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非水反应类高聚物在富水砂砾石中的注浆扩散规律试验研究

非水反应类高聚物在富水砂砾石中的注浆扩散规律试验研究

雪明
欣欣
艺超
宏远
科杰
明瑞
冰寒
善勇
复明
400

近年来,双组分发泡型高聚物因其良好的可注性、可控的凝胶时间及自身膨胀性,在渗透注浆(非开挖修复技术)修复地下工程灾害方面得到了广泛应用,但复杂的地质条件及浆液自身膨胀性使注浆过程变得更复杂。因此,本文采用自制的具有周边压力和堵水率监测功能可视化试验装置,研究主要影响参数(粒径分布、注浆量和动水泵压)对浆液扩散动力响应(周边压力)和堵水率时空分布的影响。研究结果表明:当注浆量为563 g,动水泵压为0.013 MPa时,高聚物在渗透注浆浆液扩散过程中,其自身膨胀力占主导地位,能够显著改变局部砂砾石骨架结构。在注浆量为563 g,动水泵压为0.013 MPa,砂砾石粒径分布类型为Ⅲ的情况下,高聚物的流动时间缩短、浓度增大进而迅速堵塞砂砾石孔隙,导致周边压力随着距离的增加而迅速下降,并缩短了到达拐点堵水率的时间。砂砾石孔隙的瞬时堵塞作用会导致流场堵塞信息的滞后传递。

高聚物注浆扩散规律堵水率压力动水条件
pic

1 Introduction

Grouting is a useful technique for stopping seepage and plugging water in a layer rich with water and gravel, which are frequently occurring and unfavourable geological conditions in construction areas in the field of subterranean engineering [1-3]. Considering their advantages over traditional grouting materials, i.e., rapid reaction, high expansion rate, high strength, and excellent impermeability, polymer materials have emerged as the optimal choice for managing underground engineering disasters [4-7]. ZHANG et al [8] designed a set of experimental devices that could simulate infiltration grouting in porous media and used a conventional grouting material (cement slurry) to obtain the different permeabilities of the injected media and the changing spatiotemporal grouting pressures at different grouting rates. To determine the variation in C-S (cement slurry) grouting pressure with time under various medium permeabilities and grouting rates, ZHANG et al [9] devised a one-dimensional test system to simulate the visible permeation resulting from grouting diffusion. However, the spatiotemporal evolution and diffusion characteristics of polymers in water-rich sand and gravel layers are still largely unexplored [10, 11].

DUPLA et al [12] conducted cement slurry grouting tests using a custom diffusion mould and reported that the infiltration effect notably influenced the spatial evolution of the diffusion pressure. Subsequently, LI et al [13] analyzed the effect of the percolation effect on the distributions of porosity, slurry concentration and slurry pressure in porous media; thus, they revealed the mechanisms by which the percolation effect influences the diffusion of slurry and the range of effective reinforcement. ZHENG et al [14] investigated the grout-water interaction and grouting penetration characteristics when impacted by filtering. During the cement slurry grouting process, the pressure distribution, spatiotemporal distribution of permeability, and penetration distance were measured. When ZHOU et al [15] tested cement slurry grouting under continuous flow and pressure, they discovered that in large mass fractal dimension soil, the diffusion pressure decreased with increasing distance. ZHOU et al [16] investigated the impacts of grouting factors on the penetration diffusion characteristics of cement slurry using a central combination test. They discovered that the leachate flow rate decreased faster over time as the mass fractal dimension increased. The effective diffusion distance of cement slurry undergoing infiltration grouting in porous media was investigated experimentally by ZHANG et al [17]. The evident spatiotemporal effect of the percolation effect was notably correlated with the diffusion distance and percolation time. DU et al [18] conducted a constant water flow rate grouting experiment and reported that at relatively high water flow rates, the diffusion pressure rapidly decreased with increasing distance. WANG et al [19] created the dynamic water shutdown criterion for glass fibre cement slurry and tested the flow patterns of this slurry and its consolidated bodies with varying glass fibre contents; nevertheless, they examined only the water shutoff effect of the grouting material. In an orthogonal experiment on the water-blocking attributes of permeable polymers, FANG et al [20] discovered that the primary factor controlling the WPR was grouting pressure. Then, FANG et al [21] used a custom experimental device to study the diffusion characteristics of nonaqueous reactive foaming polymers in porous media under hydrodynamic conditions. The effects of the mass fractal dimension, DWPP and grouting amount on the effective diffusion length and WPR of grout were revealed. However, in the above studies, since only one monitoring point was deployed in each device, it was not possible to study the spatial evolution of the leachate flow rate.

