4):283–296
Singh D, Tomar SK (2006) Wave propagation in micropolar mixture of porous media. Int J Eng Sci 44:1304–1323
Ojetola D, Hamidzadeh H (2012) Dynamic response of a rigid foundation subjected to a distance blast. Proceedings of 2012 ASME international mechanical engineering congress exposition (IMECE), Houston, TX, IMECE2012-86282, pp 83–88
Choudhury D, Subba Rao KS (2005) Seismic bearing capacity of shallow strip foundations. Geotech Geol Eng 23(4):403–441
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer Science+Business Media New York
About this chapter
Cite this chapter
Hamidzadeh, H.R., Dai, L., Jazar, R.N. (2014). Dynamic Response of a Rigid Foundation Subjected to a Distance Blast. In: Wave Propagation in Solid and Porous Half-Space Media. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-9269-6_7
Download citation
DOI: https://doi.org/10.1007/978-1-4614-9269-6_7
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-9268-9
Online ISBN: 978-1-4614-9269-6
eBook Packages: EngineeringEngineering (R0)