Research on the Effect of Karst on Foundation Pit Blasting and the Stiffness of Optimal Rock-Breaking Cement Mortar

Abstract

The existence of karst cavities has an important impact on the safety of foundation pit excavation projects. It is of engineering guiding value to study the influence of karst cavities on the blasting process of foundation pits and how to optimize the stiffness of cement mortar to improve the blasting effect. Based on the karst foundation pit bench blasting project of Shenzhen Dayun Foundation Pit Project, this paper adopts the SPH-FEM coupling calculation method to study the influence of karst cavities, cavity-filling water and cavity-filling silt clay on the rock-blasting process of bench blasting. We analyzed the development process of blasting damage of rock when the stiffness of karst cavity grouting filling changes under the conditions of slightly weathered, moderately weathered and strongly weathered limestone. The calculation results show that the karst cavity near the blasthole changes the direction of the minimum resistance line, which leads to the release of blasting energy; the rock breaking effect is improved when the karst cavity is filled with water medium and clay medium. Under the three limestone conditions, after the karst cavity is pretreated by cement grouting, the increase in the stiffness of the cement mortar makes the rock damage area first increase and then decrease after the karst cavity implosion, and There is a critical cement mortar stiffness that makes the best rock breaking effect. The critical cement stiffness of micro-, medium- and strongly weathered limestone is 2.2%, 6.1% and 27% of the blasted rock mass, respectively, which makes the karst cavity wall stress reach the peak value, and the rock-breaking effect is the best at this time.

1. Introduction

Karst areas are widely distributed in my country, and urban rail transit in my country inevitably encounters karst-developed strata. Under the condition of improper control of blasting and rock breaking, it is easy to cause geological disasters such as water and mud inrush, fissure seepage and dangerous rock shedding to rock underground engineering [1,2,3].

The existence of cavities has a significant effect on the development of rock cracks under blasting loads. Since the cavity is a free surface, stress wave reflection and stress concentration will occur. Due to its low tensile strength, the rock near the cavity is more likely to be damaged under the action of reflected tensile waves, which obviously promotes the development of rock cracks near the cavity [4,5]. The existence of a cavity in the rock mass makes the direction of the resistance line between the local cavity and the blast hole to be the smallest. Before the rock is completely destroyed, the explosion energy accumulates in the direction of the cavity, resulting in the release of blasting energy. As a result, cavities can cause localized energy release phenomena in blasting charges, which can lead to problems such as flying rocks and uneven fragments. Grouting [6,7] is a kind of engineering remediation measure, which is widely used in karst engineering [8]. It can prevent water seepage in karst caves [9], enhance the stability of surrounding rock [10], prevent water gushing in tunnels [11] and so on, achieving good application. However, the effect of filled karst voids on rock blasting is still unclear. At present, the blasting research of foundation pits [12] mainly focuses on the vibration and impact of foundation pit blasting on existing underground pipelines [13], nearby subway tunnels [14], buildings adjacent to the ground’s surface [15] and people on the surface. At the same time, some scholars have studied other aspects of foundation pit blasting. Li [16] analyzed the impact of blasting disturbance on the evolution of water inrush disasters in confined water-bearing karst caves. Fang [17] considered the effect of blasting shock waves against the minimum outburst prevention thickness of rock mass against water. Jiang [18] studied the calculation method of anti-water-inrush thickness of karst foundation pits considering the number of single blasting. The above article focuses on the influence of dynamic blasting load on the stability and seepage field of underground engineering rock mass in karst cave areas. However, studies on how karst and cavern media affect the rock-blasting process are still scarce.

