Study on horizontal diffusion of agent solutions in underground unsaturated soil: experiments and model simulations

The solute transport or water transport in unsaturated soil plays an important theoretical guiding role in remediation engineering. In order to study the diffusion of agent solutions in practical remediation engineering, the soil column experiments of unsaturated soil were carried out using the self-made laboratory test device. The effects of injection rate and soil pressure (confining pressure) on the solute diffusion in soil were studied. The experimental results show that the injection velocity has a great influence on the solute diffusion in soil, and the change in the diffusion rate is not proportional to the injection velocity. The effect of confining pressure on solute diffusion was first promoted and then suppressed. The fractal Richards equation (FRE) model was used to fit the water content curves. The results show that the FRE model has a fine fitting effect on this series of experiments, proving that it can provide model support for the simulation of solute diffusion in underground unsaturated soil. At the same time, the physical significance reflected by the fitting parameters can be used to analyze the mechanism of the experimental phenomena.

pollutant transport. These studies show that confining pressure is one of the crucial factors 1 affecting the diffusion of pollutants or agent solutions in underground soil. Feng Chu [15] 2 investigated soil-water characteristics of unsaturated undisturbed loess under isotropic 3 compression condition, and influences of net confining pressure on matric suction characteristics 4 of unsaturated undisturbed loess are determined and illustrated. And matric suction on water 5 transport and solute transport in soil is also self-evident [16]. To sum up the previous studies, we 6 can note that the influence of confining pressure on soil consolidation and pore water pressure 7 indirectly affects the diffusion performance of water and solute in soil. Therefore, it is necessary 8 to explore the law of water transport or solute transport in underground soil under different 9 confining pressures, and the confining pressure of soil in laboratory experiments was achieved 10 by applying external forces. 11 Considering the complexity of the actual engineering environment and the urgency of [24] developed a simple method, a horizontal one-dimensional infiltration test, to estimate water diffusivity of unsaturated soil. Moreover, several models have been proposed for the study of 1 water transport [25,26]. The classical Richards model [27], proposed by Richards in 1937, is a 2 widely recognized mathematical model of water transport in unsaturated soil. Many researchers 3 have modified and simplified the Richards model, and various mathematical models have been 4 proposed [28, 29] based on the experimental results. The water or solute transport in unsaturated 5 soil is often influenced by the complex pore structure of soil and the external conditions. 6 Previous studies have shown that particle distribution, pore structure and pore connectivity in 7 soil all present fractal characteristics [30][31][32]. More and more researchers [33][34][35]  would not be weakened by the accumulation of time or space distance, and the water or solute 14 transport could be predicted accurately. Therefore, it is necessary to explore whether the FRE 15 model can be used to characterize the diffusion law of water or solute in unsaturated soil under 16 complex conditions, and whether its parameters can reflect physical properties. It is very 17 important to solve the problem of insufficient diffusion and to predict the transport of agents in 18 soil.

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In summary, the study on the water transport or solute transport in unsaturated soil is to 20 explore the diffusion law of agents in underground soil in actual remediation engineering.

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Transport of water or solute in unsaturated soil plays an important theoretical guiding role in remediation engineering. Therefore, it is extremely important to carry out quantitative laboratory 1 simulation experiments and to find a suitable and effective mathematical model. In this paper, a 2 technical parameter (injection rate) and one physical property (confining pressure) of 3 contaminated soil are taken as research objects, and a series of experiments considering two 4 influencing factors are carried out. On this basis, the FRE model was used to characterize the 5 water retention curves, by fitting the experimental data. The rest of this work is organized as

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Considering that the diffusion of agents in soil is symmetrical in all horizontal directions, this 13 paper chooses one-dimensional horizontal diffusion as the research object. A solution of sodium 14 phosphate (Na 3 PO 4 ) was injected, as the remediation agent. The soil water content was measured 15 in real time by using the soil water content detector in each test hole of equal distance. Data was 16 collected and recorded in the process of experiments.

