Rock Reinforcement by Stepwise Injection of Two-Component Silicate Resin

Our research aims to improve the efficiency of the reinforcement of loose rocks with two-component polymer resins. The standard approach consists of the injection of two pre-mixed components into a rock massive. We propose a stepwise injection of individual components of a resin into the rock and deep extrusion of the solutions into the rock by gas between the injection stages. The experimental results indicate that the proposed method provides a reduction of polymer consumption per unit volume of the rock, and an increase in the impregnation depth, area of the resin impact, and the reinforced rock volume in comparison with the conventional method of prepared resin solution injection. The cured resin partially fills the sand rock pore space, binds the grains, and acts as a reinforcing frame. The highest reinforcement is achieved with the sequential stepwise injection of the resin by separate small portions of each component. We have shown the uniaxial compressive strength is on average more than twice as high that obtained with the conventional injection method. This can be explained by higher fracture toughness of the reinforced rock with a flexible hardened network of the cured resin in the structure.


Introduction
We consider a method of rock reinforcement by two-component synthetic polymer resins. Synthetic polymer resins are widely used to reinforce rocks and soils. Our twocomponent polymer resin reinforcement consists of the injection of two pre-mixed components into a rock massive at the required depth. The components are mixed inside hydraulic system of injection equipment and pumped through pre-formed holes. The injection sites are selected according to rock type, groundwater level, etc. [1][2][3][4][5]. A thorough mixing of the resin components is crucial. A chemical reaction of the two mixed components inside a rock causes a cure of injected liquid polymer resin solution [6][7][8][9]. The advantages of the two-component resin reinforcement method are the rock stabilization under high loads and movements, performance, and the cure time control by varying catalyst content, etc. An effectiveness of the injection reinforcement is determined by radius/depth of an impregnation, which is directly affected by the path of resin solution penetration. During the injection the resin solution should penetrate through the rock pores, distributing a homogeneous mixture over the pore space [10][11][12][13]. The loose rock impregnation depth and the injected composition distribution depend on many factors, such as rock type, hydraulic conductivity, density, particle size distribution, injection pressure, dynamic viscosity of the resin solution, temperature of the mixed components, injected resin amount, etc. [14][15][16]. Let us observe some major phenomena and the related research of the considered method of rock reinforcement by resin injection.
The particle size of granular formations and rock permeability influence the distribution of the resin solution around the injection point. To maintain the composition flow rate can be compared to low permeable clays. It shows great potential for use as an injectable hydraulic barrier [26,27]. The operational parameters of a different nanosilica-improved soils are studied after curing. The results of the uniaxial compression tests, the indirect tensile tests, and the direct shear tests allow us to estimate the potential of colloidal nanosilica and on the differences between the chemicals [28,29]. A laboratory study of crushed shale rock grouting with a two-component polyurethane composition under pressure is presented in [30]. The study includes measuring of the grouting pressure in the pump inside the reservoir with rock, volume of solution and its distribution in the rock. Initial conditions that could affect ultrafine and acrylate grout application effectiveness are studied by [31] The initial conditions are soil grain size and in situ moisture content. A dependence of grouting time on sand water saturation is studied [31]. A new type of permeable polymer material for grouting anti-seepage reinforcement of dam slopes is proposed in [32]. The analysis of the safety factor and failure probability of different types of slope before and after reinforcement, shows that the safety factor of the slope can be greatly improved after the slope is reinforced with permeable polymer grouting, but as the slope height increases, the reinforcement effect decreases gradually. In general, for medium and low slopes, the improvement effect of safety factor can reach about 50% [32].
As can be seen from the above review, there are many ways to optimize the effectiveness of the reinforcement for a specific application by handling a number of parameters. We suggest a more general approach to improve the two-component polymer resin reinforcement method, namely a component-by-component stepwise injection into the rock instead of pre-mixed solution injection. Due the proposed stepwise injection scheme, the reaction between components and the curing of the polymer resin occurs directly in the rock volume, which happens to be more advantageous. The efficiency of resin polymerization depends on a mixing uniformity and a distribution of reagent molecules in the prepared composition volume. A heterogeneity of the mixture impairs the interaction of substances, especially for quick setting polymer resins. At the same time, the usage of quick setting two-component polymer resins for rock reinforcement is complicated by a high viscosity of their pre-polymers, a limited injection volume due to the quick cure time, an increased reactivity of individual components, etc. These factors lead to decrease of the rock impregnation volume and contamination of the injection equipment [12,30]. The proposed stepwise injection method eliminates these problems. We also further enhance our approach by extrusion of the individual components of polymer resin deep into the rock by nitrogen between the injection stages. In order to advocate our scheme, we perform a series of laboratory tests.

