^{1}

^{2}

^{2}

^{1}

^{1}

^{1}

^{2}

To enhance the antidynamic and static load resistance of reinforced concrete structures, the measure of covering steel plates on the inner surface of concrete structures arises, which has been rapidly developed and applied in civil engineering and other fields and has achieved a good performance. A new shaft wall structure consisting of steel plate reinforced concrete has been widely used in shaft of deep mining. In order to investigate the stability and obtain the optimum structure parameters of the new shaft structure, the numerical software of LS-DYNA was used to analyze the influences of different factors, including the explosive payload, steel plate thickness, concrete strength grade, and the included joint angle between two plates, on the stability of steel plate reinforced concrete structures. After the verification of the accuracy of numerical simulation results, 23 simulation schemes were proposed and numerically calculated. For all the tests, the principal tensile stress and particle vibration velocity were, respectively, chosen as the failure criteria to evaluate the impacts of those four factors. The results indicate that a quadratic function can be well used to describe the relationships between each factor and both the principal tensile stress and particle vibration velocity. Based on the results, the optimum structure parameters were finally determined, which are suggested as 250 kg, 15 mm, C85, and 40° for the explosive payload, steel plate thickness, concrete strength grade, and joint angle, respectively. The research results can provide a certain theoretical basis and design guidance for solving the problem of water leakage of single-layer shaft wall structures.

With the depth increase of coal mine in China, great breakthrough has been made in the deep freezing technology. Meanwhile, the new shaft wall structure, which consists of the concrete body and steel joint plates, is bound to replace the past unreasonable single wall structure which is a superthick and simple structure. The key technology to ensure the integrity and water resistance is how to avoid the failure in concrete and along the interface between the concrete and steel plate under an applied explosive load [

Based on the study on the bend and failure modes of both the beam and plate structure under an applied explosive load, a simplified resistance model and an equivalent system of degree of freedom (DOF) of the beam and plate were proposed [

Many works, including both the theoretical calculation and numerical simulation, have been conducted to study the mechanical and stability characteristics of steel plate reinforced concrete (SPRC) structure under an applied explosive load. The break characteristics of SPRC structures under an explosive load were investigated by analyzing the changes of the deformation and stress theoretically [

The focus of this study is to determine the break rules and optimum structural forms of SPRC sidewalls under an applied explosive load by using the FEM numerical simulations. The influence of different factors, including the explosive payload, thickness of steel plate, concrete strength, and joint angle of plate, was systematically studied. Based on the simulation results, the optimum design parameters of the sidewall were obtained.

The range of stress waves is a typical plastic zone, and the rock medium will be damaged and elastically deformed; thus, both continuous and residual deformation of the rock transfer disturbance should be considered. After the shock wave enters the middle zone of blasting, its properties and waveforms have changed greatly. The relationship between the maximum radial component and the maximum tangential component of the particle velocity on the wave front and the maximum radial pressure and the maximum tangential pressure on the wave front is as follows:

Displacement of the particles corresponding to the time of

The impulse density can be calculated as

The energy flux density is

Total energy of waves can be obtained:

Because there is a cohesive force at the interface between the concrete and rock and there is no sliding at the interface, thus the displacement, particle velocity, and stress at the interface are continuous. The reflection stress and transmission stress of the normal incidence can be calculated.

An auxiliary shaft of a coal mine, whose design production capacity is 12 MT/a, was analyzed as the engineering background in this paper. The geological lithology of the mine, which has large inclined bedding and cross bedding, is mainly brown-red coarse-medium-grained sandstone, followed by fine-grained sandstone. The rock is argillaceous and cementation, mainly composed of feldspar and quartz, with subangular particles and medium sorting, presenting unconformity contact with the underlying stability group (J2A). The softening coefficient of all kinds of rocks in this area is less than 0.75, which is easy to be softened, and the core can be crushed by hand. The strength of the rock is equivalent to the weathered rock, and the weathering resistance of the rock is very weak. Under normal circumstances, the core will be broken after exposure for 2-3 days.

The net diameter of the auxiliary shaft is 10.0 m, the depth of the shaft is 755 m, and the whole shaft is constructed by using the freezing method. The single-layer shaft wall of the frozen bedrock section is sunk by using the drilling and blasting method, which saves investment and speeds up the sinking speed, and overcomes the shortcomings of thick, high cost, and slow construction of the double-layer composite borehole wall.

The study object in the numerical simulation model is the depth range from −320 m to −580 m of the shaft wall. To improve the sealing performance of jointing parts of the borehole wall, the steel plate was applied as the joint to prevent seepage, which constitutes SPRC structures with concrete of the shaft wall. The SPRC structure is shown in Figure

Layout Schematic of the SPRC structure in shaft wall.

