Nonlinear Response of Infinite Beams on a Multilayer Tensionless Extensible Geo-Synthetic: Reinforced Earth Beds under Moving Load
In this paper, analysis of an infinite beam resting on
multilayer tensionless extensible geosynthetic reinforced granular
fill-poor soil system overlying soft soil strata under moving load with
constant velocity is presented. The beam is subjected to a
concentrated load moving with constant velocity. The upper
reinforced granular bed is modeled by a rough membrane embedded
in Pasternak shear layer overlying a series of compressible nonlinear
winkler springs representing the underlying the very poor soil. The
multilayer tensionless extensible geosynthetic layer has been
assumed to deform such that at interface the geosynthetic and the soil
have some deformation. Nonlinear behaviour of granular fill and the
very poor soil has been considered in the analysis by means of
hyperbolic constitutive relationships. Governing differential
equations of the soil foundation system have been obtained and
solved with the help of appropriate boundary conditions. The solution
has been obtained by employing finite difference method by means of
Gauss-Siedal iterative scheme. Detailed parametric study has been
conducted to study the influence of various parameters on the
response of soil–foundation system under consideration by means of
deflection and bending moment in the beam and tension mobilized in
the geosynthetic layer. These parameters include magnitude of
applied load, velocity of load, damping, ultimate resistance of poor
soil and granular fill layer. Range of values of parameters has been
considered as per Indian Railway conditions. This study clearly
observed that the comparisons of multilayer tensionless extensible
geosynthetic reinforcement with poor foundation soil and magnitude
of applied load, relative compressibility of granular fill and ultimate
resistance of poor soil has significant influence on the response of
soil–foundation system.
[1] Alekseyeva.L.A. (2006), “The Dynamic of an Elastic Half Space Under
the Action of a Moving Load”, Journal of Applied Mathematics and
Mechanics, vol 71, pp. 511-518.
[2] Basu, D. (2001), “Soil Structure Interaction Analysis due to Moving
Load”. M.Tech. Thesis, Department of Civil Engineering, Indian
Institute of Technology, Kanpur, India.
[3] Chandan Ghosh and Madhav M. R. (1994), “Settlement Response of a
Reinforced Shallow Earth Bed”, Geotext. Geomembranes, Vol. 13,
pp.643– 656.
[4] Choros, J. and Adams, G. G. (1979). “A Steadily Moving Load on an
Elastic Beam Resting on a Tensionless Winkler Foundation”. Journal of
Applied Mechanics Division, ASME, Vol. 46, No. 1, pp. 175-180.
[5] Duffy, D.G. (1990), “The Response of an Infinite Railroad Track to a
Moving, Vibrating Mass”, Journal of Applied Mechanics Division,
ASME, Vol. 57, No. 1, pp. 66-73.
[6] Jaiswal, O.R. and Iyenger, R.N. (1997), “Dynamic Response of Railway
Tracks to Oscillatory Moving Masses”, Journal of Engineering
Mechanics Division, ASCE, Vol. 123 No. 7, pp. 753-757.
[7] Karuppasamy, K (2010), “Non-Linear Response of Infinite Beams on
Reinforced Earth Beds under Moving Load”. M.Tech. Thesis,
Department of Civil Engineering, Indian Institute of Technology,
Roorkee, India.
[8] Kerr A.D (1964), “Elastic and Visco-Elastic Foundation Models”,
Journal of Applied Mechanics Division, Trans. of ASME 1964; 31 (3):
491-498.
[9] Kondner, R.L. and J.S. Zelasko. (1963), “A Hyperbolic Stress-Strain
Response: Cohesive Soil”, Journal of the Soil Mechanics and
Foundations Division, ASCE, 89(SM1):115-143
[10] Lin, L., and Adams, G.G., (1987), “Beam on Tensionless Elastic
Foundation Subjected to Moving Load”, Vol. 113, No. 4.
[11] Sun Lu (2001). “Dynamic Displacement Response of Beam Type
Structures to Moving Line Loads”. International Journal of solids and
structures, vol 38, pp 8869 - 8878.