Sand
Laboratory tests were carried out with pretreated fine sand samples. The sand was singled out near Novosibirsk city, Russia. The pretreatment includes a determination of the particle size distribution, absolute and bulk density, void ratio, etc. [33,34]. The sand is sieved through a set of sieves and the sand particle size distribution is determined. A portion of the sand with a particle size less than 0.42 mm is about 80 wt. % (D 80 , Figure 1). An average grain size is 0.27 mm (D 50 , Figure 1). The specific values of gravity and bulk density of the dry sand are 2.6 g/cm 3 and 1.6 g/cm 3 , respectively. The void ratio is 0.66.

Two-Component Silicate Resin
We use a non-expanding elastified two-component silicate resin in our expe The resin was designed to reinforce loose and disturbed rocks, to fill voids in a ro to waterproof mines, etc. The two-component silicate resin is formed by mixing components (A and B) in a 1:1 volume ratio. The component A consists of sodium solution (supplier is TEKC company, Saint Petersburg, Russia), distilled water, (supplier is Himreakt Co., Moscow region, Russia) and contains an addition of (2,2-Dimorpholinodiethylether) catalyst (0.8 wt.%) (supplier is Haihang Indus Ltd., Jinan City, China). The component B is a mixture of polymethylene polyphe cyanate (supplier is Yantai Wanhua Polyurethans Co., Yantai City, China) and phthalate (supplier is Himreakt Co.) (Table 1). Conventionally, mixed componen B are injected into the rock in a volume ratio of 1:1. A part of the isocyanate rea water, which is contained in an aqueous sodium silicate solution of the compo With the non-foaming elastified silicate isocyanate resin, the carbon dioxide is sca by sodium hydroxide forming soda and simultaneously causing the precipitatio con dioxide. The other part of the isocyanate reacts with each other, yielding a po anurate. Thus, both the silicate and the isocyanate form separate polymer network penetrate each other. The thorough mixing of the two components is required t an emulsion of sodium silicate in the isocyanate component and to form a homo product [35]. An aqueous sodium silicate solution, being a strong alkali, intera with mineral grains, especially with carbonates and minerals of the gypsum gro result, the accelerated saturation of the reinforced rock with the resin solution oc Table 1. Initial materials for silicate resin components.

