Document Type : Article

**Authors**

Golestan University, Faculty of Engineering, Gorgan, Iran

**Abstract**

Temperature difference in the soil and its environments is a common phenomenon. The permeability of the soil changes with the temperature mostly because of the variation of the viscosity of water in different temperatures. More realistic estimation of the seepage value through and beneath hydraulic structures leads to more efficient design of them. In this paper, the heat conduction equation is solved by a least squares based meshfree method to calculate the distribution of the temperature in a soil. The distribution of the permeability coefficients can be varied irregularly that may make some difficulties in the mesh-based methods. In these methods the permeability changes in each mesh and finer mesh or some kinds of interpolation are required in the solution procedure. Since there is no need to form elements or grids in a meshfree method, it can handle this irregular variation simply. Here, the seepage equation is solved by the same least squares based meshfree method. The method is integral free, simple and efficient in calculation thanks to its sparse and positive definite matrices. The scheme is validated by solving a simplified version of the governing equations. More complicated problems are dealt with to investigate the phenomenon numerically.

**Keywords**

**Main Subjects**

1. Farouki, T.O., Thermal Properties of Soils, United

States Army Corps of Engineers (1981).

2. Putkonen, J. Soil thermal properties and heat transfer

processes near Ny-Alesund, northwestern Spitsbergen,

Svalbard", Polar Research, 17(20), pp. 165-179 (1998).

3. Nicholson, P.G., Soil Improvement and Ground Modi

cation Methods, Butterworth Heinemann, Elsevier

Inc., USA (2015).

4. Zihms, S.G., Switzer, C., Karstunen, M., and

Tarantino, A. Understanding the eects of high temperature

processes on the engineering properties of

soils", Proceedings of the 18th International Conference

on Soil Mechanics and Geotechnical Engineering,

Paris, France, pp. 3427-3430 (2013).

5. Cho, W.J., Lee, J.O., and Chun, K.S. The temperature

eects on hydraulic conductivity of compacted

bentonite", Applied Clay Science, 14, pp. 47-58 (1999).

6. Towhata, I., Kuntiwattanakul, P., Seko, I., and Ohishi,

K. Volume change of clays induced by heating as observed

in consolidation tests", Soils and Foundations,

33(4), pp. 170-183 (1993).

7. Villar, M.V. and Lioret, A. In

uence of temperature

on the hydro-mechanical behaviour of a compacted

bentonite", Applied Clay Science, 26(1/4), pp. 337-350

(2004).

8. Romero, E., Gens, A., and Lioret, A. Temperature

eects on the hydraulic behaviour of an unsaturated

clay", Geotechnical and Geological Engineering, 19,

pp. 311-332 (2001).

A. Tabarsa and M. Lashkarbolok/Scientia Iranica, Transactions A: Civil Engineering 25 (2018) 1907{1915 1915

9. Ye, W.M., Wan, M., Chen, B., Chen, Y.G., Cui,

Y.J., and Wanf, J. Temperature eects on the

unsaturated permeability of the densely compacted

GMZ01 bentonite under conned conditions", Journal

of Engineering Geology, 126, pp. 1-7 (2012).

10. Stetyukha, V.A. Numerical simulation of changes

in the thermal condition of soils under the eect of

channel change of a river bed", Power Technology and

Engineering, 38(1), pp. 27-29 (2004).

11. Yu, W.B., Liu, W.B., Lai, Y.M., Chen, L., and Yi,

X. Nonlinear analysis of coupled temperature seepage

problem of warm oil pipe in permafrost regions of

Northeast China", Applied Thermal Engineering, 70,

pp. 988-995 (2014).

12. Youse, S., Noorzad, A., Ghaemian, M., and

Kharaghani, S. Seepage investigation of embankment

dams using numerical modelling of temperature eld",

Indian Journal of Science and Technology, 6(8), pp.

5078-5082 (2013).

13. Cui, W., Gawecka, K.A., Potts, D.M., Taborda,

D.M.G., and Zdravkovic, L. Numerical analysis of

coupled thermo hydraulic problems in geotechnical

engineering", Geomechanics for Energy and the Environment,

6, pp. 22-34 (2016).

14. Fukuchi, T. Numerical analyses of steady-state seepage

problems using the interpolation nite dierence

method", Soils and Foundations, 56(4), pp. 608-626

(2016).

15. Belytschko, T. Meshless methods: an overview and

recent developments", Computer Methods in Applied

Mechanics and Engineering, 139(1-4), pp. 3-47 (1996).

16. Liu, G.R., Mesh Free Methods: Moving Beyond the

Finite Element Method, 1st, Ed. CRC Press, Boca

Raton, USA (2002).

17. Liu, G.R. and Gu, Y.T., An Introduction to Meshless

Methods and Their Programming, 1st, Ed. Springer

Press, Berlin, Germany (2005).

18. Ding, H., Shu, C., Yeo, K.S., and Xu, D. Development

of least-square-based two-dimensional nite-dierence

schemes and their application to simulate natural

convection in a cavity", Computer and Fluids, 33, pp.

137-157 (2004).

19. Afshar, M.H. and Lashckarbolok, M. Collocated discrete

least-squares (CDLS) meshless method: Error

estimate and adaptive renement", International Journal

for Numerical Methods in Fluids, 56(10), pp. 1909-

1928 (2008).

20. Afshar, M.H. and Shobeyri, G. Ecient simulation of

free surface

ows with discrete least-squares meshless

method using a priori error estimator", International

Journal of Computational Fluid Dynamics, 24(9), pp.

349-367 (2010).

21. Firoozjaee, A.R. and Afshar, M.H. Steady-state solution

of incompressible Navier-Stokes equations using

discrete least-squares meshless method", International

Journal for Numerical Methods in Fluids, 67(3), pp.

369-382 (2010).

22. Lashkarbolok, M., Jabbari, E., and Westerweel, J.

A least squares based meshfree technique for the

numerical solution of the

ow of viscoelastic

uids: A

node enrichment strategy", Engineering Analysis with

Boundary Elements, 50, pp. 59-68 (2015).

23. Lashckarbolok, M. and Jabbari, E. Collocated discrete

least squares (CDLS) meshless method for the

simulation of power-law

uid

ows", Scientia Iranica,

20(2), pp. 322-328 (2013).

24. Lashckarbolok, M., Jabbari, E., and Vuik, K. A

node enrichment strategy in collocated discrete least

squares meshless method for the solution of generalized

Newtonian

uid

ow", Scientia Iranica (A), 21(1), pp.

1-10 (2014).

25. Butcher, J.C., Numerical Methods for Ordinary Dierential

Equations, John Wiley, 2nd Edition (2008).

Volume 25, Issue 4 - Serial Number 4

Transactions on Civil Engineering (A)

July and August 2018Pages 1907-1915