Furthermore, in the aforementioned studies, the researchers primarily investigated nonexpansive slurries, such as cement slurries, ignoring the impacts of the expansion of nonaqueous reactive polymer slurry on its spatiotemporal diffusion characteristics [22, 23]. LU et al [24, 25] proposed a non-orthogonal plastic modeling method and established non-orthogonal elastoplastic models for soil [26] and concrete [27]. They can reasonably describe the dilatancy behavior of geomaterials without the need for the plastic potential function, and have strong application prospects for predicting the expansion laws of polymers. The stress on the skeleton of sand and gravel can fluctuate because of variations in diffusion pressure during the diffusion of expansive polymer slurries, thereby impacting the porosity and permeability properties of materials. The dispersion of the polymer slurry is impacted by changes in the parameters of sand and gravel, which can complicate the diffusion mechanism of the slurry. In order to control the adverse geological conditions of water-rich sand and gravel, the complex pore structure was simulated by setting the particle size distribution and its water-rich state was simulated by the DWPP, and then the influence process of grouting volume, sand and gravel particle size distribution and DWPP on the grouting reinforcement effect was studied, and the temporal and spatial dimensions are considered in this paper. Using self-made visualization of grout diffusion device, comprehensive analysis of grout diffusion process, reveals the slurry flow diffusion mechanisms. In practical engineering, it is challenging to assess the diffusion pressure of slurry in pores precisely because of the concealment and complexity of grouting construction. In this article, data from pressure sensors buried in gravel and sand serve as indirect proxies for the diffusion pressure (peripheral pressure) of the slurry. Then, the mechanism by which high polymers occupy sand and gravel pores in real time during the grouting procedure is elucidated, in addition to that governing the indirect characterization of the variations in the flow field by WPR indicators.

2 Materials and methods

2.1 Materials
2.1.1 Sand and gravel

Hebei manufacturers provided the sand and gravel used in this study. The sand and gravel were divided into five particle diameter ranges according to the design specifications: 0-2, 2-5, 5-10, 10-15 and 15-20 mm. Each of these ranges passed through a grading screen. By adjusting the mass ratio of each group of particles and mixing them accordingly, different particle size distributions of the sand and gravel (Ⅰ, Ⅱ, Ⅲ) were obtained. The particle size distribution is presented in Figure 1.

Figure 1
Particle size distribution map
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According to the grading curve of sand and gravel particles, the characteristic particle size and grading index of the three types of sand are obtained, as shown in Table 1. Here, dn represents the n% of the total mass of sand and gravel particles smaller than the specified size, d60 denotes the control particle size, and d10 is the effective particle size. Cu represents the uniformity coefficient of gravel, where pic>5 indicates uniform gravel; otherwise, it is uneven gravel. The calculation formula is presented in Eq. (1). pic stands for the curvature coefficient, which indicates whether the particle gradation accumulation curve is continuous. For a continuous gradation curve of sand and gravel, 1<pic<3, and the calculation procedure is detailed in Eq. (2).

pic (1)pic (2)
Table 1
Characteristic particle size and gradation index of sand and gravel
Sand and gravelpic/mmpic/mmpic/mmpicpic
14.74910.0755.0392.9272.351
13.4777.9083.3424.0321.388
11.5065.1361.7566.5521.306
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The non-uniformity and curvature coefficients of each gravel are shown in Table 1. The non-uniformity coefficient of the three gravel stones is in the range of 2.927-6.552, and the curvature coefficient is in the range of 1.306-2.351. According to the non-uniformity coefficient and curvature coefficient, it is known that gravel stone Ⅲ is a uniform gravel stone with a continuous gradation curve and is graded as excellent sand. Gravels Ⅰ and Ⅱ are uneven gravel stones, classified as continuous sand but belong to poorly graded gravel stones. Based on the non-uniformity coefficient, III>II>I, indicating that III has the most uniform size distribution of gravel stones, II is generally uniform, and I has the least uniform size distribution.

2.1.2 Polymers

In this paper, nonaqueous reactive two-component foamed polyurethane was used. A type of copolymer known as a nonaqueous reactive foaming material was created when isocyanate (material A, also called black material) and polyol (material B, also called white material) polymerized together with the help of a catalyst. The resulting solid resembled foam [28].

Polymer materials have high expansibility, and the expansion ratio of free expansion can reach 20 times. The reaction consolidates rapidly and can reach 90% of its design strength within 20 min. Its permeability resistance is strong, and the permeability coefficient reaches 10-8 cm/s; The polymer reaction process does not produce any pollutants and in the process of impermeability service, it will not be corroded by groundwater acid, and alkaline substances to produce toxic substances, so it will not pollute the surrounding environment.

2.2 Test equipment
2.2.1 Grouting system

The grouting system included an air compressor, preheating device, grouting pump, grouting gun, two slurry storage tanks, and materials A and B. The grouting pumping pressure varied from 0 to 15 MPa, and the pumping ratio of the slurry composed of materials A and B was adjustable. In this paper, the two components of the slurry were combined in a 1:1 ratio, after the slurry A and B are mixed at the grouting gun, the grouting pump provides the power for the grouting gun to inject the mixed slurry into the porous medium, and the pumping pressure was less than 6 MPa. The slurry was preheated in the slurry storage tank before grouting. This paper preheats grouts A and B to 30 ℃.