Two-Component Silicate Resin
We use a non-expanding elastified two-component silicate resin in our experiments. The resin was designed to reinforce loose and disturbed rocks, to fill voids in a rock mass, to waterproof mines, etc. The two-component silicate resin is formed by mixing of two components (A and B) in a 1:1 volume ratio. The component A consists of sodium silicate solution (supplier is TEKC company, Saint Petersburg, Russia), distilled water, glycerol (supplier is Himreakt Co., Moscow region, Russia) and contains an addition of DMDEE (2,2-Dimorpholinodiethylether) catalyst (0.8 wt.%) (supplier is Haihang Industry Co., Ltd., Jinan City, China). The component B is a mixture of polymethylene polyphenyl isocyanate (supplier is Yantai Wanhua Polyurethans Co., Yantai City, China) and dibutyl phthalate (supplier is Himreakt Co.) (Table 1). Conventionally, mixed components A and B are injected into the rock in a volume ratio of 1:1. A part of the isocyanate reacts with water, which is contained in an aqueous sodium silicate solution of the component A. With the non-foaming elastified silicate isocyanate resin, the carbon dioxide is scavenged by sodium hydroxide forming soda and simultaneously causing the precipitation of silicon dioxide. The other part of the isocyanate reacts with each other, yielding a polyisocyanurate. Thus, both the silicate and the isocyanate form separate polymer networks, which penetrate each other. The thorough mixing of the two components is required to obtain an emulsion of sodium silicate in the isocyanate component and to form a homogeneous product [35]. An aqueous sodium silicate solution, being a strong alkali, interacts well with mineral grains, especially with carbonates and minerals of the gypsum group. As a result, the accelerated saturation of the reinforced rock with the resin solution occurs. The considered resin is applied in mining and underground building. Start and finish times of the resin polymerization (after mixing of components A and B) were experimentally established with a 0.8 wt.% catalyst content. The start and finish times are 135-150 s and 210-240 s at 25 • C, respectively. A foaming factor of the two-component silicate resin is equal to 1. Uniaxial compression tests of the cured resin were carried out under loading rate of 0.5 mm/min on cylindrical samples with a diameter of 37 mm and a length of 75 mm ( Figure 2). An initial stage of the loading (strain is approximately 0.00-0.03) is characterized by a linear «stress-strain» curve (section I, Figure 2c). Then, as is typical for elastomers, the stress increases more slowly (strain is approximately 0.03-0.15; section II, Figure 2c) due to a breaking of bonds between macromolecules [37,38]. Then, the stress increases more quickly due to a reorientation of macromolecules depending on a direction of loading (section III, strain starts from 0.15, Figure 2c), and it continues until uniaxial compressive strength of the sample is reached. The uniaxial compressive strength of the cured two-component silicate resin is 20-23 MPa (Table 2). Table 2. Properties of two-component silicate resin [39].

Parameter Value
The volume ratio of components A and B for mixing 1:

Methods
We propose and experimentally test a method of sand rock reinforcement by a sequential separate stepwise injection of polymer resins. A laboratory stand was developed to carry out experiments. The stand consists of a test chamber, a two-channel hydraulic station to pump resin components, and a pneumatic system to extrude solutions with compressed gas into the rock. The test chamber is a metal case (1) with a cover (2), containing three inlets to connect injection hydraulic hoses and a compressed gas supply line. A replaceable plastic cylindrical shell (3) with an outer diameter of 10 cm and a wall thickness of 4 mm is placed in the case (1). A sand sample is placed inside a plastic shell (3). Its diameter is 9.2 cm, height is up to 30 cm. The ends of the sample are covered with perforated permeable plates (4), which form a flat resin filtration front and prevent the sand from escaping. In a bottom of the case there is an outlet (5) to drain remains of the solutions. The system of pumping the solutions into the rock samples provides both one-shot and two-shot injection of polymer solutions. During the one-shot injection, the components are pumped into a mixer (6) at the same time. A vortex mixing of the pumped solutions provides uniform distribution of their molecules in the prepared resin ( Figure 3). During the two-shot injection each component of the two-component polymer resin solution is sequentially pumped. After the injection of each component, it is extruded into the rock with compressed nitrogen. The range of injection pressure is from 0.01 to 1.5 MPa.
The considered resin is applied in mining and underground building. Start and finish times of the resin polymerization (after mixing of components A and B) were experimentally established with a 0.8 wt.% catalyst content. The start and finish times are 135-150 s and 210-240 s at 25 °C, respectively. A foaming factor of the two-component silicate resin is equal to 1. Uniaxial compression tests of the cured resin were carried out under loading rate of 0.5 mm/min on cylindrical samples with a diameter of 37 mm and a length of 75 mm ( Figure 2). An initial stage of the loading (strain is approximately 0.00-0.03) is characterized by a linear «stress-strain» curve (section I, Figure 2c). Then, as is typical for elastomers, the stress increases more slowly (strain is approximately 0.03-0.15; section II, Figure 2, c) due to a breaking of bonds between macromolecules [37,38]. Then, the stress increases more quickly due to a reorientation of macromolecules depending on a direction of loading (section III, strain starts from 0.15, Figure 2c), and it continues until uniaxial compressive strength of the sample is reached. The uniaxial compressive strength of the cured two-component silicate resin is 20-23 MPa (Table 2).  The experimental procedure of the stepwise injection includes several stages: 1.
An installation of the replaceable cylindrical shell with a sand rock sample in the test chamber.