In recent years, smooth particle hydrodynamics (SPH) and the finite element method (FEM) are two of the most commonly used numerical simulation methods in explosion engineering and blasting engineering. SPH method is often used for analysis of large deformation simulation,, while finite element calculations are more stable on model boundaries. In order to accurately simulate the blasting action process in all directions in space, and to realize the stability of rock mass rupture and large deformations near the blasting area and the calculation of the boundary position of the model, the SPH-FEM coupling calculation method is gradually applied to numerical analysis [19,20,21], such as projectile penetration into concrete [22], slotted charge blasting [23] and other research directions. For karst engineering, some scholars have used the SPH-FEM coupling calculation method to study the flow of karst aquifers [24], small-scale infiltration dynamics in fractures [25], and inrush water in karst areas [19]. However, no scholars have used the SPH-FEM coupling calculation method to study on the effect of the variation of filling medium in karst cavity on the rock breaking effect of blasting.

In order to guide the field practice and realize the active prevention of karst geological foundation pit blasting engineering disasters, this paper relies on the underground station project of Shenzhen Universiade Comprehensive Transportation Hub and adopts the SPH-FEM coupling calculation method to analyze the blasting effect of karst cavities and filling media on foundation pits. The influence of karst cavity grouting pretreatment was studied, and the rock damage process of cement mortar with different parameters under blasting was studied. Finally, the optimal rock-breaking cement mortar stiffness was determined according to the peak dynamic stress of the rock.

2. SPH-FEM Coupling Analysis Method

2.1. Introduction to SPH Method

A system state in SPH is represented by a set of particles that can be assigned material properties and interact within the scope of a smoothing function or weighting function. The motion of these particles is governed by the SPH formulation of the physical partial differential equations that characterize the fluid flow. Substitute the SPH approximation into the N-S equation with a function and its derivative, thereby transforming the SPH governing equation of motion into the N-S equation [26].

$$\frac{D{\rho }_i}{Dt}={\displaystyle \sum _{j=1}^N{m}_j{v}_{ij}^{\beta }\frac{\partial W_{ij}}{\partial x_i^{\beta }}}$$

(1)

$$\frac{D{v}_i^{\alpha }}{Dt}=-{\displaystyle \sum _{j=1}^N{m}_j(\frac{{\sigma }_i^{\alpha \beta }}{{\rho }_i^2}+\frac{{\sigma }_j^{\alpha \beta }}{{\rho }_j^2}})\frac{\partial W_{ij}}{\partial x_i^{\beta }}+F_i$$

(2)

$$\frac{D{e}_i}{Dt}=\frac{1}{2}{\displaystyle \sum _{j=1}^N{m}_j\left(\frac{P_i}{{\rho }_i^2}+\frac{P_j}{{\rho }_j^2}\right)v_{ij}^{\beta }\frac{\partial W_{ij}}{\partial x_i^{\beta }}}+\frac{{\mu }_i}{2{\rho }_i}{\epsilon }_i^{\alpha \beta }{\epsilon }_j^{\alpha \beta }$$

(3)

In the formula, ρ_i, $v_i^{\alpha }$, e_i are the density, velocity component and internal energy of particle i, respectively; N denotes the number of particles; α and β denote the coordinate directions; $x_i^{\beta }$ is the coordinate component of x along β; P_j denotes the isotropic pressure; W_ij denotes the smooth function between particles i and j and m_j denotes the particle mass.

From Formula (1) to Formula (3), it can be found that SPH can calculate the speed and energy changes of particles in the system, and the calculated data between particles can be connected and interact with each other, and the entire interaction process changes with time. Further, the meshless feature of SPH allows direct processing of large deformations, avoiding the problem of large deformation and distortion of the mesh in numerical calculations.

Specifically, when the SPH calculation method is applied to blasting, the SPH method can reflect the large deformation in the near area of the blasting through particle motion. Compared with the finite element model, the large deformation and distortion of the mesh are avoided. SPH has the advantage of reflecting the large deformation of blasting through particle motion, which gives the SPH calculation method obvious advantages compared with the finite element method in the calculation of the blasting near area.

Although SPH has the advantage of simulating large deformations, it suffers from severe boundary defects in the far field of the computational model due to particle inconsistencies. In order to overcome this defect, a coupled analysis method using the SPH method in the near field and the FEM method in the far field was developed and applied. This method combines the advantages of SPH simulation of large deformation and the more stable advantages of finite element boundary calculation, which can effectively overcome the problems of large deformation distortion and boundary instability. Under the action of blasting, the schematic diagram of the deformation of the near and far areas of blasting is shown in Figure 1.

