Abstract
The vibrationisolating rate of vibration isolating slot under buried pipe subjected to blasting seismic waves can been investigated by using the numerical method. For achieving a good vibration isolating effect, the depth of the vibrationisolating slot needs to be larger with the increase of the depth of the pore. The difference of the superdepth h leads to the difference in the trend of vibration isolating. The depth of the vibrationisolating slot is larger than the depth of the hole, which can improve the vibrationisolating rate. The different type of rock and soil medium is a significant effect on the vibrationisolating rate. To obtain ideal vibrationisolating effect, vibrationisolating slot depth compared with pipeline buried depth is greater than a certain value.
Highlights
 The vibrationisolating rate of vibration isolating slot under buried pipe subjected to blasting seismic waves can been investigated by using the numerical method.
 For achieving a good vibration isolating effect, the depth of the vibrationisolating slot need to be larger with the increase of the depth of the pore.
 The difference of the superdepth h leads to the difference in the trend of vibration isolating.
 The depth of the vibrationisolating slot is larger than the depth of the hole, which can improve the vibrationisolating rate.
 To obtain ideal vibrationisolating effect, vibrationisolating slot depth compared with pipeline buried depth is greater than a certain value.
1. Introduction
When an explosive explodes in the rock mass, it will release a huge amount of energy. Apart from the breaking of the rock, some of the energy propagated outward in the form of waves to form seismic waves. Although the energy of the seismic wave is only a small part of the explosive energy, it will cause some harm to the oil and gas pipeline, if it is not controlled or controlled properly. Therefore, it is necessary to take effective measures to control the blasting vibration in the safety range. In view of the causes and propagation characteristics of blasting vibration, many effective measures have adopted to control the vibration caused by explosion. The vibrationisolating slot is widely used in explosion engineering because of its good vibrationisolating effect and barrier function. The vibrationisolating slot can obstruct the propagation of the blasting seismic wave to the oil and gas pipeline, which reduce the blasting vibration and the damage to the oil and gas pipelines.
Lou Jianwu et al. [1] studied the propagation law of deephole blasting seismic wave in a depth 8 m, length 38 m, width l0 m vibrationisolating slot. With the analysis of the measured data, the proportion of distance is 0.0180.038 (kg^{1/3}·m^{1}), vibrationisolating effect of vibrationisolating slot to blasting seismic waves is best, vibrationisolating rate can reach 5070 %. Prakash et al. [2] conducted experiments on the impact of slot depth on the vibrationisolating rate. The ratio of slot depth and pore depth was 0.3, 1.0 and 1.125, and the vibrationisolating rate was 16.655 %. Venkatesh [3] studied the peak vibration velocity of the particles on both sides of the slot when the depth of the vibrationisolating slot was more than the hole depth, and obtained the vibrationisolating rate between 1118.5 %. Meng Haili et al. [4] simulated the propagation process of stress wave using ANSYS/Lsdyna software, analyzed the attenuation rule of the stress wave near the precrack and obtained the prefracture of no material, and the vibrationisolating rate was over 90 %. The prefracture vibrationisolating rate of the filling cuttings was 61.37 %. Anony [5] according to the dynamic’s theory, used the finite element program, analyzed damage model of modified fragmentation effect on surrounding rock under different ways of initiation.
In addition to the structural parameters of the vibrationisolating slot, the vibrationisolating rate of the vibrationisolating slot influenced by various factors such as blasting geology (site media), blasting parameters, depth of pipe, and the distance of the pipe to the detonation zone. This paper investigated the vibrationisolating rate of vibrationisolating slot subjected to blasting seismic waves. The results obtained from the present study can used for improvement in protective design of steel pipelines.