2.
A preparation of the required volume of component A of the resin solution and its injection into the rock sample. The component A is pumped in two ways. The first one is the sequentially pumping of small portions of the component A. To increase the impregnation of the sand rock the system is kept under pressure after each injection stage (Figure 4a). The second pumping approach is the injection of the full volume of the component A into the rock (Figure 4b).

3.
A pumping of the compressed nitrogen through the rock sample to extrude the injected component A deep into the rock (Figure 4a,b).

4.
A preparation and an injection of the component B into the rock sample. The component B is also pumped in the same two ways as the component A (see p.2). The injection schemes are shown in Figure 4a,b.

5.
A pumping of the compressed nitrogen through the rock sample to extrude the injected component B deep into the rock (Figure 4a,b). 6.
A time delay, which is required for the complete polymerization and achieving of sufficient strength properties of the cured resin.
ness of 4 mm is placed in the case (1). A sand sample is placed inside a plastic shell (3). I diameter is 9.2 cm, height is up to 30 cm. The ends of the sample are covered with perf rated permeable plates (4), which form a flat resin filtration front and prevent the san from escaping. In a bottom of the case there is an outlet (5) to drain remains of the sol tions. The system of pumping the solutions into the rock samples provides both one-sh and two-shot injection of polymer solutions. During the one-shot injection, the comp nents are pumped into a mixer (6) at the same time. A vortex mixing of the pumped sol tions provides uniform distribution of their molecules in the prepared resin ( Figure 3 During the two-shot injection each component of the two-component polymer resin sol tion is sequentially pumped. After the injection of each component, it is extruded into th rock with compressed nitrogen. The range of injection pressure is from 0.01 to 1.5 MPa.

Figure 3.
Test chamber of the laboratory stand to reinforce loose rocks: 1-metal case; 2-cover co taining three inlets to pump solutions and compressed gas into a rock; 3-cylindrical shell; 4-pe forated permeable plates; 5-outlet; 6-mixer; 7-receptacle.  The injection of prepared two-component silicate resin solution has also been studied. The resin solution is pumped immediately after mixing components A and B in a 1:1 volume ratio. The experimental procedure includes several stages: • An installation of the replaceable cylindrical shell with a rock sample in the test chamber.

•
Mixing the equal volumes of the two-component silicate resin components A and B. The injection of the prepared resin solution into the rock sample with a time delay at the maximum value of the injection pressure ( Figure 5). • A time delay, which is required for the complete polymerization and achieving sufficient strength properties of the cured resin.  The injection of prepared two-component silicate resin solution has also been studied. The resin solution is pumped immediately after mixing components A and B in a 1:1 volume ratio. The experimental procedure includes several stages:

•
An installation of the replaceable cylindrical shell with a rock sample in the test chamber.

•
Mixing the equal volumes of the two-component silicate resin components A and B. The injection of the prepared resin solution into the rock sample with a time delay at the maximum value of the injection pressure ( Figure 5). • A time delay, which is required for the complete polymerization and achieving sufficient strength properties of the cured resin.
The total volume of the resin solution is 220 cm 3 for all considered injection schemes, which is 1.4-1.5 times less than the pore volume of the sand rock sample. The injection pressure is 0.5 MPa. This is enough to pump the selected volume of resin components or the prepared resin. In the case of portioned injection, the volume of one portion of each component (A and B) is 20-22 mL. The time delay of the system under the pressure after injection of the next portion is 60 s. Both in the case of the stepwise portioned injection and the full volume injection of the A and B components a compressed nitrogen is pumped through the sample to extrude the resin components deep into the rock at a pressure of 0.5 MPa. The injection of the prepared resin solution lasts 10 min. The cylindrical shell with impregnated rock is left for 24 h. Then the reinforced rock is extracted for the laboratory tests. We estimate the volume of the reinforced rock and perform a microstructural analysis of the obtained samples.

•
An installation of the replaceable cylindrical shell with a rock sample in the test chamber.

