Laboratory and field experiment on measurement of soil thermal conductivity by probe method

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1 Global Geology doi /j. issn Article ID Laboratory and field experiment on measurement of soil thermal conductivity by probe method ZHANG Tong ZHANG Yanjun LIU Tong XIE Yangyang and ZHANG Chi College of Construction Engineering Jilin University Changchun China Abstract The authors presented a new measuring method of the soil thermal conductivity the probe method which is designed and made based on the theory of line heat source. This method is used to measure thermal conductivity of coarse sand fine sand and silty clay in different water contents. The results that measured by the probe method are well consistent with those of QTM-D 2. The soil thermal conductivity increases in different levels with the increase of the water content. Compared the soil thermal conductivity measured by the probe method in laboratory with in-situ experiment it shows that the measuring gap gradually increases with the increase of the depth. The reason is that the in-situ measuring thermal conductivity can reflect the actual situation of the soil mass. Key words probe method thermal conductivity water content in-situ measurement 1 Introduction On behalf of the heat conduction ability of soil thermal conductivity is one of the most important parameters of soil thermal properties Yin et al The measurement of the soil thermal conductivity has great significance on developing and utilizing of shallow geothermal energy Fang et al Generally the measuring methods mainly include laboratory experiment and in-situ measurement. Ground source heat pump GSHP is most commonly used to measure thermal conductivity which can collect underground temperature data Yu et al Although the soil thermal conductivity calculated by GSHP has high accuracy the expense of this method is increasingly limiting its use. Laboratory method consists of steady state and the unsteady state Xu et al The former mainly consists of the heat-flow meter method tube-form method and steady flat measuring method etc. The method has high accuracy but the test time is relatively long. The latter mainly includes hot-strip method which needs short test time and achieves high accuracy. It is the most commonly used method to measure the soil thermal conductivity at present. A new measuring method of the soil thermal conductivity is presented namely the probe method which is designed and made based on the theory of line heat source. This method can not only measure soil thermal conductivity in situ but also measure thermal conductivity in laboratory. The probe method is firstly used to measure the thermal conductivities of coarse sand fine sand and silty clay in different water content. Then the results are compared to those of QTM-D 2 Zhang et al and the influential regularity of water content on the soil thermal conductivities is analyzed. Final- Received 8 April 2015 accepted 15 May 2015 Supported by Project of National Natural Science Foundation of China No

2 222 Zhang T. Zhang Y. J. Liu T. et al. ly the differences between the thermal conductivity measured by the probe method in laboratory and field are analyzed. 2 Test principle of the probe method The heat source model is based on unsteady heat conduction in unbounded media Hou Assuming that the underground soil mass is an unbounded heat-conducting media relative to the probe the initial temperature of layer is stable and thermal parameters are not changing as fluctuating temperature for soil the probe can be regarded as a line heat source. The heat conduction is a one-dimensional axisymmetric problem around the probe. The distribution function of surplus temperature field can be described as follows [ ] θ = t - t 0 = - q 4πλ E i - r2 4ατ 1 Where θ is the surplus temperature τ is heating time q is heating power λ is the soil thermal conductivity a is thermal diffusivity r is the distance between a point and line heat source t is the temperature at time τ t 0 is the initial temperature E i is exponent-integral function when r is small enough and τ is big enough E i can be calculated from E i - μ = C + ln μ 2 Where μ = r 2 /4a C is Euler's constant which value is Substitute equation 2 into equation 1 [ ( ) ] θ = t - t 0 = - q 4πλ - C - ln r 2 4aτ 3 Calculated by equation 3 the temperature of r can be written as ( ) q θ 2 - θ 2 = t 2 - t 1 = 4πλ ln τ 2 τ Equation 4 can be written as 4πλ q 1 4 = lnτ 2 - lnτ 1 t 2 - t 1 5 It can be seen from equation 5 that lnτ and t are linear relationship. The curve of lnτ and t can be obtained by the least-square method. The relationship of lnτ and t can be defined as lnτ = α 0 + α 1 t 6 The sum of deviation square of lnt i and lnτ j can be seen as optimal criterion. So α 0 and α 1 can be calculated from α 0 = lnτ i - a 1 t i n α 1 = n t ilnτ i - t i lnτ i n t 2 i - ( t ) i The soil thermal conductivities λ i can be calculated from λ i = q n t i lnτ i - t i τ i 9 4π n t 2 i - ( t ) 2 i Based on the above principles thermal conductivity measurement system is designed with the probe method and its simplified diagram is shown in Fig. 1. In order to meet the requirement that the soil samples are unbounded heat-conducting media relative to the probe and avoid axial heat conduction the ratio of length to diameter needs bigger than 80 for the probe thus the diameter of the probe is 2 mm and the length of the probe is 200 mm. The probe is made of stainless steel whose interior is filled with thermal grease to reduce the impact of heat capacity of the probe. Fig. 1 Thermal conductivity measurement system of the probe method The thermal conductivity measurement software is composed by C #. When the thermal conductivity is