2. Calculation model
According to the characteristics of the problem studied, the coupling algorithm of multi material Euler and Lagrange structure applied to calculate the interaction between explosives, air and other solid structures. In the actual modeling process, it defines explosives and air as Euler grids, and ensures the common nodes between them. It defines the site medium, the fine sand in the pipe trench, the backfill soil medium and the steel pipe as the Lagrange mesh. The interaction between the fine sand in the trench and the steel pipe adopts the surfacesurface contact analysis, on contact surface in fine sand and steel pipe, steel pipe will take the master contact surface (Master Surface, for larger stiffness), soil for the slave contact surface (Slave Surface, relatively soft). Because the middle hole is located on the center line of the step width, in order to improve the mesh accuracy and save computing resources, we only need to establish the 1/2 model relative to the hole axis and adopt the gcms system. In order to simulate accurately the detonation of explosives and their impact on surrounding rocks, the meshes of explosives and surrounding rock are dense when dividing the grid. Because the rock affected by blasting seismic waves, which is in the range of elastic deformation, so the mesh is sparse. The SOLID164 element used to mesh the threedimensional model of the above numerical calculation.
3. Results and analysis
3.1. Superdepth
The important blasting parameters of the open pit step blasting are the pore diameter, pore depth, superdepth (or superdrill), block length and so on. The source of the blasting seismic wave is the charge in the gun hole. With the increase of the pore depth, the depth of the wave source is larger. In order to achieve good effect of vibration isolating, the larger the vibrationisolating slot depth ${H}_{d}$ is needed. In fact, for the same blasting engineering area, different blasting engineering parameter designers have their own design ideas and understanding, so it is possible to take different superdepth $h$ within a reasonable range. Therefore, the key blasting parameters $h$ of the open deephole step blasting are worthy of our special attention.
Keep bench height, pore diameter, pore spacing and row spacing, depth of the filling, charging length is unchanged, and deep respectively 1.5 m, 2.0 m, 2.5 m, 3.0 m (reference existing domestic mine blasting parameters of superdepth range). Finite element numerical calculation of the mathematical model is set up according to the above parameters, the numerical calculation model under various working conditions will submit Lsdyna program to calculate $K$ file. The location the maximal vertical vibration extracted, through the postprocessing software data. Fig. 1 shows the relationship between the vibrationisolating rate and the deep ${H}_{d}$ of the vibration isolating under four superdepth $h$ conditions.
According to numerical calculation results, the data is fitted with the superdepth $h$ = 1.5 m, 2.0 m, 2.5 m and 3.0 m respectively, and it can express by following equation:
$\lambda =93.1\left(1{e}^{0.381{H}_{d}}\right)\times 100\%,\left(h=2.0\mathrm{m}\right),$
$\lambda =92.1\left(1{e}^{0.348{H}_{d}}\right)\times 100\%,\left(h=2.5\mathrm{m}\right),$
$\lambda =91.3\left(1{e}^{0.307{H}_{d}}\right)\times 100\%,\left(h=3.0\mathrm{m}\right).$
In the formula, $\lambda $ is vibrationisolating rate (%); ${H}_{d}$ is the depth of the vibrationisolating slot (m); $e$ is the natural constant, and the value is 2.718. The distribution of the four fitting formulas and their data points in Eq. (1) shown in Fig. 2. It can be seen that the fitting effect of the expression type of this function is relatively good correlation.
The results show that for achieving a good vibration isolating effect, the depth of the vibrationisolating slot need to be larger with the increase of the pore depth. In addition, it can be shown from Eq. (1) that the maximum difference of each fitting formula is the power index value, which should lead to the difference in the trend of vibration isolating, due to the difference of the superdepth $h$. As a result, the fitting formula reflects the important message, namely for the same open blasting region, blasting in many different ways of design parameters summed up, the super depth (charge depth) is a critical parameter, and it can reflect the power index values in fitting formula, the smaller the charge is, the larger the power exponent is. This conclusion for actual engineering design has very important reference value, namely, to obtain ideal vibrationisolating effect, the depth of the vibrationisolating slot is larger than that of the pore depth.