•
Mixing the equal volumes of the two-component silicate resin components A and B The injection of the prepared resin solution into the rock sample with a time delay at the maximum value of the injection pressure ( Figure 5). • A time delay, which is required for the complete polymerization and achieving suf ficient strength properties of the cured resin.  We use scanning electron microscopy to determine the structural features of the reinforced sand rock samples. Samples are studied using a MIRA 3 LMU scanning electron microscope. We use this method to establish a relationship between the spatial distribution of sand grains and aggregates of the cured polymer resin. The sand grains, the cured polymer aggregates, structure heterogeneities, and voids, etc., are identified on the core scale [40]. In addition, the inter-granular distance is determined to estimate the compaction of bulk sand rock as a result of the resin injection. To characterize the filling of voids in the reinforced rock, a quantitative porosity estimation on basis of the obtained images fragments is performed [41].
We also perform deformation-strength tests of the reinforced sand. 3 cm diameter and length cylindrical samples are drilled out. They are used for uniaxial compression tests with an INSTRON 8802 servo-hydraulic press. We implement a speed-controlled traverse to measure and record the applied force and deformation [42,43]. All tests are made at a constant traverse speed of 0.5 mm/min. The samples are loaded up to their destruction. As a result, the uniaxial compressive strength is determined.

Results and Discussion
We consider two methods of two-component silicate resin rock reinforcement: the stepwise component-by-component injection, which is a novel approach, and the injection of a prepared two-component mixture. We study and compare the distributions of the cured resin in sand pore space. In the case of the stepwise injection with the extrusion of the components with compressed nitrogen deep into the rock, the cured resin forms films on mineral grains, which partially fill the pores. It happens both when the resin components are injected by portions and in the full volume. The films of the cured resin form aggregates, which provide an adhesion of sand grains, and form a reinforcing three-dimensional frame, which connects mineral grains into aggregates ( Figure 6). We observed large inter-granular voids in the reinforced rock. Also, we observed small voids, which are localized in the cured silicate resin. An average size of the large inter-granular voids is 41 µm with an inter-void distance of 204 µm. The size of small pores is about 8 times smaller than the large ones ( Figure 6). A residual porosity of the sand rock, reinforced by the stepwise injection of two-component silicate resin, is 5.8-12% with an average of 9%. An average distance between sand grains in the reinforced rock samples is about 245 µm. In the case of the sand reinforcement by prepared two-component silicate resin solution the structure of the obtained samples is more homogeneous. The cured polymer resin almost completely fills the pore space of the reinforced rock (Figure 7). Residual voids are small closed pores inside the cured resin and near the surface of the sand grains. The porosity is 2-4.5% with an average of 3.4%. The average void size is 5 µm with a distance between voids of 32 µm (Figure 7). The average distance between sand grains in 253 µm. It can be noted that the sizes of the closed voids inside the cured silicate resin for both considered methods of the resin injection are similar, with average values of 4-5 µm. The stepwise injection of the two-component polymer silicate resin (both injection in portions and injection of the full volume of each component) with the compressed nitrogen driven extrusion provides 42% reinforcement of the sand sample. The injection of the prepared silicate resin provides 14% reinforcement of the sand sample. The stepwise injection increases the impregnation depth and the volume of the reinforced rock by a factor of approximately 3, compared with the injection of the prepared silicate resin. The average polymer consumption per unit volume of the reinforced sand rock is 0.37 with the stepwise injection and 0.29 with the injection of the prepared silicate resin solution. The lower penetration of the prepared resin is probably due an increase of its viscosity during polymerization after mixing the components. Dynamic viscosities of the unmixed compo-nents A and B are 137 mPa·s and 135 mPa·s respectively for temperature 25 • C [30]. The experimentally determined viscosity of the prepared polymer silicate resin is approximately 3000 mPas in 10 s after mixing the A and B components and increases up to 8400 mPas in 80 s.