2.2.2 Dynamic water system

The dynamic water system was composed of a water tank, pipeline and variable-frequency constant-pressure feed pump. If the pressure sensor detected excess pressure, it will immediately cut off the water supply and reduce the pipe pressure to a predetermined level. The variable-frequency constant-pressure pump automatically increased the water supply flow when the water supply pressure was too low so that the pipeline pressure increased to a predetermined value. A large volume of water was input to ensure a continuous water supply, and a filter was set between the water tank and the water pump to prevent sundries from blocking the pipeline and affecting the water supply.

2.2.3 Diffusion system

The diffusion system is composed of a diffusion device, pressure sensor, and seepage test valve. The diffusion device is a cuboid with a length of 225 cm, a width of 20 cm, and a height of 15 cm. It is made of transparent acrylic material, and the whole is composed of bolts and tie rods. Silicone gaskets are arranged between the acrylic plates to ensure the sealing performance of the equipment. Furthermore, through drilling holes into the diffusion device cross sections at both ends, holes with sizes of 3.2 and 6.3 cm were drilled to represent the input and output of the device, respectively. PPR pipes were used to connect the diffusion device to the dynamic water system. A filter screen was placed at the diffusion device output to prevent significant amounts of sand and gravel from exiting the system with water flow and harming the general structure of the injection medium.

The grouting pipe was arranged 30 cm from the dynamic water inlet, and pressure sensors were set up 30 cm downstream from the grouting pipe. As shown in Figure 2, the same pressure sensor horizontal coordinate is used to drill the bottom of the diffusion device than to install the mini water valve, and then five seepage test points are obtained.

Figure 2
Schematic diagram of test point
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2.2.4 Monitoring system

A measuring container, a high-precision electronic scale, and a BW-type micropressure sensor constituted the monitoring system. By using a BW-type micropressure sensor, grouting allowed for the real-time collection of pressure data at several test points. The pressure sensor is fixed on the diffusion device to reduce the error caused by gravel sliding. Table 2 displays the configuration settings. To avoid measuring the seepage fluid level incorrectly, the percolation fluid of the valve at the test point was taken from the measuring container at a designated time. Next, the weight of the percolation fluid at the collected test point was obtained at the corresponding time point using high-precision electronic scales. Finally, the weight of the percolation fluid was converted into percolation flow.

Table 2
Main parameters of BW type micro pressure sensor
Range ability/MPaBridge resistance/ΩDiameter/mmSampling frequency/HzSensitivity coefficient/(mV·kPa-1)
0-0.13502850.00697
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A Donghua Test DH8303N dynamic signal collection device was used to obtain the pressure data. Combined with the DHDAS testing system, parameters such as strain, stress, and displacement could be accurately collected.

2.3 Test procedure

1) Materials A and B were preheated to 30 ℃ through the heating system of the grouting machine to facilitate a relatively complete reaction of these materials in a slurry during grouting.

2) The inner surface of the acrylic diffusion device was coated with polymer demoulding oil to avoid affecting the demoulding process after grouting due to the adhesion between the polymer and the acrylic plate. Once the diffusion device upper plate was opened, the prepared sand and gravel were uniformly poured inside. A grouting pipe was buried once the diffusion device was filled to half of its height, and the filling process continued until the device was filled. Bolts and pull rods were used to secure the diffusion device upper plate.

3) The valve of the pump was opened until the water was ejected to discharge the air to ensure sufficient water supply, after which it was closed. Furthermore, the corresponding DWPP was set, the inlet valve of the diffusion device was opened, and the water supply process was initiated.

4) The seepage fluid was collected by the measuring cup for 5 s at each test site until the seepage flow at the same test point was consistent, providing that the pressure indication at the diffusion device input was stable. At this point, the seepage flow rates after 5 s at different test points were recorded as the initial seepage flow rates.

5) The seepage flow at each test point was recorded for 5 s at the following time after the grouting process began: 20 s, 40 s, 60 s, 80 s, 100 s, 120 s, 180 s, 240 s, 300 s, 360 s, 420 s, 480 s, 540 s and 600 s. This measurement was conducted after the pressure sensor data were cleared to zero. The pressure data collection process was stopped after 600 s of grouting, and the moving water pump was shut down.

The rate of water plugging could be determined by the following equation:

pic (3)

where pic is the seepage flow rate prior to grouting, pic is the rate of seepage following grouting, and S is the rate of water plugging. The significance of the WPR is not only in evaluating the water plugging effect but also in describing the changes in the slurry flow field.

pic (4)pic (5)

where pic is the cross-sectional area of the section where the water valve is set at the bottom of the diffusion system, and pic is the fluid flow rate. When the water valve is a cylinder of equal diameter, that is, when the cross section of the liquid outflow process is constant, the WPR can be converted into the flow rate ratio. This ratio could somewhat represent the variations in flow velocity before and after grouting.

The range of the DWPP and grouting amount when porous media can be injected in this experiment were determined through pre-experiment. The influence of DWPP, grouting amount and the homogeneity of the particle size distribution on grouting effect was studied by setting control groups. The experimental combinations are shown in the Table 3.