Fig. 1The vibrationisolating rate λ of the different superdepth
Fig. 2The relationship curve between vibrationisolating rate λ and depth Hd with the different superdepth h
3.2. Propagating medium
The blasting seismic wave propagated in rock and soil medium, which has the characteristics of medium structure and physical and mechanical properties. When blasting seismic waves pass the rock and soil medium, physical and mechanical properties and the original structure properties are different, which lead to a certain difference of the dynamic response in the propagation and attenuation characteristics. The use of the M.·A.·Sadov empirical formula can predict the intensity of blasting seismic waves, which also takes into account the impact of blasting seismic wave propagation media. In the process of actual engineering construction, the oil and gas pipeline laid in the rock and soil medium with different characteristics. Therefore, it is necessary to consider the medium factors of surrounding rock and soil in the explosion zone during the study. For this purpose, three representative geotechnical media selected for calculation, namely, medium granites (hard rock), hard limestone (medium hard rock) and medium solid marl (soft rock). The related physical and mechanical properties parameters of the three types of rock and soil shown in Table 1.
In order to study vibrationisolating effect of the propagating medium on blasting seismic wave, the research based on the blasting pore network parameters. It is to maintain the height of the steps, pore diameter, pore spacing, row spacing, filling depth, depth, and length of charge, while the explosive zone medium is different. The finite element numerical calculation model is set up according to the above principles, it will submit Lsdyna program to calculate $K$ file under various working conditions and extract the maximal vertical vibration through the postprocessing software data. Fig. 3 shows the relationship between the vibrationisolating rate and the deep ${H}_{d}$ of the vibrationisolating in three kinds of rock and soil.
Table 1The physical and mechanical properties parameters of the three types of rock and soil
Type  Density (kg/m^{3})  Modulus of elasticity (GPa)  The bulk modulus (GPa)  Shear modulus (GPa)  Poisson’s ratio  The compressive strength (MPa) 
Medium granites  2680  62.80  40.92  28.42  0.26  160 
Limestone  2490  48.67  25.95  20.58  0.29  116 
Marl  2370  33.40  20.72  16.46  0.31  55 
According to the above numerical calculation results, the calculation data of rock and soil media in the three detonation zones fitted, which expressed by Eq. (2):
In the formula, $\lambda $ is vibrationisolating rate (%); ${H}_{d}$ is the depth of the vibrationisolating slot (m); $e$ is the natural constant, and the value is 2.718. The distribution of the three fitting formulas and their data points in Eq. (2) shown in Fig. 4. The fitting effect of the expression type based on this function still presents a relatively good correlation.
Fig. 3The vibrationisolating rate λ in three kinds of rock and soil
Fig. 4The relationship curve between vibrationisolating rate λ and depth Hd with the different rock and soil
The results show that there is a significant effect on the vibrationisolating rate of rock and soil. It shown from the calculation results that with the increase of the depth of the vibrationisolating slot, the difference is slightly increased. In addition, it can be seen from Eq. (2) that there is a slight difference in the power index value of each fitting formula, and its biggest difference lies in the coefficient outside the formula parenthesis (referred to the influence coefficient of blasting dielectric). As a result, the fitting formula reflects the important message is that the explosive medium influence coefficient is a key parameter, for different blasting open regional site media and similar blasting parameters. This conclusion is of great reference value for the design of vibrationisolating engineering.
3.3. Buried depth
Specified in the specifications for engineering design of transmission gas pipeline: “laying pipeline should be buried way, the layer soil thickness of buried pipeline should comply with the provisions of the Table 2. When It can’t meet the requirements of layer soil thickness, external load is larger, external operations may endanger pipeline, protection measures should be taken”.
Table 2Minimum layer thickness (m)
Regional level  Soil type  Rock  
Dry land  Paddy field  
Level 1  0.6  0.8  0.5 
Level 2  0.6  0.8  0.5 
Level 3  0.8  0.8  0.5 
Level 4  0.8  0.8  0.5 
The above specification only specifies that the minimum layer soil thickness is the depth of the pipe (from the top of the pipe). In actual engineering, burial depth is actually a certain range. We need to study the influence rule of deep ${h}_{g}$ on the vibrationisolating rate of different pipelines, under certain blasting parameters and vibrationisolating slot.