2.2. SPH and FEM Contact Setup

The connection between particles in the SPH system is generated in the calculation. The N-S equation is the control equation for each particle in the system. The equation calculation process is reflected in the connection between the particles changing with time. The contact between the SPH particles is shown in Figure 2.

In the formula, i and j represent the particle number, kh_i and kh_j represent the support domain of i and j particles, r_ij represents the distance between i and j particles and f_ij represents the contact force between i and j particles.

The key to the coupling of SPH and FEM is that the interface can effectively transfer the information of SPH particles to the finite element mesh. The common method is to make the SPH particles bond with the finite element mesh by setting the interface and realize the displacement coordination of the two methods by means of point-surface bonding contact. Contact parameters are adjusted by setting the keyword *CONTROL_CONTACT. The schematic diagram of the contact is shown in Figure 3.

3. Engineering Background

Karst geology is widely distributed in Shenzhen’s underground space, and its impact on engineering safety has attracted attention. The underground station project of Shenzhen Universiade Comprehensive Transportation Hub (referred to as the Dayun hub) will realize the intersection of four-line tracks after completion. The Dayun hub is 375 m long. From top to bottom, the rock formations in the large-mileage open-cut section are plain fill (6.17 m thick), silty clay (6.83 m thick) and slightly weathered limestone. The geological map is shown in Figure 4.

Before construction, the area near the foundation pit was drilled to detect the distribution of karst caves in the vicinity, and the drill holes were arranged in plum-shaped holes with a hole spacing of 2.0 m. Drilling detection shows that karsts are widely distributed in the large-mileage open-cut section and the middle section of the Dayun hub. With the outer edge of the enclosure structure expanding 3 m as the boundary, the total area of karst development area in the large-mileage open-cut section is 8781.5 m². Among them, the area of the karst cave obtained from the detection is 1837.84 m². Among the caves revealed by drilling, the caves are 0.20–8.20 m high and 0.20–13.7 m thick. The revealed filling conditions are divided into full filling (accounting for 79.2%), half filling (accounting for 1.9%) and no filling (accounting for 18.9%); the filling material is mainly flow-soft plastic clay soil, which is partially plastic. Part of the cavity is filled with gravel, while a small part of the cavity is not filled. The karst distribution map is shown in Figure 5.

The excavation of the foundation pit of the Dayun hub is a combination of step-loosening blasting and mechanical demolition. Step-loosening blasting is adopted. The blasting parameters are designed as follows: the height of the step is 3.0 m, the chassis resistance line of the outermost row of blastholes is generally 1.5 m, the blastholes are vertical holes with a diameter of 5.0 cm, the blasthole depth is generally 3.0 m and the charge length is 1.0 m. The karst distribution cross-section map and survey drilling map are shown in Figure 6.

4. SPH-FEM Numerical Model

4.1. Materials and Boundary Conditions

A two-dimensional grid model is established, and the model size is 28 m × 18 m (width × height). The diameter and length of the blast hole refer to the on-site setting. The blast hole is arranged on the first step, the minimum resistance line is 1.5 m, and the super depth is 0.3 m. The karst cavity refers to the size of the karst cave on site, and is set as a circle with a radius of 1.0 m. The distance between the center of the karst cavity and the axis of the blast hole is equal to the minimum resistance line, which is 1.5 m. Taking the bottom of the blast hole as the center, the blasting near field is divided into particles, and the rest is the Lagrangian finite element mesh, and the contact between the particles and the finite element mesh is established. Normal constraints and non-reflection boundaries are set at the bottom and left and right of the model, and the top is a free boundary. The details of the model are shown in Figure 7.

