ORIGINAL Numerical modelling of effective thermal conductivity for modified geomaterial using lattice element method Zarghaam Haider Rizvi 1 & Dinesh Shrestha 1 & Amir S. Sattari 1 & Frank Wuttke 1 Received: 28 February 2017 /Accepted: 21 August 2017 /Published online: 6 September 2017 # Springer-Verlag GmbH Germany 2017 Abstract Macroscopic parameters such as effective thermal conductivity (ETC) is an important parameter which is affect- ed by micro and meso level behaviour of particulate materials, and has been extensively examined in the past decades. In this paper, a new lattice based numerical model is developed to predict the ETC of sand and modified high thermal backfill material for energy transportation used for underground power cables. 2D and 3D simulations are performed to analyse and detect differences resulting from model simplification. The thermal conductivity of the granular mixture is determined numerically considering the volume and the shape of the each constituting portion. The new numerical method is validated with transient needle measurements and the existing theoreti- cal and semi empirical models for thermal conductivity pre- diction sand and the modified backfill material for dry condi- tion. The numerical prediction and the measured values are in agreement to a large extent. Keywords Lattice element method . Effective thermal conductivity . Soil thermal conductivity . Needle probe method . Numerical modeling 1 Introduction Soil thermal conductivity corresponds to ability of the soil mass in dissipating the heat generated. Soil thermal conduc- tivity has an important role in the design of high-voltage buried power cables, oil and gas pipelines, nuclear waste dis- posal facilities, ground-modification techniques employing heating and freezing, shallow geo-energy storage systems and ground source heat pumps [1]. One of the critical factors in the design of energy systems is the knowledge of ETC in dry condition which acts as the critical limit. Heat transport process in granular media is largely affected by the quantity and quality of the thermal conduction paths. Enhancement of contact quality and quantity are achieved by fillers, cementing agents and modification of gradation [2]. ETC of granular assembly is measured or predicted by 1) Theoretical & semi-empirical models 2) Experimental mea- surement and 3) Numerical models. ETC at macro scale is modeled with theoretical models using fitting parameters which are related to physical parameters such as density, po- rosity and degree of saturation. A critical review of the various expressions used for predicting the ETC values for a soil indicates their dependency on various empirical coeffi- cients, which cannot be estimated precisely, leading to uncertain results. These theoretical & semi-empirical models are derived for specific materials and particular geometries. These equations also fail to consider for example the anisotropy of media, particle shapes, and distribution in the sample. These equa- tions are conditioned with the help of controlling parameters, to match the experimental values. Mathematical modeling is an effort to estimate ETC of soils once these physical properties are known. For dry soils, equations have been presented by Smith [3], Mickley [4], and de Vries [5] using different models. Only few empirical models have been developed to esti- mate dry thermal conductivity for different types of soil ac- cording to soil fabric, gradation, mineral thermal conductivity and porosity or dry density. Johansen [7] proposed two em- pirical models for natural soils and crushed rocks considering * Zarghaam Haider Rizvi zarghaam13@gmail.com 1 Department of Geomechanics & Geotechnics, University of Kiel, 24118 Kiel, Germany Heat Mass Transfer (2018) 54:483–499 DOI 10.1007/s00231-017-2140-2