[12] Maheshwari, P., Basudhar, P. K., and Chandra, S. (2004b) “Response of
Beams on a Tensionless Extensible Geosynthetic-Reinforced Earth Bed
Subjected to Moving Loads”. Computer and Geotechnics, Vol. 31, pp.
537 – 548.
[13] Rao N.S.V. Kameswara (1974), “Onset of Separation between a Beam
and Tensionless Foundation due to Moving Loads”, Journal of Applied
Mechanics Division, Trans. of ASME 41 (1): 303-305.
[14] Saito, H. and Teresawa, T. (1980), “Steady-State Vibrations of a Beam
on a Pasternak Foundation for Moving Loads”, Journal of Applied
Mechanics Division, Trans. of ASME, Vol. 47, pp. 879-883.
[15] Selvadurai APS (1979), “Elastic Analysis of Soil–Foundation
Interaction”. Elsevier Scientific Publication Company, Amsterdam, The
Netherlands, 543 pp. [16] Wang. M.C., Badie. A. and Davids. N. (1984), “Traveling Waves in
Beam on Elastic Foundation”, Journal of Engineering Mechanics
Division, ASCE, Vol. 110, No. 6, pp. 879-893.
[17] Yin J. H. “Modeling of Geosynthetic-Reinforced Granular Fill over Soft
Soil”. Geosynthetic International 1997; 4(2): 165-85.
[18] Yin JH. “A Nonlinear Model of Geosynthetic-Reinforced Granular Fill
over Soft Soil”, Geosynthetic International 1997; 4(5): 523-37.
[19] Yin JH, “Closed Form Solution for Reinforced Timoshenko Beam on
Elastic Foundation”, J Appl Mech Div Trans, Am Soc. MechEng 2000;
12(8): 868-74.
[20] Islam, M. R., Rahman, M. T. and Tarefder, R. A. (2012). “Laboratory
Investigation of the Stiffness and the Fatigue Life of Glass Grid
Reinforced Asphalt Concrete.” International Journal of Pavements, Vol.
11, No. 1, pp. 82-91.
[1] Alekseyeva.L.A. (2006), “The Dynamic of an Elastic Half Space Under
the Action of a Moving Load”, Journal of Applied Mathematics and
Mechanics, vol 71, pp. 511-518.
[2] Basu, D. (2001), “Soil Structure Interaction Analysis due to Moving
Load”. M.Tech. Thesis, Department of Civil Engineering, Indian
Institute of Technology, Kanpur, India.
[3] Chandan Ghosh and Madhav M. R. (1994), “Settlement Response of a
Reinforced Shallow Earth Bed”, Geotext. Geomembranes, Vol. 13,
pp.643– 656.
[4] Choros, J. and Adams, G. G. (1979). “A Steadily Moving Load on an
Elastic Beam Resting on a Tensionless Winkler Foundation”. Journal of
Applied Mechanics Division, ASME, Vol. 46, No. 1, pp. 175-180.
[5] Duffy, D.G. (1990), “The Response of an Infinite Railroad Track to a
Moving, Vibrating Mass”, Journal of Applied Mechanics Division,
ASME, Vol. 57, No. 1, pp. 66-73.
[6] Jaiswal, O.R. and Iyenger, R.N. (1997), “Dynamic Response of Railway
Tracks to Oscillatory Moving Masses”, Journal of Engineering
Mechanics Division, ASCE, Vol. 123 No. 7, pp. 753-757.
[7] Karuppasamy, K (2010), “Non-Linear Response of Infinite Beams on
Reinforced Earth Beds under Moving Load”. M.Tech. Thesis,
Department of Civil Engineering, Indian Institute of Technology,
Roorkee, India.
[8] Kerr A.D (1964), “Elastic and Visco-Elastic Foundation Models”,
Journal of Applied Mechanics Division, Trans. of ASME 1964; 31 (3):
491-498.
[9] Kondner, R.L. and J.S. Zelasko. (1963), “A Hyperbolic Stress-Strain
Response: Cohesive Soil”, Journal of the Soil Mechanics and
Foundations Division, ASCE, 89(SM1):115-143
[10] Lin, L., and Adams, G.G., (1987), “Beam on Tensionless Elastic
Foundation Subjected to Moving Load”, Vol. 113, No. 4.