The site explosive is 2# rock emulsion explosive, using the material model for high-energy explosives (MAT_HIGH_EX-PLOSION_BURN) and the equation of state is described by JWL. The Jones–Wilkins–Lee (JWL) equation of state describes more accurately the pressure, volume and energy characteristics of the blast gas products during the explosion [26]. Air materials are modelled using the blank material model MAT_NULL and described using the linear polynomial equation of state EOS_LINEAR_POLYNOMIAL [27]. Aqueous materials are also modelled using the blank material model MAT_NULL and described using the linear polynomial equation of state EOS_GRUNEISEN [28]. The silt clay medium material setting * MAT_FHWA_SOIL, which is an isotropic material with damage, has a modified Mohr–Coulomb surface to determine the pressure-dependent peak shear strength. Parameters such as the cohesion of the material and the angle of internal friction are obtained from engineering geological tests. The limestone and cement mortar material is set to * MAT_HJC, which is a damage material model suitable for concrete and rock under large deformation and high strain rate. The parameters of clay and limestone are mainly obtained from geological tests on site. The parameters of the hardened cement mortar are referred to in [29].

Among them, the water medium material adopts the SECTION-SPH unit algorithm, the explosive and air adopt the SECTION-SOLID-ALE algorithm and the rock and lining adopt the SECTION-SOLID algorithm. Material parameters can be seen in

Table 1. Explosives parameters.

ρ (kg/m3)	D (m/s)	A (GPa)	B (GPa)	R1	R2	w	E0 (GPa)	Pcj (GPa)
1.24	3200	214.4	0.182	4.2	0.9	0.15	4.192	7.4

,

Table 2. Air parameters.

ρ (kg/m3)	C0	C1	C2	C3	C4	C5	C6	E0	V0
1.25	0	0	0	0	0.4	0.4	0	2.50 × 105	1.0

,

Table 3. Water medium parameters.

ρ (kg/m3)	C (m/s)	S1	S2	S3	${\mathit{\gamma }}_0$	a	e0	v0
1020	1647	2.56	1.986	1.2268	0.50	0	0	1.0

,

Table 4. Clay medium parameters.

ρ (kg/m3)	Gs	k (GPa)	G (GPa)	c (MPa)	$\mathit{\phi }\left({}^{°}\right)$	w (%)	vn	epsmax
2030	2.66	0.035	0.006	0.03	17.4	21.5	1.1	0.8

,

Table 5. Cement mortar medium parameters.

ρ (kg/m3)	E (GPa)	G (GPa)	A	B	C
2.40	30	12.3	0.79	1.6	0.007
N	T(GPa)	K1(GPa)	K2(GPa)	K3(GPa)	v
0.63	0.001	86	−173	204	0.20

and

Table 6. Limestone parameters.

Lithology	ρ (kg/m3)	G (GPa)	μ	Fc (MPa)	T (MPa)
micro-weathered limestone	2440	48.7	0.27	58.8	5.6
medium weathered limestone	2370	28.7	0.26	22.5	3.8
strongly weathered limestone	2200	8.7	0.28	9.8	1.6

.

4.2. Calculation Case Settings

According to the karst filling situation of the Universiade Junction Station, the complete filling situation is the main situation (accounting for 79.2%), and the filling material is mainly cohesive soil. The second is a no-filling situation (accounting for 18.9%), and there are a small number of karst caves that are hollow. Considering that Shenzhen is a coastal area with a high groundwater level and abundant supply, four working conditions are set in this paper, including the karst cavity condition, the fully filled water medium condition, the fully filled clay medium condition and the cement mortar filling condition. The schematic diagram of the calculation conditions is shown in Figure 8.

5. SPH and FEM Coupling Effect

In order to verify the coupling effect of the SPH-FEM method at the junction, two pairs of coupling nodes are selected to compare the effective stress–time history curve. The node selection is shown in Figure 7, and the effective stress–time history curve is shown in Figure 9. It can be seen from the figure that the stress–time history curves of particles and finite element meshes almost coincide, the corresponding times of effective stress rise and fall are the same, and the corresponding effective stress peaks are close to the same, indicating that the interface contact of the model can effectively transfer the particle calculation information to the adjacent finite element meshes. It should be pointed out that in the later stage of model calculation (t > 4000 μs), the effective stress of SPH particles fluctuated significantly. However, the failure of surrounding rock studied in this paper mainly depends on the stress peak, so the numerical model used is reliable.

