Relationship Between Induced Polarization Relaxation Time and Hydraulic Characteristics of Water-Bearing Sand

: Induced polarization method has become a popular method for evaluating formation 46 permeability characteristics in recent years because of its sensitivity to water body and water- 47 bearing pore structure. Especially, the induced polarization relaxation time can reflect the 48 macroscopic characteristics of the pore structure of rock and soil. Therefore, in order to study 49 the relationship between relaxation time and permeability, eight different sizes of quartz sand 50 were used to simulate water-bearing sand layers under different working conditions, and the 51 induced polarization experiment and Darcy seepage experiment were carried out on the same 52 sand sample in this paper, respectively. The experimental results show that the relation time 53 and the evolution of the permeability are closely correlated with the sizes of quartz sand. 54 According to the experimental data, with the particle size of the quartz sand as the link, the 55 power function equation is fitted to better describe the relationship between the permeability 56 and the relation time. It is worth noting that the equations obtained are only empirical 57 equations for quartz sand and are not suitable for general applications.


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With the increase of number of deep and long tunnels, disaster-causing water-bearing structures 61 have caused water and mud bursts in front of tunnels, it has become an important problem in some tunnels.

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The water permeability of the water-bearing structure, that is, the permeability characteristics, directly 63 determines the magnitude and scale of water inrush. It is essential to estimate the magnitude and scale 64 of water inrush with proper evaluation of the permeability characteristics of water-bearing structures 65 (Ni et al., 2010). In general, laboratory measurement of borehole sampling, field experiment methods 66 such as pumping experiment or pressure experiment are being used to understand the permeability 67 characteristics of water-bearing structures in front of tunnel face (Attwa et al., 2013). However, these 68 methods are expensive and due to the limitation of the number of samples and ex-situ experiment s, their 69 results often have hysteresis and one-sidedness. The induced polarization method has the advantage of 70 being sensitive to the pore structure of the formation and not being affected by topographical factors, and it is more and more used to predict the hydraulic characteristics of the formation (Slater, 2007).

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The induced polarization method is a geophysical method based on the induced polarization effect 73 of the geological body, which is based on the difference of induced polarization parameters between 74 different rock and soil media. Observing the complex conductivity and polarizability of the rock-soil 75 medium, we can get information such as the real part characterizing the charge conduction characteristics 76 and the imaginary part characterizing the charge storage characteristics in the complex conductivity.

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Permeability determines the resistance of porous materials to fluid flow (Lesmes et al., 2001;Revil et al., 78 2010). In the detection of disaster-causing water-bearing structures in tunnels, the fluid is usually 79 groundwater and its properties are relatively stable. Therefore, the permeability (k) can be used to 80 evaluate the permeability of the formation. In 1957, the induced polarization method was first proved to 81 be applicable to groundwater detection, and pointed out that the permeability of shallow aquifers can be 82 evaluated by the relevant parameters of the induced polarization attenuation curve (Vacquier et al., 1957).

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In the past ten years or so, more and more articles have shown that the imaginary component of the

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The sieved quartz sand still has some impurities. In order to avoid clay or other impurities having a poured with water to saturation for testing. The water sample used was the site water of the tunnel project 129 to simulate the actual engineering conditions. The quartz sand after screening and cleaning is shown in

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The used transmission period and reception period are both 64s. In order to eliminate the influence 160 of DC offset caused by unidirectional power supply, each cycle uses square wave pulses of opposite 161 polarity to supply power with a duty cycle of 50%, that is, the power supply duration is the same as the 162 power failure duration. At the same time, in order to reduce accidental errors in the data process, multiple 163 cycles of power supply and power failure measurements were performed, so the power supply current 164 signal of the transmitter is shown in Fig. 3(a).

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In terms of data collection, the receiver adopts a late synchronization method for data collection, 166 without manual synchronization of the transmitted signal. The obtained observation signal is shown in 167 Fig. 3(b). It can be seen that the secondary field voltage slowly decays within a certain period of time 168 after the power supply signal is turned off. In order to experiment the actual permeability coefficient of the quartz sand samples and calculate 180 the permeability, the Darcy seepage experiment device was used to conduct seepage experiments on 181 quartz sand samples with different particle sizes. Since the sample is highly water-permeable, the 182 measurement is carried out by the constant head method. The experimental instrument is shown in Fig.5; 183 the current experiment system is mainly comprised of five parts:

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(1) Water supply device: it can realize continuous replenishment of experimental water and keep the 185 water head stable during the experiment;

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(2) Permeation device: an acrylic cylinder is used to place the experiment sample, the upper end is equipped with a water inlet, the side is equipped with a pressure measuring hole, the lower end is 188 equipped with a water outlet, and the bottom is equipped with a permeable filter plate;

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(3) Pressure measuring device: connect the pressure measuring tube with the pressure measuring hole  (2) 214 Where I is the hydraulic gradient, H1 and H2 are respectively the head of the piezometer, and L is 215 the length of the seepage path, both in m.

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(4) Experimental measurement: After the water level of the piezometric pipe is stable, record the 217 piezometric water level and start to measure the seepage flow out of the permeation device within a 218 certain period of time. After repeating the measurement, change the hydraulic slope of the device 219 and repeat the above process for measurement. In order to prevent the osmotic pressure in the device 220 from changing too drastically and damaging the original structure of the sample, the hydraulic 221 gradient should be increased or decreased step by step to avoid jumping changes.

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The permeability coefficient K can be used to evaluate the difficulty of the fluid passing through 223 the pore framework of rock and soil, and its definition is shown in Eq. (3): Where ρ is the fluid density, g is the acceleration due to gravity, and μ is the hydrodynamic viscosity 226 coefficient.

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The Darcy seepage experiment is used to test samples of different particle sizes. According to the 228 above operation method, the flow rate is changed 2 to 3 times to obtain the flow rate, time, head and

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Where  s is polarization rate , UT  () is the total field potential difference measured before the 240 power is cut off by supplying power to the body polarized medium with a stable current for a period of 241 time T, 2 Ut  () is the secondary field potential difference measured at time t after power failure.

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We obtain the polarizability decay curve of the corresponding particle size under a certain current 243 from the average of multiple sets of data, and fit it with the second nonlinearity of the Cole-Cole model 244 to obtain the relaxation time curve under the corresponding particle size. The relaxation time curves of eight different particle sizes of quartz sand are shown in Fig.6.  It can be seen that as the particle size of the quartz sand sample increases, the time required to reach 261 the same seepage flow has a significant difference, and the difference between the minimum and

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In this paper, 8 kinds of quartz sands with different particle sizes are used to measure the relaxation 281 time and permeability of sand samples with different particle sizes using the field time domain induced 282 polarization experiment system and the indoor Darcy flow experiment system. According to the 283 experimental data, the following conclusions can be made:

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(1) The relaxation time and permeability increase with the increase of quartz sand particle size, and the 285 increasing trend gradually increases, which has a significant positive correlation.

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(2) Using the particle size of the water-containing sand sample as the intermediate quantity, the 287 relationship curve of permeability and relaxation time under the same particle size is formed by 288 mathematical fitting. Finally, the power function equation to describe the correlation between relaxation 289 time and permeability is obtained.

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In this paper, the obtained relationship is the experiment equation of quartz sands. They are not 291 for the universal equations application, and their coefficients may be different in different experiment 292 conditions and rock samples.