Table 3
Design of experiments matrix
GroupDynamic water pump pressure/MPaGrouting amount/gSand and gravel
10.013563
20.047563
70.03563
30.03878
40.03248
70.03563
50.03563I
60.03563III
70.03563
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3 Results and discussion

3.1 Dynamic response and water plugging characteristics of polymer grouting considering time factors

The polymer slurry makes it difficult for passive water to disperse, and it has strong retention qualities, the majority of which are concentrated in front of test point 1. Thus, the primary goal is to investigate the mechanisms by which various grouting parameters affect the real-time peripheral pressure and WPR evolution attributes at test point 1.

3.1.1 Impacts of grouting factors on real-time peripheral pressure

The evolution curve of the peripheral pressure at test point 1 over time during the grouting process of the central point test (Group 7) is shown in Figure 3. Owing to the diffusion properties of the polymers, the peripheral pressure increases very little in the first 40 s and then increases significantly between 40 and 80 s before steadily becoming stable. In the first 40 s, the reaction of the slurry is incomplete, and the expansion force generated by the reaction of the slurry in the first 40 s is smaller than that of the complete reaction of the slurry in the later stage. At this moment, the slurry diffusion pressure is partially provided by water flow, and its main diffusion mode is osmotic diffusion, which reduces the force on the injection medium skeleton. Therefore, the increase in peripheral pressure is relatively small. After 40 s, the slurry reaction is relatively complete, and the slurry rapidly foams and expands. The diffusion pressure of the slurry is provided by its foaming expansion, which places a large force on the skeleton. Thus, the peripheral pressure increases greatly. The slurry expansion force and the sand-gravel binding force reach a limit equilibrium state after 120 s, and the peripheral pressure remains stable.

Figure 3
Time evolution diagram of peripheral pressure in central point test
pic

Figure 4 depicts the changes in peripheral pressure over time under various DWPP conditions, with the sand and gravel Ⅱ and a grouting amount of 563 g. According to Figure 4, the peripheral pressure decreases with increasing DWPP. The evolution characteristics of peripheral pressure over time vary under different DWPP conditions. When the DWPP is 0.013 MPa, the peripheral pressure first increases and subsequently decreases over time, with the increase rate being the fastest and the decrease rate being the slowest. The peripheral pressure first increases at a pumping pressure of 0.03 MPa, after which the growth rate decreases and stabilizes, with no discernible decreasing trend. When the DWPP is 0.047 MPa, the peripheral pressure first increases, then decreases, then increases again and finally stabilizes.

Figure 4
Influence of dynamic water pump pressure on the time evolution of peripheral pressure
pic

Because fluid water can suppress slurry swelling, the higher the DWPP is, the less sufficient the reaction of the high polymer, the smaller the expansion force of the polymer, and the smaller the squeezing effect of the slurry on the sand and gravel, resulting in a lower peripheral pressure. In addition, when the reaction is sufficient and the slurry expansion force is large, the sand and gravel skeleton is destroyed, as shown in Figure 5. This destruction causes the rearrangement of local sand and gravel particles and results in uneven pore distribution and dissipation of diffusion energy towards the local large pores, significantly decreasing peripheral pressure. The rate of decrease in the peripheral pressure slows in the later stage, indicating that the polymer still reacts and increases the compactness of the sand-gravel skeleton.

Figure 5
Grout-filled pores and sand-gravel skeleton recombination diagram
pic

When the DWPP is 0.03 MPa and the grouting amount is 563 g, the change curves of the peripheral pressure with time under the different sand and gravel are shown in Figure 6. Figure 6 shows that the more uniform the size distribution of sand and gravel is, the greater the peripheral pressure is. The time curve of the peripheral pressure is similar when the sand and gravel is Ⅱ or III, both of which show trends of first increasing and then stabilizing. However, when the sand and gravel is I, the peripheral pressure first increases, then decreases and then increases again with time.

Figure 6
The time-varying curve of peripheral pressure for different types of sand and gravel
pic

The reason for this difference is that with the more uniform size distribution of sand and gravel, the distribution of pores size and spatial locations becomes relatively uniform, the same amount of grouting polymer is more and more squeezed by gravel, and the slurry diffusion is limited. On the contrary, with the less uniform size distribution of sand and gravel, the pore size and spatial location distribution is relatively uneven, which is conducive to the dissipation of the energy of slurry dispersion into the bigger pores, thereby reducing the peripheral pressure. Subsequently, due to the rapid increase in viscosity during the cementitious reaction, the framework of compacted sand and gravel is compacted, but the diffusion range does not increase.

Figure 7 illustrates the impact of the grouting amount on the peripheral pressure during grouting diffusion (groups 3, 4 and 7). The peripheral pressure increases and subsequently decreases when the grouting amount is 878 g. When the grouting amount is 248 g, the peripheral pressure gradually increases. When the grouting amount is 878 g, the slurry reacts quickly and is minimally impacted by dynamic water. This change shortens the infiltration and diffusion time and causes the slurry to expand quickly to compact the pores, making the peripheral pressure increase quickly. The excessive expansion force can significantly change the local structure of the sand and gravel skeleton, leading to the rearrangement of sand and gravel particles, as shown in Figure 6, and the leakage of energy accumulated by the slurry to the large pores of the new skeleton structure. This phenomenon results in a decrease in peripheral pressure. However, the rate of decrease slows in the later stage, indicating that the slurry still compresses the sand-gravel skeleton in reverse.