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The principle of high pressure jet grouting technology is to inject chemical agents into 20 underground soil by air flow and liquid flow with high pressure. And then pollutants are oxidized 21 by the chemical oxidant (the remediation agent), degraded or transformed to low toxic products.
The effective action range of high-pressure jet grouting technology includes core cutting part, 1 diffusion part or extrusion part. As shown in Fig. 1, the effective range is a cylindrical 2 consolidation body composed of the agent and soil mixing slurry body, the stirring mixing part 3 and the diffusion part [5]. However, it is understood that core cutting part will mainly depend on 4 the cutting action of the jet and on the soil resistance to disaggregation. This is mainly a physical 5 effect on soil, extremely complex to be quantified [38]. In practical projects, the radius of 6 effective range in the horizontal direction is often to measure the remediation effect and 7 efficiency. Therefore, the study on the water or solute transport in underground soil mainly 8 focuses on the diffusion part in the horizontal direction, and the diffusion in the vertical direction 9 is not considered in this paper. The diffusion conditions were simulated by laboratory 10 experiments, and influences (injection rate and confining pressure) were discussed.

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The laboratory scale experiment of water transport in horizontal unsaturated soil column, the 14 most widely used in experimental research, can eliminate the influence of gravity on water 15 transport in unsaturated soil, which can make the influencing factors of water transport single 16 and parameters more accurate. Horizontal soil column method is a laboratory method for the 17 determination of unsteady flow in soil hydraulic diffusion, which was first proposed by Bruse

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In order to minimize the error between laboratory experiments and actual situations, the 20 experimental soil used in this paper was undisturbed. Soil samples were shallow soil, taken from 21 the middle area of Jiangsu province. After removing impurities and drying, soil samples were reconfigured to meet the required water contents. The initial water content of undisturbed soil 1 was 17.58%. When the in-situ remediation is carried out by high-pressure jet grouting 2 technology, the agent is required to be water-soluble, relatively stable under high-pressure 3 conditions, and has little side effect on the environment [5]. Sodium phosphate (Na 3 PO 4 ) 4 selected in this paper is a kind of inorganic compound, and it is easily soluble in water (its 5 solubility is 28.3 g/100 mL). 6 In view of problems in practical engineering application of high-pressure jet grouting 7 technology, such as agent overflow and insufficient diffusion, which are mainly affected by 8 injection rate and confining pressure. Therefore, two factors are selected to study the influence 9 on the diffusion rate of agents in soil, namely, injection rate (60 ml/min, 40 ml/min, 20 ml/min), 10 and confining pressure (5 kPa, 10 kPa, 15 kPa, 20 kPa, 30 kPa, 40 kPa, 50 kPa).

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The experimental pipe was placed vertically to fill with the prepared soil samples and where,  is the water content,   D  is the water diffusivity, which is assumed to only related to 16 water content, x is the transport distance of water in soil, and t is the ordinary time. The  Where the dimensionless exponent The transport of water in unsaturated soil is often affected by the complex pore structure 6 and boundary conditions inside the soil, and the pore structure is not fixed during the transport 7 process of water. So, it is difficult to describe the transport law of water in unsaturated soil where the initial condition is    Table S1. Fig. 4 indicates that FRE can describe the trend of water transport in soil column 1 experiments under three different injection rates, and they fit well at all positions. The R-square 2 and RMSE in Table S1 were computed by pooling data from all curves shown.

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The parameter n of the FRE is positively correlated with the change rate of water content 4 in soil [37]. And, the parameter n in the three groups of experiments is drawn as the change 5 curves in Fig. 5. Fig. 5 shows that the lower injection rate is, the faster the water content of soil 6 changes, that is, the faster the diffusion rate of the simulated agent in the soil column increases, 7 which is consistent with the law reflected in Fig. 4. In addition, the R-square and RMSE in Table   8 S1, reflecting a fitting effect, show that the FRE fits the water transport under a low injection rate 9 more closely than the high group. Especially, in the experimental group (c) with higher injection 10 speed, it can be found that the fitting effect of the forward position (X = 200 mm, 400 mm…) is 11 significantly decreased.

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The diffusion of solute or transport of water in soil mainly flows through pore channels 13 formed by the liquid phase of soil and self-infiltration [49]. With the increase in injection rates, 14 more and more pore channels will participate in the diffusion. When the injection rate is too high, 15 pore channels are not enough to pass through a large amount of liquid, so the growth rate of 16 diffusion will gradually slow down. Moreover, due to the injection of a large amount of liquid in 17 a short period of time, the liquid that has no time to diffuse and gradually accumulates, which 18 will cause a certain degree of damage to the originally stable structure of the soil, and the pore 19 channels used for liquid diffusion and transfer will also be damaged to a certain extent. When the 20 injection rate is relatively low, the agent has enough time to permeate and diffuse, and it provides 21 a stable environment for the agent filled in pores of the soil to react with pollutants. Therefore, with the decrease of injection rates, the remediation is improved and the utilization rate of agents 1 will be higher.

