An equivalent method for blasting vibration simulation

https://doi.org/10.1016/j.simpat.2011.05.012Get rights and content

Abstract

Due to the complicated blasting load, the diversified medium models and various constitutive relations of the rock mass, and a huge job for simulating blasting of multiple holes, it is very difficult and costly to simulate the blasting vibration accurately in numerical computation. This paper presents an equivalent simulation method so as to transform this complex dynamic problem into an approximate initial-boundary problem. The equivalent elastic boundary applied by the blasting load was developed for multiple holes according to the spatial distribution of rock damage around each blasthole. The equivalent mechanics process of the complex blasting load was performed through analysis of the expansion of the borehole volume, the growth of cracks, the movement of stemming and the outburst of detonation gases. In combination with the blasting excavation of the tailrace tunnel in the Pubugou Hydropower Station, particle vibration velocities in the surrounding rock at different distances from the explosion source were simulated by applying this equivalent method based on the dynamic finite element method. The comparison with field monitoring data indicates that this equivalent simulation method is applicable to predicting the far-field dynamic response of the ground subjected to blasting load, and the selection of rock mass properties near the equivalent elastic boundary has a significant impact on simulation results.

Introduction

Because of better adaptability to different geological conditions, drill and blast is still a common excavation technique for rock foundations and underground caverns in the fields of hydropower, transportation and mining. The prediction and control of blasting vibration has long been considered to be an important issue in the blasting design and construction, however, thumb-rule formulas derived by different authors according to their own data obtained from different sites are still the most commonly used method to predict the propagation laws of blasting vibration [1], [2], [3]. Recently, some new control theories, such as the neural network technology, have also been used in this problem [4]. However, these methods depend on a large number of test data and cannot take into account the influence of vibration frequency and duration [5], so they have some limitations in practice.

In recent years, with the rapid development of explosion theory and computer technology, numerical simulation has become a promising approach to studying blast and wave propagation. Researchers worldwide tried to investigate the stress wave propagation in the rock mass with different numerical methods and gained a series of achievements. Ma et al. [6], Wu et al. [7], Toraño et al. [8] and Saharan and Mitri [9], using the finite element method (FEM), predicted blast waves from bench blasting or underground explosion, evaluated and quantified some factors affecting the blasting vibration to simulate complex waves accurately enough in real blasts. Chen and Zhao [10] applied the discrete element method (DEM) for the study of blast wave propagation in jointed rock masses with the universal distinct element code (UDEC). However, propagation of explosive detonation, possible phase transition of rock mass induced by the shock wave, breakage of rock mass, piling of fragments, and finally excitation of seismic waves, all of these processes occur instantaneously and are accompanied by complicated physical and mechanical action procedure. It is still very difficult to simulate blasting vibration precisely during rock fragmentation by blast.

First of all, after the initiation of explosive at the blasthole bottom, the detonation wave rapidly transits to the orifice along the axis and the whole blasthole is filled with detonation gases under a very high pressure and temperature. Under blasting load the blasthole volume expands dynamically in radial direction, fractures occur and further grow driven by explosive gases, the stemming moves outward, and gases escape rapidly from the orifice and gaps, leading to an attenuation of the blasting load. This complex mechanical process is hard to describe by using current numerical simulation methods; an attempt to model the pressure variation applied to the blasthole wall for a typical bench blast was made by Mortazavi and Katsabanis [11] employing discontinuous deformation analysis (DDA), but their study is limited to the expansion of blast chamber in connection with pressure decay. Thus the semi-empirical formula as a direct input of dynamic pressure [12], [13], [14], [15] and the Jones–Wilkens–Lee (JWL) equation of state for detonation products [6], [7], [10] are normally used to simulate the operating load due to their simple forms. Whereas, empirical formulas including the decay function and the triangular load function require assumptions of some parameters [9], and fail to fully consider blasting parameters and the quasi-static load by detonation gases; the JWL equation can only accurately describe the relationship between the load attenuation and the expansion of the blast chamber under an effective stemming without taking the outburst of gases into account. Some authors, e.g. Ding and Zheng [16], demonstrated that the impulse, the form of the time function, is more important in some cases, but the methods mentioned above cannot get close to the real physical characteristics of the blasting load.