Figure 7
Influence of grouting amount on peripheral pressure
pic
3.1.2 Influences of grouting factors on the real-time WPR

The variation in the WPR of the test point 1 with time can be observed in Figure 8. Figure 8 shows that the WPR increases slowly during the first 40 s, while the WPR increases rapidly from 40 s to 80 s,and after 80 s, the WPR increases slowly. This slow increase occurs because the slurry reaction in the first 40 s is not sufficient, its fluidity is strong, and its flow rate is higher. However, the grouting pressure provides a certain driving force for the flowing water, resulting in an insignificant increase in WPR. During the period from 40 s to 80 s, due to the sufficient reaction of the slurry, the pores are compacted through the expansion force, and the slurry flow rate decreases, resulting in many blocked seepage channels and a significant increase in the WPR. The polymer slurry then progressively changes from a liquid to a solid because of its gelation process, and the ability of the material to block water is enhanced. The diffusion range stops expanding, and the slurry stops spreading; therefore, the increase in the rate of water plugging is minimal.

Figure 8
Evolution law of water plugging rate in center point test
pic

The evolution curves of the real-time WPRs for test groups 1, 2 and 7 in Table 3 are chosen for comparison to determine the effect of the DWPP on the WPR in real time during the grouting process. This comparison results in the plotting of the change curves of the WPR with time under various DWPPs, as illustrated in Figure 9. The point of change in the water plugging rate from a fast to a slow rate is known as the inflection point. The higher the DWPP is, the poorer the water plugging effect is, and the longer it takes to reach the WPR inflection point. The greater the water plugging effect is, the longer it takes to reach the inflection point of the WPR as the DWPP increases. This phenomenon arises because a relatively high DWPP decreases the efficient diffusion range of the slurry, reduces the pore volume occupied, and increases the inhibitory effect of water flow on slurry expansion. At this point, the swelling property of the polymer decreases with its filling and compressing effect on the sand and gravel skeleton, worsening the water plugging effect. Furthermore, a higher DWPP causes the slurry to react slower, which increases both the time required to reach the inflection point and the rate of water clogging. Notably, the WPR rapidly hits the inflection point within 40-60 s when the DWPP is 0.013 MPa, which is a significantly greater growth rate than that of the other two groups. This difference arises because of the quick reaction of the slurry to low DWPP, which causes it to foam and expand quickly and to clog the seepage channel, hence increasing the pace at which the water plugs.

Figure 9
Influence of dynamic water pump pressure on the time evolution of water plugging rate
pic

The real-time WPR evolution curves in test groups 5, 6 and 7 in Table 3 are chosen for comparison, and the curves of the changes in WPR with time for sand-gravel media with different particle size distribution are obtained, as displayed in Figure 10. Figure 10 illustrates that the more uniform size distribution of sand and gravel results in a better WPR. This trend occurs because the more uniform of the sand and gravel, that is, a more uniform pore distribution, leads to a smaller pore water flow rate, which not only facilitates simple filling, but also shorts the time to reach the WPR inflection point. Specifically, with the most uniform of the sand and gravel-III, the WPR of the slurry increases significantly more during the 40-60 s time period than it does for the other two groups, suggesting that the more uniform of the sand and gravel enhances the likelihood of seepage channel blockage.

Figure 10
Influence of the homogeneity of the particle size distribution on time evolution of water plugging rate
pic

Figure 11 shows the change curves of the WPR with time under the various grouting amounts. The evolution curves of the real-time WPR in three groups of central point combination tests (3, 4 and 7) are chosen for comparison to determine the impact of the grouting amount on the real-time WPR during the grouting process. The time required to reach the inflection point WPR decreases as the grouting amount increases. This reduction occurs because greater grouting indicates that more pores are occupied at the injection start, and less dynamic water affects slurry accumulation. The pores of the injection medium become filled and compact because of the quick expansion of the slurry, which causes the rate of water plugging to increase quickly.

Figure 11
Influence of grouting amount on the time evolution of water plugging rate
pic
3.1.3 Comprehensive analysis of real-time peripheral pressure and WPR

A large amount of experimental data indicate that the change in the WPR for each group of experiments becomes stable within 120 s. Furthermore, the first 120 s is a stage of rapid increase in peripheral pressure. Therefore, three typical sets of tests (test groups 3, 5 and 7) are selected to conduct a simultaneous analysis of the changes in the peripheral pressure and WPR in the first 120 s to explore the relationship between the two indicators.