The shape, size, and boundary of the model are all displayed in Figure

Numerical simulation model of the vertical shaft wall. (a) Schematic diagram of the model. (b) Front view of the model. (c) Top view of the model. (d) Meshing of the model.

The model was built and meshed using the software of ANSYS and the material parameters are defined in LS-DYNA. The established numerical simulation model of the vertical shaft wall is shown in Figure

Dynamic analysis software LS-DYNA was used for numerical simulation analysis in this study. The built model includes the explosive unit, concrete unit, surrounding rock medium unit, and steel unit, all of which are solid elements under dynamic loads, and the SOLID164 solid unit was selected.

In LS-DYNA, the material of MAT_HIGH_ EXPLOSIVE_BURN was used to simulate high explosive materials and the state equation of EOS_JWL was applied to control the explosion process. In the initialization stage, the ignition time

The form of the EOS_JWL state equation is as follows:

According to the water-gel explosive used in the field, the parameters of the simulated explosive and state equation of JWL are shown in Table

Parameters used in the explosive materials and state equation.

1.02 | 4000 | 5.3 | 374 | 7.33 | 4.15 | 0.95 | 0.30 | 7∗10^{9} |

The elastoplastic material of MAT_PLASTIC_KINEMATIC in LS-DYNA was applied to simulate the rock and concrete in this paper. The material model is a typical kind of isotropic and follow-up hardening mixture, which is related to the strain rate and takes the failure into account. The same material model was applied to simulate the rock and concrete, with the parameters shown in Table

Parameters of related rock and concrete.

Item | Yield stress | |||
---|---|---|---|---|

Rock | 2.12 | 10 | 0.22 | 35 |

Concrete | 2.50 | 35 | 0.19 | — |

Generally, under the action of stress waves, the steel plate is considered to produce elastic deformation only, without plastic deformation or failure; thus, the elastic ∗MAT_JOHNSON_COOK material mode was selected. The parameters of the steel and state equation of GRUNEISEN are shown in Table

Parameters of the related steel plate.

Item | |||||||
---|---|---|---|---|---|---|---|

Steel | 7.8 | 210 | 0.27 | 0.45 | 1.49 | 0.0 | 1.0 |

In order to maximize economic benefits, new mines are often required to be built and put into production as soon as possible. Therefore, in the process of shaft excavation, the construction party often increases the explosive charge quantity in pursuit of progress. The larger amount of primary explosives will induce serious influences on the wellbore structures. Therefore, in order to clarify the specific impacts of the change of the explosive quantity on the steel plate concrete composite structures in shaft lining, this paper will study the dynamic response of the steel plate concrete composite structure under different explosive quantities based on the actual explosive quantity, from which, whether the current explosive quantity is reasonable is judged and the appropriate explosive quantity is obtained.

The increase of the steel plate thickness has little effect on the propagation of stress waves, while the tensile stress at the steel plate concrete interface will decrease significantly. The particle vibration velocity will only change the component size in each direction and has little effect on the actual particle vibration velocity. Therefore, this paper mainly studies the influence of the change of the steel plate thickness on the structural stress and determines the reasonable steel plate thickness.

The wave impedance of two adjacent media determines both the direction and value of the reflection and transmission of stress waves, and the change of the concrete strength grade will not affect the propagation of stress waves. When the stress wave causes the same stress in the steel plate and concrete, damage may occur when the strength grade of the concrete is too low. However, if the strength of the concrete is too high, it will not only increase the particle velocity but also make the strength surplus too large and cause waste. Therefore, it is necessary to study this factor and determine the reasonable strength grade of the concrete.

Considering the convenience of assembly and lifting, the included angle between the vertical and inclined steel plates is designed to be 45° in engineering fields. The changing included angles will vary the propagation path of the stress wave to some extent, resulting in differences between the reflection and transmission of stress waves and differences between the stress value and particle vibration velocity responses. Therefore, it is necessary to study the influences of the included angle between the steel plate and concrete and finally determine the appropriate angle.

Combined with the engineering practice, the influences of four factors including the explosive payload, thickness of steel plate, concrete strength, and included angle between steel plates on the failure and security of SPRC structures were studied in this paper. The initial scheme of this shaft is as follows: quantity of the primary explosive is 215 kg, thickness of steel plate is 8 mm, strength grade of concrete is C65, and the included angle between the vertical and inclined steel plates is 45°, with the scheme number of “215-8-65-45,” based on which, 24 schemes were designed, as shown in Table

Numerical simulation schemes.