Secondly, in the rock mass blasting, the shock wave and detonation gases pressurize on the blasthole wall immediately, and induce the crushed zone, the fractured zone and the elastic seismic zone of surrounding rock mass depending on the distance away from the blasthole. The pressure on the blasthole wall is much higher than the rock compressive strength, and thus, the rock mass in the crushed zone behaves similarly to a fluid. In the fractured zone, the stress wave and the permeation of gases at high pressure encourage the development and growth of radial cracks, while tangential cracks come about as the stress releases in this zone. In terms of constitutive relation, the rock mass in this zone can be considered an elasto-plastic body. In the elastic seismic zone the stress wave has attenuated to a seismic wave, where no direct damage happens to the rock mass. It is clear that different medium models are required in simulation because during the whole blast process the rock mass near the blasthole is broken into discontinuum and finally into fragments from continuum, yet in the far area can still be regarded as a continuum. Furthermore, different constitutive equations need to be adopted as the rock mass around charge are respectively hydro-plastic, elasto-plastic and elastic medium in accordance with its stress state at different distance. Moreover, in the elasto-plastic constitutive relation it is very difficult to judge the loading and unloading process. Considerable efforts have been directed towards developing a continuum–discontinuum model of the rock mass. Chen and Zhao [10], using a coupled method of UDEC (discontinuum-based approach) and AUTODYN (continuum-based approach), modeled a field explosion test and investigated the response of the jointed rock mass. Elasto-plastic model such as Mohr–Coulomb criterion and Drucker–Prager criterion, both isotropic and anisotropic damage models were used in the past to simulate the behavior of rock mass subjected to blasting load [7]. Medium models and constitutive equations near the charge correlate well with the propagation characteristics of the blasting seismic wave, but unfortunately, few of the previous studies have taken a global view of different constitutive equations in the blasting vibration simulation.

Finally, in practice it is a common occurrence to detonate an array of blastholes in the same delay simultaneously, while the dimension of blasthole is much smaller than that of engineering rock mass. This presents a considerable challenge when developing the model as to how to mesh and how to deal with the contact of explosive and rock mass. Previous simulation studies of blasting vibration were always limited to a single blasthole or chamber, and cannot be directly applied to actual engineering applications.

As indicated above, due to the complicated blasting load, the diversified medium models and various constitutive relations of the rock mass, and the difficulty of simulating the blasting of multiple holes, it is uneconomical, even impossible to accurately simulate the whole rock fragmentation by blast from the explosive detonation to the propagation of seismic waves. Seeking a simple and practical equivalent method is necessary for blasting vibration simulation in engineering application. In this regard, Toraño et al. [8] suggested that the pressure pulse lasting for a few milliseconds can be applied against the bench face in bench blasting; Ding and Zheng [16] and Gibson et al. [17] proposed an equivalent source model for the blasting vibrations of fragmentation blasting. Inspired by these works, this study focuses on an equivalent boundary for multiple hole blasting to which the blasting load is applied as an initial and boundary condition. In addition, we will also discuss in theory the equivalent process of the complicated blasting load. As an actual case study of applying this equivalent simulation method, in combination with the No. 1 tailrace tunnel blasting excavation in the Pubugou Hydropower Station, particle vibration velocities of the surrounding rock at different distances from the explosion source are simulated by employing the dynamic finite element software ANSYS/LS-DYNA. Results are compared with field monitoring data.

Section snippets

Equivalent boundary of blasting load application

It is well known that the far-field vibration induced by blasting excavation results from the propagation of elastic seismic waves, to which the elastic model is appropriate. For the purpose of adopting a unified constitutive relation based on continuum mechanics to simulate the blasting vibration, the crushed zone and the fractured zone are treated as parts of the blasting vibration source, and the blasting load is applied to the boundary of equivalent vibration source which is called the

Equivalent process of blasting load

The lasting load variation on a blasthole wall is a complex mechanical process. With the propagation of the detonation wave, the gas pressure in a hole rises to a maximum. It drives the expansion of borehole volume, the growth of cracks, the movement of stemming, which in turn cause the expansion of high-pressure gases and initially reduce the blasting load. After the ejection out of stemming and the interconnecting of cracks, gases escape out quickly, producing a bunch of rarefaction waves.

Project background and field test

The Pubugou Hydropower Station is located in the western part of Sichuan Province in China and in the midstream of Tatu River, a branch of Yangtze River. Its total installed capacity is 3300 MW. This project includes two parallel tailrace tunnels with a horseshoe-shaped cross-section measuring 20.0 m long by 24.2 m wide. Surrounding rock mass is granite with a P-wave velocity value of 4500 m/s. The maximum principal in situ stress is horizontal and perpendicular to the longitudinal axis of the

Results and discussion

To justify this equivalent method, particle vibration velocities simulated both in vertical and horizontal radial directions are compared with field monitoring data at No. 1, No. 3 and No. 4 measurement points. The horizontal distances of these points from the explosion center are 25.0 m, 33.5 m and 49.0 m, respectively as shown in Fig. 3.

Fig. 7 shows the measured and numerically simulated particle vibration velocities in the first calculated condition (only the first measurement point is given in

Conclusions

In this paper, the problems of numerical simulation for the far-field blasting vibration are summarized, including the complicated blasting load, the diversified medium models and various constitutive relations of the rock mass, as well as the difficulties in simulating the blasting of multiple holes. It is much better to use a simple and practical equivalent numerical simulation method for engineering application to predict and control the effect of blasting vibration. For this purpose, this

Acknowledgements

This work is supported by Chinese National Programs for Fundamental Research and Development (973 Program) (2010CB732003), Chinese National 11th 5-year Plan Support Program of Science and Technology (2008BAB29B01), and Chinese National Natural Science Foundation (50779050 and 50909077).

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