In order to more clearly observe the relationship between peripheral pressure and WPR at the central test point, the evolution curves of peripheral pressure and WPR within 120 s before Figures 3 and Figure 8 are extracted. Peripheral pressure is then transformed, as depicted in Figure 12. According to Figure 12, the growth rates of the peripheral pressure and WPR in the first 40 s are relatively small. From 40 s to 80 s, the peripheral pressure and WPR both rapidly increase. However, from 80 s to 120 s, the growth rate of both decreases, and the WPR reaches a stable value earlier than the peripheral pressure. This phenomenon occurs due to the incomplete reaction of the slurry in the first 40 s, during which the slurry permeates and diffuses in the medium in liquid form. In addition, the pore filling is not dense, resulting in a low force on the sand-gravel skeleton. After 40 s, the slurry begins to foam and expand, and while the pores are filled and compacted, they are hindered by the large framework of sand and gravel. After 80 s, the slurry stops moving, and the diffusion range stops increasing. The WPR remains stable and the slurry continues to react and increase the compactness of the skeleton, which is the reason for the delay in peripheral pressure increase.

Figure 12
Relationship between peripheral pressure and water plugging rate in central point test (test points 1)
pic
3.2 Dynamic response and water plugging characteristics of polymer grouting considering temporal and spatial factors

The dynamic response of sand and gravel media and the spatial distribution of the flow field during the diffusion process of polymers are important aspects of the diffusion mechanism that can assist in distinguishing the flow conditions of polymers. In engineering, it is important to avoid excessive disturbance of the surrounding environment by grouting, and monitoring the surrounding environment is also highly important. Therefore, the time and space are introduced to determine the spatiotemporal distributions of peripheral pressure and WPR during the diffusion of polymers.

3.2.1 Spatiotemporal variation in peripheral pressure

The peripheral pressure change curve for the point test is depicted both spatially and temporally in Figure 13. Figure 13 shows that there is a slight disturbance in the polymer at test points 2-5 of group 7, which is in agreement with the field test results. These results suggest that polymer diffusion is mostly concentrated before test point 1. The spatiotemporal variations in peripheral pressure at approximately four test points (test points 2-5 of group 7) are depicted in Figure 13. Figure 13 illustrates the mechanism by which the peripheral pressure increases during the first 60 s and subsequently decreases to a constant level. This trend arises due to the diffusion of slurry flow in the first 60 s, which drives pore water and increases peripheral pressure. At approximately 60 s, the slurry rapidly foams to seal the pores, and the slurry diffusion mode changes from infiltration diffusion to compaction diffusion. Compaction diffusion has little effect on the effective diffusion range. In this paper, the duration of pore plugging is taken as the flow time of the polymer. At this moment, the peripheral pressure at test points 2-5 decreases as the slurry diffusion process stops, preventing the diffusion pressure from spreading. Since the slurry still reacts to compact the pores, the peripheral pressure at test point 1 increases 60 s later, and the time when the peripheral pressure at test points 2-5 starts to decrease is the time when the flow of the polymer slurry ends.

Figure 13
Spatiotemporal evolution of peripheral pressure in the center point test
pic

Figure 13 also illustrates the mechanism by which the peripheral pressure rapidly decreases with distance at 60 and 100 s. The peripheral pressure at test points 2-5 at 20 s is greater than that at 60 s and 100 s because the expansion of the slurry causes the sand-gravel skeleton to gradually compact, and the starting pressure required for polymer flow increases accordingly. Water flow is inhibited by slurry expansion at 60 and 100 s because the slurry plugs the pores and the seepage channel.

Since the peripheral pressure evolution curves at test points 2-5 in each test group exhibit the same trend, in this paper, the peripheral pressure evolution curve at test point 2 is selected to explore the impacts of the DWPP, grouting amount and the homogeneity of the particle size distribution on the flow time of the polymer slurry. Based on the above analysis, the time when the peripheral pressure starts to decrease on the peripheral pressure curve at test points 2-5 is the time when the polymer flow stops. The peripheral pressure evolution curves over time at test point 2 of groups 1, 2 and 7 with varying DWPPs are depicted in Figure 14. After approximately 60 s, the pressure is passed while the DWPP is 0.013 MPa. The flow time is approximately 80 s when the DWPP strength is 0.03 MPa. After approximately 120 s, the DWPP reaches 0.047 MPa. Figure 14 illustrates the mechanism by which an increase in the DWPP can greatly extend the polymer flow time. This extension occurs because water flow can increase the length of the polymer slurry in liquid state. Simultaneously, water flow can inhibit the foaming reaction, making it harder for the slurry to expand and block the pores, which leads to an early end of the flow.

Figure 14
Influence of dynamic pump pressure on the peripheral pressure of test point 2
pic

Figure 15 depicts the change in peripheral pressure at test point 2 over time with varying grouting amounts. Figure 15 illustrates the mechanism by which the grouting amount increases and the polymer flow time decreases. On the one hand, as the amount of grouting increases, the concentration of the two components of the polymer increases, which accelerates the reaction rate and ultimately shortens the time needed for the liquid polymer to form. On the other hand, as the slurry expands, it becomes much easier to compact the sand-gravel skeleton, which leads to the rapid end of slurry diffusion due to seepage channel blockage.