6. Influence of Karst Cavities

The damage change of the rock mass with karst affected by the explosive detonation wave is shown in Figure 10. After the explosive explodes, the detonation wave gradually expands the blast hole space, and the detonation wave acts on the blast hole wall to generate stress waves in the rock mass. In the initial stage (t = 350 μs), the stress wave with strong energy quickly caused rock damage, and the range was the oblong area around the blast hole. When the stress wave is transmitted to the karst cavity (t = 750 μs), the free surface effect of the cavity makes the stress wave reflect to form a tensile wave, and the rock mass on the near-explosion side of the cavity is the first to suffer tensile failure. The stretching wave formed by reflection is transmitted repeatedly between the cavity and the blasthole (t = 2000~4000 μs), the rock mass between the two cavities becomes a stress concentration tension zone, and the rock mass damage on the side of the cavity is obviously greater than that of the blasthole Symmetrical position, the final result is that the rock mass moves into the cavity after being broken, and the blasting energy accumulates in the cavity;When the stress wave is transmitted along the chassis resistance line to the empty surface of the step (t = 4000–6000 μs), the damage development on one side of the cavity is more rapid and severe and the rock mass flocks into the cavity after being broken. The final stress nephogram shows (t = 8000 μs) that the cracks on the side of the void face are not sufficiently developed due to blasting, while most of the rock mass on the side of the cavity is broken. This shows that when there is a karst cavity in the vicinity of an explosion, the blasting energy will accumulate in the direction of the cavity to cause blasting energy release, which will affect the rock-breaking effect.

6.1. The Mechanism of the Effect of the Cavity on the Resistance Line

The influence mechanism of the dissolution cavity on the blasting resistance line is shown in Figure 11. After the explosive is detonated, the detonation wave propagates uniformly as an elastic compression wave outside the crushing area. Before reaching the free surface, the stress wave has reached the hole area and is reflected at the hole wall to form a reflected wave. Because the tensile strength of the rock is relatively low, under the action of a large tangential stress σ_θθ, a circumferential crack will be formed in the area near the hole wall. At the same time, the cylindrical wave formed after the explosive detonation continues to propagate outward and interacts with the reflected stretching wave reflected from the hole wall, resulting in the tensile crack formed near the explosive and the ring formed near the hole wall. The direction of the blasting resistance line is changed from the side of the free surface to the direction of the side of the hole.

6.2. Influence of Filling Water and Clay Medium inside the Cavity

Compared with the unfilled karst cavity, the rock mass damage changes of the rock mass under the fully filled water and clay scenarios under the impact of the explosive detonation wave are shown in Figure 12 and Figure 13, respectively. When the karst cavity is filled with a water medium (as shown in Figure 12), the shock waves and stress waves generated by blasting act on the water medium to generate high-intensity stress waves inside, which then act on the karst cavity wall and form cracks. The compressibility is relatively poor, and the SPH particles in the water medium are squeezed around by the stress, which promotes the development of cracks. This action process is more obvious (t = 8000 μs) directly above the karst cavity, where the rock mass above the karst cavity produces surface uplift due to the pressure transfer of the water medium.

It can be seen from Figure 13 that under the condition that the cavity is filled with a silt clay medium, when t = 2000 μs, the SPH particles rushing in by the blasting stress wave reach the edge of the karst cavity, but from the damage cloud diagram at t = 4000 μs, the high-energy SPH particles that began to pour in at 2000 μs moved slowly due to the obstruction of clay. At the same time, the blasting stress wave on the side of the air side caused continuous damage to this side area. It can be seen from the damage cloud diagram at t = 8000 μs that when the clay medium is fully filled, there is obvious extrusion deformation on the side of the empty surface. However, the blasting energy is not fully utilized, an empty space still appears in the cavity and part of the blasting energy still accumulates in the direction of the cavity.