Item | Scheme | |||||
---|---|---|---|---|---|---|

EP | 100-8-65-45 | 150-8-65-45 | 200-8-65-45 | 215-8-65-45 | 250-8-65-45 | 300-8-65-45 |

TSP | 215-6-65-45 | 215-10-65-45 | 215-12-65-45 | 215-15-65-45 | 215-20-65-45 | 215-25-65-45 |

CS | 215-8-C25-45 | 215-8-35-45 | 215-8-45-45 | 215-8-55-45 | 215-8-75-45 | 215-8-85-45 |

JA | 215-8-65-30 | 215-8-65-40 | 215-8-65-45 | 215-8-65-50 | 215-8-65-60 |

In order to verify the accuracy of the numerical simulation results, the peak pressure values at different positions of the cylindrical charge with an explosive quantity of 215 kg were calculated and then compared with the numerical simulation results. According to the observation data of the impact pressure in rock with the distance, the relationship between the shock pressure and distance follows an attenuation law [

The charge mode is a coupled cylindrical charge, according to the explosion force on the interface between the shock waves and stress waves, that is, the pressure at the interface between the rock and explosive, shown as the empirical formula [

The explosion wave pressure at the interface of the blast hole at different positions calculated by equation (

Comparison of the theoretical calculation and numerical simulation results.

Value (MPa) | |||
---|---|---|---|

Position (m) | Theoretical result | Simulation result | Relative error (%) |

0 | 720 | 610 | 15 |

0.5 | 207 | 212 | 2 |

1.0 | 62.9 | 58.4 | 7 |

3.0 | 9.5 | 9.2 | 3 |

5.0 | 4.0 | 3.95 | 1 |

Due to the fact that the dynamic tensile strength of the rock and concrete materials is far less than its dynamic compressive strength, the material in the SPRC structure is prone to brittle failure when subjected to a tensile stress. Thus, the first strength theory (the maximum tensile stress theory) is taken as one of the criteria to judge whether the concrete is damaged. In blasting engineering, the maximum vibration velocity

Vibration velocity requirement for a roadway.

PVF (Hz) | |||
---|---|---|---|

15∼18 | 18∼25 | 20∼30 |

Vibration velocity requirement for the newly poured concrete.

PVF (Hz) | |||||||||
---|---|---|---|---|---|---|---|---|---|

Age (day) | <3 | 3∼7 | 7∼28 | <3 | 3∼7 | 7∼28 | <3 | 3∼7 | 7∼28 |

1∼2 | 3∼4 | 7∼8 | 2∼2.5 | 4∼5 | 8∼10 | 2.5∼3 | 5∼7 | 10∼12 |

As shown in Section

Partial enlargement of the joint plate.

When the explosive explodes, it first produces a shock wave with a very strong peak pressure, then attenuates to a stress wave, and finally becomes an elastic wave until it disappears. The stress wave propagation law of the stress waves in the infinite rock mass is relatively clear, which radiates from the blasting center to the surrounding. However, when the stress wave propagates in an irregular structure, it will be affected by the shape and nature of the medium, and it is difficult to accurately describe its real propagation process. Figure

Spread process of stress waves. (a)

Then, the stress and vibration velocity values of 3 measure points (edge of the inclined steel plate, central section of the inclined plate, and the central section of the vertical plate) were, respectively, selected from the board and compared to finally determine the most dangerous point for research.

The tensile stress curves of those three points in the two steel platelayers are shown in Figure

Principal tensile stress at different positions of the lower and upper steel plates. (a) Principal tensile stress curves at different positions of the lower plate. (b) Principal tensile stress curves at different positions of the upper plate.

Comparing Figures

With various explosive payloads, the principal tensile stress nephogram at the interface of the steel and concrete is shown in Figure

The relationships between principal tensile stress and explosive payloads. (a) Nephogram of the principal tensile stress at the center of the steel plate. (b) Principal tensile stress history curves with different explosive payloads. (c) Maximum tension stress with different explosive payloads in the steel center.

The time history curves of the principal stress at point B with different explosive payloads are shown in Figure

The fitting curve of the relationship between the maximum tensile stress at the center of the steel plate and the explosive payload is shown in Figure

The dynamic strength of the concrete materials is significantly different with different strain rates. When the strain rate reaches 10^{2}/s, the dynamic tensile strength of the concrete materials could reach about 10 times larger than the static tensile strength [^{4}/s when subjected to stress waves, and the induced dynamic strength of the concrete will be very large. In this study, a concentrated charge with a radius of 0.13 m was used, and the scope of the stress wave was 120∼150 times larger than the charging radius [

Because the maximum value of the first principal stress is greater than the absolute value of the third principal stress under the same factor, the maximum particle velocity in the positive direction should be greater than the maximum particle velocity in the negative direction. Thus, the maximum vibration velocity of the structure particle was selected as the study object in this section, and the positive vibration velocity of the particle at point B was analyzed. The time history curves of the particle vibration velocity at point B with different explosive payloads are shown in Figure

Vibration velocity of steel central position with different explosive payloads. (a) Velocity history curves of particle under different explosive payloads. (b) Positive velocity fitting curve under different explosive payloads.