Figure 15
Influence of grouting amount on peripheral pressure of test point 2
pic

Figure 16 shows the change in peripheral pressure at test point 2 with time under different particle size distribution. Based on the examination of the correlation between peripheral pressure and polymer flow time, Figure 16 shows that the slurry diffusion time decreases with the more uniform of sand particle size distribution. The reason for this trend is that as the sand particle size distribution becomes more uniform, the pore distribution also becomes relatively uniform and the pore size becomes smaller. Under the same DWPP, the pore water flow rate and slurry flow rate decrease rapidly, that is, when the sand particle size distribution is more uniform, the flow of flowing water and slurry is hindered greatly, the pore water and slurry flow rate become relatively smaller, and the mud is less affected by scour of flowing water. However, the slurry is less affected by the dilution of pore water, the slurry concentration becomes larger, the slurry is easier to expand, and the pore channel is easier to block by slurry expansion. As a result, the slurry flow time is reduced. Correspondingly, with the less uniform of sand particle size distribution, the pore distribution is relatively uneven, and the pore increases. Under the same DWPP, the flow of flowing water and slurry is hindered minimally, and the flow rate of pore water and slurry decreases slowly, that is, the less uniform the sand particle size distribution, the larger the flow rate of pore water and slurry. The slurry is greatly affected by pore water dilution, the slurry flow time becomes longer, the reaction is slower, and in addition, the slurry is less likely to bubble and expand. Moreover, the pore distribution is relatively uneven and the pore size increases, and the the pore is less likely to be blocked, leading to the early termination of slurry diffusion.

Figure 16
Influence of the homogeneity of the particle size distribution on the peripheral pressure of test point 2
pic

Figure 17 shows the spatial evolution of the peripheral pressure under different DWPPs for 60 s. As shown in Figure 17, the peripheral pressure at test points 1-2 decreases rapidly under the three working conditions. This rapid decrease arises because slurry diffusion occurs before test point 1, the disturbance to test points 2-5 is low, and the peripheral pressure decreases quickly with distance. In addition, test points 1-2, indicate an increase in peripheral pressure; test points 2-5 indicate a decrease in peripheral pressure with a decrease in DWPP. This phenomenon is caused by the rapid reaction of the slurry under a low DWPP, which leads to foam expansion, compaction of the pores and a decrease in the porosity of the sand-gravel skeleton. Furthermore, the start-up pressure that slurry expansion and diffusion must overcome increases. Because the grout blocks the pores, which leads to blockage of the water flow and transmission pressure, the peripheral pressure at the subsequent test point decreases.

Figure 17
Influence of dynamic water pump pressure on the spatial evolution of peripheral pressure
pic

The spatial changes in the peripheral pressure at 60 s under the various grouting amounts are shown in Figure 18. Figure 18 shows the mechanism by which the peripheral pressure gradient at test points 1-2 increases and the peripheral pressure at test points 2-5 decreases as the grouting amount increases. These changes occur because as the amount of grouting increases, the slurry reaction is accelerated, which leads to a stronger compaction effect on the sand-gravel skeleton, manifested as greater peripheral pressure. With increasing slurry volume, the expansion volume increases, and the seepage channel is more easily blocked, eventually leading to the blockage of water pressure transmission. Therefore, the peripheral pressure at test points 2-5 decreases. Correspondingly, with decreasing grouting amount, the grout expansion volume decreases, which not only reduces the compaction effect but also reduces the starting pressure to be overcome, and the pressure gradient at test points 1-2 decreases. As the expansion volume of the slurry decreases, the pores are less likely to be blocked, which ensures smooth pressure transmission and increases the slurry flow.

Figure 18
Influence of grouting amount on the spatial evolution of peripheral pressure
pic

The spatial changes in the peripheral pressure at 60 s under the different particle size distributions of sand and gravel are displayed in Figure 19. It can be seen from Figure 19 that the more uniform the gradation of sand and stone particles, the greater the drop in peripheral pressure from test point 1 to test point 2. This phenomenon results from the more uniform size distribution of sand and gravel, the distribution of pores size and spatial locations becomes relatively uniform, the flow speed of pore water and slurry decreases rapidly, and the pressure at position 1 is relatively greater. Under the same water pressure, the slurry expansion is inhibited by contraction. The narrower the pore channel is, the easier it is to be blocked, and the deeper channel is more likely to be blocked, which further leads to poor pressure transmission. The pressure at position 2 is relatively small. Correspondingly, when the distribution of sand and gravel becomes less uniform, the pore distribution is complex and the pore is relatively large, grout and flow first fill the pore, the flow speed of pore water and slurry is slowly reduced, leading to a smaller pore water flow rate, and the pressure at position 1 is relatively small. The greater the inhibition of slurry expansion is, the more difficult it is to expand and clog the pores, and the less the influence of pressure transmission channel. The position 2 by the pressure is relatively small.