7. Best Cement Mortar Stiffness for Blasting Rock

The stiffness of the filling medium in the cavity has an obvious effect on the blasting rock-breaking effect, and the blasting rock-breaking effect will continue to deteriorate as the stiffness of the filling medium decreases [30]. Therefore, it is not suitable to blast the rock in the initial stage of cement mortar grouting in the karst cavity. On the other hand, the rigidity and strength of the cement mortar will increase significantly after a long period of time. At this time, blasting the rock will increase the consumption of explosives. Therefore, it is necessary to analyze the best cement mortar stiffness for rock breaking effect.

The model used in the analysis in this section is the same size as the model in Section 4.1; the difference is that the karst cavity is divided by SPH particles and given the material properties of cement mortar, and a blast hole with the same parameters as in Section 2.2 is added on the centerline of the karst cavity—that is, the diameter of the blast hole is 6cm, and the length of the charge is 1m, which is used to break the rock mass near the cavity. The model diagram is shown in Figure 13. In this paper, the problem is simplified when analyzing the change of the stiffness of the cement mortar. The change of the stiffness of the cement mortar is reflected by changing the value of the elastic modulus of the cement mortar E_c alone. The stiffness of the cement mortar E_c is adjusted based on the elastic modulus of the rock E₀, and the relative stiffness ε = E_c/E₀ is set to 0.1%, 1%, 10%, 20%, 60% and 100%, respectively. In this paper, the damage cloud map of rock mass after blasting under the condition of medium weathered limestone with different cement mortar stiffness is listed, as shown in Figure 14.

It can be seen from Figure 15 that there are significant differences in the rock-breaking effect under different relative stiffness conditions. When the stiffness of the cement mortar is relatively 0.1% and 1% of the rock mass stiffness, the slurry is not sufficiently hardened at this time, so there is no obvious damage under the action of the blasting stress wave, and only the area near the blast hole is squeezed by the stress wave. The blasting stress wave transmitted by the slurry acts on the karst cavity wall, causing damage to the rock mass near the cavity wall in a large range, and when the mortar stiffness is large enough, for example, the relative stiffness is 60% and 100%. The damaged rock mass between the blastholes is not obvious, and the rock-breaking effect is not optimal.

When the relative stiffness of the cement mortar is within a range, the tensile cracks of the rock have a better expansion after blasting. When the stiffness of the mortar is 10% to 20% of the stiffness of the rock mass (Figure 12), the karst cavity after filling is nearly completely damaged and destroyed under the action of the blasting stress waves. The damage cloud map analysis shows that there is obviously a critical cement mortar stiffness to achieve the best rock-breaking effect.

Since the purpose of grouting in a karst cavity is to break the rock mass outside the cavity, the stress state at the edge of the cavity contour most intuitively represents the rock-breaking effect of the rock mass outside the cavity. Extract the stress of the characteristic measuring points near the contour of the karst cavity with different grouting stiffness under different lithological conditions. The characteristic measuring point is located on the cavity wall of the rock mass cavity on the side away from the air surface, as shown in Figure 13. The stress at the characteristic measuring point is analyzed, and the functional relationship between the measuring point stress σ and the relative stiffness of the cement mortar ε under the three lithologies is obtained by fitting:

$$\begin{array}{cc}\mathrm{micro-weathered\; limestone}& \sigma =0.066-\frac{0.346}{1+{(\frac{\epsilon }{0.166})}^{2.51}}\sin (\epsilon -2.19)\end{array}$$

(4)

$$\begin{array}{cc}\mathrm{medium\; weathered\; limestone}& \sigma =0.0412-\frac{1.0912}{1+{(\frac{\epsilon }{0.1908})}^{2.09}}\sin (\epsilon -2.86)\end{array}$$

(5)

$$\begin{array}{cc}\mathrm{strongly\; weathered\; limestone}& \sigma =0.244+0.175e^{\frac{-{(\epsilon -0.27)}^2}{0.336}}\end{array}$$