3 Laboratory and field experiment on measurement of soil thermal conductivity by probe method 223 measured the thermal conductivity measurement circuit is opened after the probe inserted into soil sample then the heating wire and the thermocouple both begin to work. Timing when τ = 0 and the time of temperature collection is recorded when i = 0. The thermal conductivity λ i at time τ i is calculated by equation 9. The tablet PC can display the variation curve of the soil thermal conductivity and the stable value is the thermal conductivity of the soil sample when the curve is stable. conductivity of fine sand varies from W m - 1 K - 1 to W m - 1 K - 1 the thermal conductivity of silty clay varies from W m - 1 K - 1 to W m - 1 K - 1. The measuring range can meet the general requirement of the soil thermal conductivity. The measuring curves of the thermal conductivity by the probe method is well consistent with those of QTM-D 2. The relative errors are less than 5%. So the thermal conductivity measured by the probe method has high precision and stability. 3 Laboratory experiment scheme 3. 1 Preparation of soil samples In the laboratory experiment the soil samples were dried to constant weight in a vacuum oven which includes coarse sand fine sand and silty clay. Later on the dehydrated samples were saturated by adding distilled water with 2% of the gradient until the samples are saturated. The soil samples were compacted and put into the soil sample box which size is 200 mm 100 mm 50 mm Laboratory experiment QTM is an unsteady method on the basis of hotstrip method. In order to verify the precision and stability of the probe method the probe method and QTM-D 2 are used to measure every soil samples. The probe was inserted into the middle of the soil sample and heated with the power of 5 W. Temperature sensors placed around the soil sample box showed that the heat emitted by the probe would not affect the edge of soil sample. Thus the soil sample is unbounded heatconducting media relative to the probe. Each soil sample was measured for five times with the probe method and QTM-D2. The average results was seen as the thermal conductivity of the soil sample. 4 Results of laboratory experiment The variation curves of thermal conductivity changing with the increase of the water content are shown in Figs. 2 3 and 4. It is concluded that the thermal conductivity of coarse sand varies from W m - 1 K - 1 to W m - 1 K - 1. The thermal Fig. 2 Fig. 3 of coarse sand of fine sand With the increase of water content the soil thermal conductivity increases in different levels. The thermal conductivity increases obviously when the water content is low. Since the thermal conductivity of water and air are 0. 6 W m - 1 K - 1 and W

4 224 Zhang T. Zhang Y. J. Liu T. et al. inevitably when sampling which causes the difference of the results. Fig. 4 of silty clay m - 1 K - 1 in the standard case respectively Yuan et al The conducting condition is poor because the porosity of soil sample is filled with air when the water content is 0%. The thermal conductivity is low. The air in the soil sample is replaced by water when the water content increases and the thermal contact resistance is reduced because water forms an aqueous film between soil particles. Thus thermal conductivity increases. The thermal conductivity is basically stable when soil samples are saturated. 5 Comparison between laboratory and field experiment The soil thermal conductivities of different depth 0. 4 m 0. 6 m 0. 8 m 1. 0 m and 1. 2 m had been measured by the probe method in Changchun where the soil is reworked loss. With the depth increasing the water content of soil gradually increases. Then the undisturbed soil samples were measured by the probe method. The comparison between laboratory and field measurements is shown in Fig. 5. It shows that the field measurement results are always bigger than the results of the laboratory measurement. And measuring gap gradually increases with the increases of the depth. In-situ result is % higher than the result in laboratory when the depth is 1. 2 m which obviously exceeds the error value of the probe method. Although the undisturbed samples are obtained according to the specification the water loss is Fig. 5 Comparison of laboratory and field measurement Based on the different results between laboratory and field measurement the in-situ method is the best choice for measuring the soil thermal conductivity. Compared with the laboratory measurement the probe method has a great advantage in measuring the soil thermal conductivity in field. 6 Conclusions 1 The probe method can not only measure the soil thermal conductivity in field but also measure thermal conductivities in laboratory for all kinds of soil samples. 2 The probe method is used to measure the thermal conductivity of coarse sand fine sand and silty clay in different water content. The results show that the probe method is well consistent with those of QTM-D2. With the increase of the water content the soil thermal conductivity increases in different levels. The thermal conductivity is basically stable when soil samples are saturated. 3 Compared the soil thermal conductivities measured by the probe method in laboratory with insitu experiment it shows that the measuring gap gradually increases with the increase of the depth. In-situ measurement of the soil thermal conductivity can reflect the actual situation of the soil mass.

5 Laboratory and field experiment on measurement of soil thermal conductivity by probe method 225 Acknowledgements We are grateful to Mr. Yin Renchao and Mr. Gao Ping for their advice and as sistance in the experiment. This study was supported by National Natural Science Foundation of China No Research Program Study on hydrothermal model of groundwater and software for Tangshan shallow geothermal utilization from The 2nd Geological Brigade of Hebei Geology and Mineral Exploration Bureau. References Fang J T Zhang Y J Huang X L et al Research and development of database management system for shallow geothermal energy resource based on C# and SharpMap. Global Geology in Chinese with English abstract Hou F Z Measurement of thermal conductivity of materials bythe probe method. Journal of University of Petroleum China in Chinese with English abstract Xu M Wang D Jiang L W et al Review on thermal conductivity coefficient and rock and soil mass. Journal of Earth Science and Environment in Chinese with English abstract Yin R C Zhang Y J Wu F et al Research on influence factors of rock-soil thermal properties by laboratory test. Global Geology Yu M Z Peng X F Fang Z H A simplified method onsite measurement of the thermal conductivity of deep-layer rock soil. Journal of Engineering for Thermal Energy and Power in Chinese with English abstract Yuan X Z Li N Zhao X Y et al Study of thermal conductivity model for unsaturated unfrozen soils. Rock and Soil Mechanics in Chinese with English abstract Zhang Y J Yu Z W Huang R et al Measurement of thermal conductivity and temperature effect of geotechnical material. Chinese Journal of Geotechnical Engineering in Chinese with English abstract

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