The efficiency of the considered methods of the two-component silicate resin injection is estimated according to the strength tests of the reinforced sand samples. The results of the stepwise injection of the two-component silicate resin are shown in Figure 8. The results of the prepared two-component silicate resin injection are shown in Figure 9. The analysis of the obtained experimental data indicates that the stepwise injection of the two-component silicate resin with the extrusion of the components by compressed nitrogen provides the higher mechanical strength of the reinforced sand. The highest uniaxial compressive strengths are achieved by the sequential pumping of the small volumes of the components A and B with a retention of the system under the pressure after each stage, which increases the impregnation of the sand rock ( Figure 8; the injection scheme is shown in Figure 4a). The average uniaxial compressive strength is 19,4 MPa, which is 1.6 times higher than the value, obtained for sand, reinforced with the stepwise injection of the full volumes of components A and B ( Figure 8; the injection scheme is shown in Figure 4b).
Polymers 2022, 14, 5251 12 of 16 provides the higher mechanical strength of the reinforced sand. The highest uniaxial compressive strengths are achieved by the sequential pumping of the small volumes of the components A and B with a retention of the system under the pressure after each stage, which increases the impregnation of the sand rock ( Figure 8; the injection scheme is shown in Figure 4a). The average uniaxial compressive strength is 19,4 MPa, which is 1.6 times higher than the value, obtained for sand, reinforced with the stepwise injection of the full volumes of components A and B ( Figure 8; the injection scheme is shown in Figure 4b).
The uniaxial compressive strength of sand, reinforced by the injection of the prepared two-component silicate resin solution, is on average 7.4 MPa, which is significantly lower than the values obtained for the sand, reinforced by a stepwise injection of a two-component polymer resin ( Figure 9; the injection scheme is shown in Figure 5). At the same time, the sand impregnated with the prepared resin solution, withstands more significant longitudinal deformations. The uniaxial compressive strength is reached at strain 0.35-0.75, while the same parameter for the stepwise injection is reached at strain 0.18-0.25 ( Figures  8 and 9). The ascending curves of the stress-strain diagrams of the reinforced sand show that the stress increment increases from the certain load. We observe the similar stressstrain dependence for the cured two-component silicate resin, which has the properties of the elastomer. However, if the stress increment is noticeable from a stress of 6-8 MPa for the samples of the cured resin, then for the reinforced sand the increment begins at 1.5-3 MPa (Figures 8 and 9). Thus, the reinforced rock exhibits the properties inherent in elastomers, but less than the cured polymer resin.  Figure 4a); grey curves-stressstrain diagrams for the sand reinforced by the stepwise injection of the full volumes of components A and B into the rock and their extrusion by compressed nitrogen deep into the rock (the injection scheme is shown in Figure 4b).  Figure 4a); grey curves-stress-strain diagrams for the sand reinforced by the stepwise injection of the full volumes of components A and B into the rock and their extrusion by compressed nitrogen deep into the rock (the injection scheme is shown in Figure 4b). The performed deformation-strength tests demonstrate that the best sand reinforcement is achieved with the stepwise injection of the two-component silicate resin by small portions of each component, combined with their extrusion by compressed nitrogen. Compared with conventional methods, the proposed one provides a higher strength of the reinforced rock at lower specific consumption of the polymer resin per rock volume. This can be explained by the higher fracture toughness of the rock, reinforced with a flexible hardened framework, which is formed of thin films of the cured polymer resin mainly located on the surfaces of the rock grains that bind individual grains into consolidated rock aggregates. In case of the prepared solution injection, a more homogeneous, brittle structure with a continuous filling of the pore space with a polymer resin is observed. Thus, a higher crack resistance is achieved for the stepwise injection. The proposed stepwise sequential injection provides the reduction of the resin consumption per unit volume of the reinforced rock while improving its physical and mechanical properties.

Conclusions
We improve the method of the physical and chemical reinforcement of loose and disturbed rocks by the injection of the two-component polymer resins instead of the injection of two pre-mixed components, which is a conventional approach. We suggest the sequential stepwise injection of the two components of the polymer resin with the extrusion of each component by compressed gas deep into the rock. Due this injection scheme, the reaction between components and the curing of the polymer resin occurs directly in the rock volume, which is advantageous.
We experimentally studied the proposed method and compared it with the conventional one. A series of laboratory tests on fine sand samples were performed and several results have been obtained: • The reduction of polymer consumption per unit volume of the reinforced rock in comparison with the conventional method of prepared resin solution injection is observed. The increase of impregnation depth and the triple increase of the reinforced rock volume are observed.