(6)

In this paper, the idea of obtaining the best rock-breaking cement mortar stiffness based on the fitting curve is as follows: first, the stress fitting curves of the characteristic points under the three weathered limestone conditions are derived, and the stress change rate curve of the characteristic points with the change of the cement mortar is obtained. Then, find the zero point of the stress change rate curve, and the characteristic point stress corresponding to the zero point value is the maximum stress value. When the characteristic point stress reaches the maximum value, the blasting effect on the rock mass outside the cavity is the best. The optimal rock-breaking cement stiffness corresponds to the cement mortar stiffness corresponding to the zero point of the stress change rate curve.

In Figure 16, It can be seen from the fitting curve that with the increase in the stiffness of the cement mortar, the detonation wave pressure of the cavity wall first increases and then decreases. The zero point of the curve change rate can be obtained. When the relative stiffness of the cement mortar is 2.2%, 6.1% and 27%, respectively, under the three lithological conditions, the stress value of the characteristic measuring point reaches the maximum. At this time, it can be seen that when the elastic modulus of the cement mortar is 2.2%, 6.1% and 27% of the elastic modulus of the slightly weathered limestone, the moderately weathered limestone and the strongly weathered limestone, respectively, the solution cavity grouting medium can be the most effective. The elastic stress wave after the detonation of the explosive is transmitted, and the rock-breaking effect is the best at this time.

8. Engineering Site Application

According to the regulations of “Urban Rail Transit Engineering Survey”, before the blasting construction, it is necessary to drill holes in the designated area. The hole spacing is 2 m. After understanding the plane distribution and burial depth of the karst cave, adopt the method of static pressure grouting to grout through the sleeve valve pipe, so that the filling is compressed, split, squeezed, hydrated, and the filling is transformed into a certain strength. stone body or hard plastic. At the same time, it can isolate the water and prevent the cavity from being eroded by water again during the operation period. The on-site grouting diagram is shown in Figure 17.

The blasting test before and after grouting was carried out on a blasting step of the foundation pit where the existence of karst caves has been proved. It can be seen from Figure 18 that the blasting energy is dissipated along one side of the cavity because the existing cavity is not grouted, which weakens the impact on the free surface of the step. The rock effect is not obvious. It can be seen from Figure 18 that after grouting the karst cave, the blast pile on the side of the free surface becomes significantly larger, and the rock-breaking effect is obvious. The field blasting test shows that grouting and strengthening the karst cavity before blasting will help the blasting energy to accumulate along the side of the free surface, thereby enhancing the rock-blasting effect of foundation pit bench blasting.

9. Conclusions

Relying on the foundation pit project of Shenzhen karst formation station, this paper adopts the calculation method of coupling blasting near-field SPH and far-field FEM to accurately simulate the influence of karst cavities and filling media on the blasting effect of foundation pits. The main conclusions are as follows:

(1)

The karst cavity will cause the blasting energy to dissipate along the interior of the cavity, which will change the blasting resistance line, making the resistance line between the cavity and the blasthole the direction of the minimum resistance line, and the energy of the explosive will be concentrated in the direction of the cavity, resulting in blast energy release.

(2)

When the cavity is fully filled with water medium and clay, the effect of blasting energy dissipation along the cavity is significantly improved, which is conducive to rock breaking in the area on the side of the air surface.

(3)

There are significant differences in rock-breaking effects under different grout stiffness conditions. As the cement mortar stiffness increases, the rock mass damage area inside the karst cavity first increases and then decreases. There is a cement mortar stiffness that makes the rock-breaking effect reach the maximum.

(4)

By fitting and analyzing the blasting stress of the karst cavity wall under different grouting stiffness under slightly weathered limestone, moderately weathered limestone and strongly weathered limestone, it is obtained that when the elastic modulus of cement mortar is 0.022 of that of slightly weathered limestone times, 0.0613 times the elastic modulus of moderately weathered limestone, and 0.270 times the elastic modulus of strongly weathered limestone, the rock breaking effect in the cavity is the best.