In order to study the effect of buried depth ${h}_{g}$ on vibration isolating, the parameters of blasting holes are set up. Particular way is to keep bench height, pore diameter, pore spacing and row spacing, depth of the filling, charging length is unchanged, and the pipeline buried depth ${h}_{g}$ were taken according to actual condition of 0.5 m, 1.2 m, 2.0 m, 2.5 m (reference existing domestic mine blasting parameters of superdepth range). The finite element numerical calculation model is set up according to the above principles, a numerical calculation model under various working conditions will submit Lsdyna program to calculate $K$ file and extract the maximal vertical vibration through the postprocessing software data. Fig. 3 shows the relationship between the vibrationisolating rate and the deep ${H}_{d}$ of the vibrationisolating under different buried depth conditions.
Fig. 5The vibrationisolating rate λ under different buried depth
Fig. 6The relationship curve between vibrationisolating rate λ and depth Hd under different pipe buried depth
According to the above numerical calculation results, the calculation data of buried deep ${h}_{g}$ in different pipelines fitted, which expressed by Eq. (3):
$\lambda =92.1\left(1{e}^{0.348{H}_{d}}\right)\times 100\%,\left({h}_{g}=1.2\mathrm{m}\right),$
$\lambda =92.9\left(1{e}^{0.275{H}_{d}}\right)\times 100\%,\left({h}_{g}=2.0\mathrm{m}\right),$
$\lambda =91.3\left(1{e}^{0.246{H}_{d}}\right)\times 100\%,\left({h}_{g}=2.5\mathrm{m}\right).$
In the formula, $\lambda $ is vibrationisolating rate (%); ${H}_{d}$ is the depth of the vibrationisolating slot (m); $e$ is the natural constant, and the value is 2.718. The distribution of the fitting formula and its data points in Eq. (3) shown in Fig. 6. The fitting effect of the expression type of this function still shows a good correlation.
The calculation results show that the depth ${h}_{g}$ has a significant effect on the vibrationisolating ratio. Under the condition of certain superdepth pore, the larger the pipe depth is, the lower the vibrationisolating rate is. In the case of large pipe buried depth, if the intensity peak of blasting seismic wave exceeds the allowable threshold value of the pipeline vibration, it needs a large depth of vibrationisolating slot to achieve a good vibrationisolating effect. This gives us some enlightenment that the depth of the vibrationisolating slot in the actual project should be at least greater than the depth of the pipe. In addition, it shown from Eq. (3) that the maximum difference of each fitting formula is the power index value, which should be the difference in the vibrationisolating trend, due to the difference of the buried depth ${h}_{g}$ of the pipe. Therefore, the important information reflected in the fitting formula is the influence of the buried depth ${h}_{g}$, which reflected as the power exponent value in the fitting formula. That is, the lower the depth ${h}_{g}$ is, the greater the power exponent value is. This conclusion for actual engineering design of vibrationisolating slot has very important reference value. To obtain ideal vibrationisolating effect, vibrationisolating slot depth compared with pipeline buried depth is greater than a certain value.
4. Conclusions
1) For achieving a good vibration isolating effect, the depth of the vibrationisolating slot needs to be larger with the increase of the depth of the hole. The difference of the superdepth $h$ leads to the difference in the trend of vibration isolating. The depth of the vibrationisolating slot is larger than the depth of the hole, which can improve the vibrationisolating rate.
2) The different type of rock and soil medium is a significant effect on the vibrationisolating rate. There is explosive engineering with different blasting media and similar blasting parameters. The medium influence coefficient of explosive region is a key parameter, which is of great reference for the design of vibrationisolating engineering.
3) The depth ${h}_{g}$ has a significant effect on the vibrationisolating ratio. The depth of the vibrationisolating slot in the actual project should be at least greater than the depth of the pipe. To obtain ideal vibrationisolating effect, vibrationisolating slot depth compared with pipeline buried depth is greater than a certain value.
Acknowledgements
This research was financially supported by the National Nature Science Foundation of China, Nos. 51678567, 11102233 and 51608530.
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