•
As seen in Figure 6, the cured polymer resin partially fills the sand pore space, binds the grains, and affects the reinforcing frame. As the result, large voids, located in the rock inter-granular space, are formed. Their size is on average 8 times larger than the small pores, which are located in the structure of the cured silicate resin; The uniaxial compressive strength of sand, reinforced by the injection of the prepared two-component silicate resin solution, is on average 7.4 MPa, which is significantly lower than the values obtained for the sand, reinforced by a stepwise injection of a twocomponent polymer resin ( Figure 9; the injection scheme is shown in Figure 5). At the same time, the sand impregnated with the prepared resin solution, withstands more significant longitudinal deformations. The uniaxial compressive strength is reached at strain 0.35-0.75, while the same parameter for the stepwise injection is reached at strain 0.18-0.25 (Figures 8 and 9). The ascending curves of the stress-strain diagrams of the reinforced sand show that the stress increment increases from the certain load. We observe the similar stress-strain dependence for the cured two-component silicate resin, which has the properties of the elastomer. However, if the stress increment is noticeable from a stress of 6-8 MPa for the samples of the cured resin, then for the reinforced sand the increment begins at 1.5-3 MPa (Figures 8 and 9). Thus, the reinforced rock exhibits the properties inherent in elastomers, but less than the cured polymer resin.
The performed deformation-strength tests demonstrate that the best sand reinforcement is achieved with the stepwise injection of the two-component silicate resin by small portions of each component, combined with their extrusion by compressed nitrogen. Compared with conventional methods, the proposed one provides a higher strength of the reinforced rock at lower specific consumption of the polymer resin per rock volume. This can be explained by the higher fracture toughness of the rock, reinforced with a flexible hardened framework, which is formed of thin films of the cured polymer resin mainly located on the surfaces of the rock grains that bind individual grains into consolidated rock aggregates. In case of the prepared solution injection, a more homogeneous, brittle structure with a continuous filling of the pore space with a polymer resin is observed. Thus, a higher crack resistance is achieved for the stepwise injection. The proposed stepwise sequential injection provides the reduction of the resin consumption per unit volume of the reinforced rock while improving its physical and mechanical properties.

Conclusions
We improve the method of the physical and chemical reinforcement of loose and disturbed rocks by the injection of the two-component polymer resins instead of the injection of two pre-mixed components, which is a conventional approach. We suggest the sequential stepwise injection of the two components of the polymer resin with the extrusion of each component by compressed gas deep into the rock. Due this injection scheme, the reaction between components and the curing of the polymer resin occurs directly in the rock volume, which is advantageous.
We experimentally studied the proposed method and compared it with the conventional one. A series of laboratory tests on fine sand samples were performed and several results have been obtained:

•
The reduction of polymer consumption per unit volume of the reinforced rock in comparison with the conventional method of prepared resin solution injection is observed. The increase of impregnation depth and the triple increase of the reinforced rock volume are observed. • As seen in Figure 6, the cured polymer resin partially fills the sand pore space, binds the grains, and affects the reinforcing frame. As the result, large voids, located in the rock inter-granular space, are formed. Their size is on average 8 times larger than the small pores, which are located in the structure of the cured silicate resin; • The higher strength properties at lower specific resin consumption per unit volume of the rock are observed. As seen in Figures 8 and 9, the uniaxial compressive strength is on average more than 2 times higher than that obtained with the conventional injection method. The highest reinforcement efficiency is achieved with the sequential stepwise injection of the resin by separate small portions of each component. This can be explained by the higher fracture toughness of the reinforced rock with a flexible hardened network of the cured polymer resin compared to a more homogeneous structure, which is observed for the prepared resin solution injection. The cured polymer resin network probably prevents a formation of macro-cracks. The reinforced rock exhibits properties inherent in elastomers, but to a lesser extent than the cured polymer resin. These effects should be considered in further research. Institutional Review Board Statement: Not applicable.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author.

Conflicts of Interest:
The authors declare no conflict of interest.