From Figure

By means of the postprocessing software of LS-Prepost, the main vibration frequency was obtained after the transformation of the particle vibration curves by FFT (fast Fourier transform), and the calculated main frequency of the structure is 633 Hz. In the engineering field, the concrete setting time is about 3∼7 days when the blasting construction is applied. Table

The nephogram and the time history curves of the principal tensile stress at point B as well as the fitting curves of the relations between the third principal stress and thickness of the steel plates are shown in Figure

Tensile stress curve corresponding to different steel plate thickness. (a) Nephogram of the principal tensile stress at the center of the steel plate. (b) Principal tensile stress curves with different steel plate thickness. (c) Maximum tension stress corresponding to different steel plate thickness.

From the fitted curve in Figure

The effects of variations in the steel plate thickness on the vibration velocity of the structural particles are shown in Figure

Vibration velocity curves corresponding to different steel plate thickness. (a) Vibration velocity curves with different steel plate thickness. (b) Vibration velocity fitting curve under different steel plate thickness.

From Figure

The nephogram and time history curves of the principal tensile stress at point B with different concrete strength grades are shown in Figure

Principal tensile stress of the steel central position with various concrete strengths. (a) Nephogram of the principal tensile stress at the center of the steel plate. (b) Principal tensile stress curves with different concrete grades.

Corresponding to different concrete grades (C35, C45, C55, C65, C75, and C85), the maximum tensile stress value is 3.6 MPa, 3.7 MPa, 3.9 MPa, 4.0 MPa, 3.9 MPa, and 4.0 MPa, respectively. The maximum tensile stress increases generally with the increasing concrete strength grades. However, when the concrete strength grade is greater than C55, the maximum tensile stress remains almost constant values. Note, the increase in strength grades can significantly improve the dynamic tensile/compressive ability of the concrete. Thus, a high concrete grade of C75 or C85 is recommended considering the strength of the SPRC structures.

The influence of the concrete strength grade on the vibration velocity curves of the structural particles is shown in Figure

Velocity history curves under different concrete strength in the steel center.

The nephogram and time history curves of the principal tensile stress in the SPRC structures with various joint angles are shown in Figure

Relationships between the tensile stress in SPRC structures and joint angles. (a) Nephogram of the principal tensile stress at the center of the steel plate. (b) Tensile stress curves with different joint angles between two steel plates. (c) Fitting curves between the maximum tensile stress and joint angles.

From Figure

From the above studies, an obvious correspondence between the particle vibration velocity and principal stress value can be obtained; that is, the greater the principal tensile stress, the greater the negative vibration velocity of particles. Therefore, in this section, the positive vibration velocity of the particle at point B is mainly taken as a reference and compared with the safe vibration velocity.

The influence of the changes in the joint angle on the particle vibration velocity of the SPRC structures is shown in Figure

Relationships between vibration velocity and joint angles. (a) Velocity history curves with different joint angles of plates. (b) Fitting curves of vibration velocity with different joint angles.

From Figure

In this study, numerical simulations were applied to investigate the influences of the explosive payload, thickness of steel plate, concrete strength grade, and the joint angle between the inclined and vertical plates on the SPRC structures. The maximum tensile stress and vibration velocity were selected as the failure criteria. From those above studies, some conclusions can be drawn as follows:

The stress analysis was carried out on the same position of the upper and lower steel joint plate structures, the maximum stress was determined at the center section of the inclined steel plates of the lower steel plate structures (position B), and this point was taken as the study object of different influence factors.

The change of explosive payloads has little effect on the shape of the stress waves, but the maximum principal tensile stress and particle vibration velocity could be varied significantly. It is found that both the tensile stress and particle vibration velocity increase with the increasing explosive payload. It is suggested that the explosive payload should be less than 250 kg.

The change of the thickness of steel plates has little effect on the shape of the stress waves. With an increase in the thickness of steel plates, the tensile stress is significantly reduced, but the particle vibration velocity is almost unchanged. It is suggested that the thickness of the steel plate should be 15 mm.

The change of concrete strength grades has little effect on the form of stress waves. With the increase in the concrete strength grades, the tensile stress and particle velocity increase and decrease, respectively. It is suggested that the strength grade of the concrete should be C85.

Different from the above three factors, the change of joint angles has a great influence on the shape of stress waves and changes the propagation path of the stress waves. It is found that the principal tensile stress increases significantly with the increase of the joint angle, but the particle vibration velocity always increases with no matter decreasing or increasing joint angles. The joint angle is recommended to be 40°.

All data during this study are available from the corresponding author upon request.

The authors declare that they have no known conflicts of interest or personal relationships that could have appeared to influence the work reported in this paper.

The financial support from the National Natural Science Foundation of China (51874292 and 51934007); National Key Basic Research and Development Program of China (no. 2016YFC0801403), and Key Basic Research and Development Program of Jiangsu Province (no. BE2015040) is gratefully acknowledged.