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In actual construction processes, on the one hand, sampling should be carried out in advance 3 to determine the optimal injection rate. On the other hand, if the remediation agent is expensive, 4 the injection speed should be appropriately reduced on the premise of the remediation effect.

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Balancing the time cost and economic cost is to achieve the maximum benefit. In engineering application, the high-pressure jet grouting technology is mostly used in the 10 polluted soil with a depth of 0 ~4 m (the corresponding confining pressure of soil is 0~ 40 kPa).

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Confining pressure is an important factor affecting the diffusion of agents in underground soil.

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Therefore, the influence of a certain confining pressure (no higher than 50 kPa) on solute 13 transport in subsurface soil will be considered in this paper.
14 In this group of experiments, the agent solutions with the concentration of 15 g/L was 15 injected at the rate of 10 ml/min, and the pressure diffusion was carried out in the soil sample 16 with the initial water content of 15%. Fig. 6 shows the time for the water content of soil samples 17 to reach 20% after agents diffusion, under various confining pressures. It can be seen from Fig. 6 18 that the time for the diffusion of agents decreases first and then increases with the increase of 19 confining pressure of soil, that is, the diffusion velocity of agents increases first and then 20 decreases with the increase of confining pressure. In addition, there is an obvious optimal 21 confining pressure value (15 kPa) in this group of experiments. By decomposing Fig.6 into Fig.  6(a) and Fig. 6(b), it can be clearly seen that when the confining pressure of soil is 15 kPa, the 1 diffusion time of remediation agent is the shortest. In the process of diffusion, the appropriate 2 increase of confining pressure can promote the diffusion of agents in underground soil. And 3 when the confining pressure increases gradually, the effect of promoting diffusion decreases 4 gradually, and it presents a restraining trend when the confining pressure is larger.  Table S2.
14 The fractal order α of the FRE can characterize the underlying water transport 15 environment property in heterogeneous soil, and CHEN Wen [47] pointed out that the smaller 16 the value of α, the more complex the water transport environment would be. Fig. 8 shows curves 17 of parameter α, fitted by FRE in each group, and according to the experimental law shown in Fig.   18 6, they are also divided into two groups: (a) and (b). Fig. 8 indicates that with the increase of the 19 confining pressure, values of α first decreases (Fig. 7(a)) and then increases (Fig. 7(b)), which is 20 consistent with Fig. 6. This represents that the rate of water transport is related to the complexity of soil environment caused by the confining pressure, which can also be seen from the change of 1 parameter C 0 in Table S2.

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After the agent solution is injected into the soil column, it diffuses from the injection 3 point to all directions. For the reason of the horizontal loading pressure in this experiment, 4 proximal soil samples will be compressed first and pores will be reduced. Since liquid diffusion 5 is mainly formed by filling soil pores to form water channels, so compact pores of soil particles 6 shrinking make diffusion easier, and the diffusion speed tends to increase with the increase of 7 confining pressure. When the confining pressure reaches a certain value, the pores in all 8 directions are squeezed to a certain extent, and the compactness of soil reaches a certain degree.

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The shrinkage of pores in the soil will lead to the obstruction of flow paths for the liquid, and the 10 diffusion of agents becomes very difficult. At this time, with the increase of the confining 11 pressure, the diffusion rate of agents will gradually slow down.

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Due to different confining pressures on contaminated soil at different depths in 13 engineering projects, the diffusion in the remediation process is also different, leading to 14 different remediation effects. For the shallow underground soil, some confining pressure can 15 promote its diffusion. Owing to the deep underground soil under the higher confining pressure, 16 the diffusion velocity will be restrained to some extent. Therefore, through changing other 17 external conditions, the diffusion can be accelerated to achieve an optimal remediation effect.  That is to say, it exists a confining pressure value to optimize the diffusion velocity. Under the 7 high confining pressure, due to the compaction of soil, non-uniform diffusion and accumulation 8 of agents will occur, and the effect of remediation is highly uncertain.

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In addition, water content curves were presented, fitting the FRE from the experimental