[11] Sun Lu (2001). “Dynamic Displacement Response of Beam Type
Structures to Moving Line Loads”. International Journal of solids and
structures, vol 38, pp 8869 - 8878.
[12] Maheshwari, P., Basudhar, P. K., and Chandra, S. (2004b) “Response of
Beams on a Tensionless Extensible Geosynthetic-Reinforced Earth Bed
Subjected to Moving Loads”. Computer and Geotechnics, Vol. 31, pp.
537 – 548.
[13] Rao N.S.V. Kameswara (1974), “Onset of Separation between a Beam
and Tensionless Foundation due to Moving Loads”, Journal of Applied
Mechanics Division, Trans. of ASME 41 (1): 303-305.
[14] Saito, H. and Teresawa, T. (1980), “Steady-State Vibrations of a Beam
on a Pasternak Foundation for Moving Loads”, Journal of Applied
Mechanics Division, Trans. of ASME, Vol. 47, pp. 879-883.
[15] Selvadurai APS (1979), “Elastic Analysis of Soil–Foundation
Interaction”. Elsevier Scientific Publication Company, Amsterdam, The
Netherlands, 543 pp. [16] Wang. M.C., Badie. A. and Davids. N. (1984), “Traveling Waves in
Beam on Elastic Foundation”, Journal of Engineering Mechanics
Division, ASCE, Vol. 110, No. 6, pp. 879-893.
[17] Yin J. H. “Modeling of Geosynthetic-Reinforced Granular Fill over Soft
Soil”. Geosynthetic International 1997; 4(2): 165-85.
[18] Yin JH. “A Nonlinear Model of Geosynthetic-Reinforced Granular Fill
over Soft Soil”, Geosynthetic International 1997; 4(5): 523-37.
[19] Yin JH, “Closed Form Solution for Reinforced Timoshenko Beam on
Elastic Foundation”, J Appl Mech Div Trans, Am Soc. MechEng 2000;
12(8): 868-74.
[20] Islam, M. R., Rahman, M. T. and Tarefder, R. A. (2012). “Laboratory
Investigation of the Stiffness and the Fatigue Life of Glass Grid
Reinforced Asphalt Concrete.” International Journal of Pavements, Vol.
11, No. 1, pp. 82-91.
@article{"International Journal of Earth, Energy and Environmental Sciences:70674", author = "K. Karuppasamy", title = "Nonlinear Response of Infinite Beams on a Multilayer Tensionless Extensible Geo-Synthetic: Reinforced Earth Beds under Moving Load", abstract = "In this paper, analysis of an infinite beam resting on
multilayer tensionless extensible geosynthetic reinforced granular
fill-poor soil system overlying soft soil strata under moving load with
constant velocity is presented. The beam is subjected to a
concentrated load moving with constant velocity. The upper
reinforced granular bed is modeled by a rough membrane embedded
in Pasternak shear layer overlying a series of compressible nonlinear
winkler springs representing the underlying the very poor soil. The
multilayer tensionless extensible geosynthetic layer has been
assumed to deform such that at interface the geosynthetic and the soil
have some deformation. Nonlinear behaviour of granular fill and the
very poor soil has been considered in the analysis by means of
hyperbolic constitutive relationships. Governing differential
equations of the soil foundation system have been obtained and
solved with the help of appropriate boundary conditions. The solution
has been obtained by employing finite difference method by means of
Gauss-Siedal iterative scheme. Detailed parametric study has been
conducted to study the influence of various parameters on the
response of soil–foundation system under consideration by means of
deflection and bending moment in the beam and tension mobilized in
the geosynthetic layer. These parameters include magnitude of
applied load, velocity of load, damping, ultimate resistance of poor
soil and granular fill layer. Range of values of parameters has been
considered as per Indian Railway conditions. This study clearly
observed that the comparisons of multilayer tensionless extensible
geosynthetic reinforcement with poor foundation soil and magnitude
of applied load, relative compressibility of granular fill and ultimate
resistance of poor soil has significant influence on the response of
soil–foundation system.", keywords = "Infinite beams, multilayer tensionless extensible
geosynthetic, granular layer, moving load, nonlinear behavior of poor
soil.", volume = "9", number = "9", pages = "1037-13", }