Figure 19
Influence of the homogeneity of the particle size distribution on spatial evolution of peripheral pressure
pic
3.2.2 Spatiotemporal variation in the WPR

Figure 20 shows the real-time WPRs at different test points in the centre point test. Figure 20 shows that the steady WPR value decreases from test point 1 to test point 5 and that the evolution trends of the WPR at the various test points are similar. This phenomenon occurs because when the internal water flow rate is high, the water flow rate can transmit flow field information to each position of the diffuser in the 20 s time interval, and the WPRs at different test points change synchronously. The water blocking effect worsens with increasing distance from the grouting spot, which is commensurate with the results from real-world engineering projects.

Figure 20
Temporal and spatial evolution of water plugging rate in the center point test
pic

Figure 21 shows the spatial variation curves of the WPRs for various DWPPs. According to Figure 21, the WPRs at test points 1-2 dramatically decrease at a DWPP of 0.013 MPa. This decrease occurs due to the low DWPP, and the slurry reacts quickly. The slurry reaction is characterized by rapid foaming and blocking. The flow field at test point 1 changes dramatically, and the flow field flow rate decreases sharply. However, the flow field change information is not transferred to a later position within 20 s. The WPRs at test points 1-2 rapidly decrease, and as indicated by the above study, flow field in WPR change has delayed.

Figure 21
The influence of dynamic water pump pressure on the spatial evolution of water plugging rate
pic

Figure 22 shows the spatial variation in the WPR under the different grouting amounts. Figure 22 shows that the WPRs of test points 1-2 change dramatically when the amount of grouting is 878 g, but the other test points change more subtly. When grouting is applied in high quantities, the polymer slurry response at the same DWPP is less influenced by dynamic water. This phenomenon causes the reaction to foam and to swell violently, immediately plugging the seepage channel. Due to the intense reaction, the flow field information cannot be transmitted to a later position in time, and the WPR decreases rapidly.

Figure 22
Influence of grouting volume on the spatial evolution of water plugging rate
pic

Figure 23 shows the spatial variation in the WPR under the impacts of different particle size distributions. According to Figure 23, when size distribution of the sand and gravel III is the most uniform, the WPRs at test points 1-2 decrease significantly because the characteristics of the sand and gravel Ⅲ are relatively uniform pore distribution, pore is relatively reduced, the pore water and slurry flow rate decreases relatively quickly. At the same time, the diffusion range of slurry is relatively small, and the slurry concentration is opposite bigger, so slurry influenced by water dilution is reduced, and the slurry has strong reaction. The pores are more likely to be blocked. According to the above analysis, the instantaneous sealing effect of the slurry on the pores leads to the delayed transmission of flow field information.

Figure 23
Influence of the homogeneity of the particle size distribution on spatial evolution of water plugging rate
pic

4 Conclusions

In this paper, spatiotemporal data on peripheral pressure and the WPR collected during diffusion tests are used to analyze the influences of the DWPP, particle size distributions, and grouting amount on the slurry diffusion flow time, dynamic response, and spatiotemporal distribution of the WPR. The following conclusions can be drawn.

1) Under poor dynamic pump pressure or a large grouting amount, an excessive expanding force of the slurry can significantly change the local structure of the sand–gravel skeleton, ultimately leading to the dissipation of diffusion energy towards local macropores and a decrease in peripheral pressure. With increasing DWPP, the less uniform size distribution of sand and gravel, and decreasing grouting amount, due to the low expansion force of the polymers, the squeezing effect of the slurry on sand and gravel is relatively small, which in turn makes it easier for diffusion energy to dissipate into the pores and decrease the peripheral pressure. The cementitious reaction that occurs after slurry diffusion stops compacts the sand-gravel skeleton, and the peripheral pressure curve shows a secondary increase.

2) With the increase in grouting amount and the more uniform size distribution of sand and gravel, the DWPP decreases, resulting in not only a faster slurry reaction but also a shorter time to reach the WPR inflection point.

3) The blockage effect of slurry expansion on pores under low DWPPs, high grouting amounts, and the more uniform size distribution of sand and gravel can significantly hinder the transmission of pressure, leading to a rapid decrease in peripheral pressure with distance.

4) The WPR decreases with increasing distance. Instantaneous pore plugging caused by a relatively large grouting amount, the more uniform size distribution of sand and gravel and low DWPP lead to delayed flow field plugging and information transmission.

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注释

DU Xue-ming, LIU Chang, MENG Xin-xin,FANG Hong-yuan, RUI Yi-chao, LI Bin, ZHAI Ke-jie, ZHANG Chao, DU Ming-rui,XUE Bing-han,WANG Shan-yong and WANG Fu-ming declare that they have no conflict of interest.

DU Xue-ming, LIU Chang, MENG Xin-xin, RUI Yi-chao, FANG Hong-yuan, LI Bin, ZHAI Ke-jie, ZHANG Chao, DU Ming-rui, XUE Bing-han, WANG Shan-yong, WANG Fu-ming. Diffusion law of nonaqueous reactive expansive polymers in sand and gravel media [J]. Journal of Central South University, 2025, 32(2): 420-436. DOI: https://doi.org/10.1007/s11771-025-5901-y.

杜雪明,刘畅,孟欣欣等.非水反应类高聚物在富水砂砾石中的注浆扩散规律试验研究[J].中南大学学报(英文版),2025,32(2):420-436.