حل تحلیلی انتشار امواج انفجار در سنگ با استفاده از تئوری الاستودینامیک

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشکده مهندسی معدن و متالورژی، دانشگاه یزد، یزد، ایران

2 دانشکده مهندسی معدن، دانشگاه تهران، تهران، ایران

چکیده

عملیات انفجار در سنگ کاربردهای مختلفی در موارد گوناگون دارد. بیشترین کاربرد این عملیات در خردایش سنگ در معادن بوده که برای استخراج ماده معدنی انجام می‌شود. حفاری کانال، ترانشه، تونل و شیروانی‌های سنگی نیز از دیگر کاربردهای عملیات انفجار در سنگ است. پدیده‌های دینامیکی مانند زلزله و انفجار در سنگ عوامل انتشار امواج دینامیکی تنشی در سنگ هستند. ازاین‌رو انتشار امواج و مطالعه چگونگی انتشار آنها از اهمیت بالایی در شناخت اثرات بعدی پدیده‌های دینامیکی در سنگ برخوردار هستند. به‌منظور حل چنین مسئله‌ای می‌توان از روش‌های مختلفی استفاده کرد، ولی در میان این روش‌ها حل تحلیلی مسئله ازنظر دقت نسبت به سایر روش‌ها برتری دارد. در مطالعه حاضر یک تابع گرین الاستودینامیک دوبعدی برای حل مسئله انتشار امواج انفجار در سنگ توسعه داده شده است. ابتدا از معادلات حرکت و انفجار به‌عنوان معادلات حاکم استفاده شده و درنهایت تابع گرین مربوطه برحسب جابجایی به دست آمده است. همچنین میدان سرعت ذره‌ای بر اساس تابع حاصله توسعه داده شده‌اند. بر همین اساس یک چال انفجاری در یک محیط الاستیک همگن همسانگرد ایزوتروپ بی‌نهایت سنگی مورد تحلیل قرارگرفته و نتایج حاصل از آن ارائه شده است. سپس به‌منظور بررسی صحت نتایج حاصل از روند تحلیلی ارائه‌شده، یک مسئله واقعی با استفاده از راه‌حل پیشنهادی مدل‌سازی و حل شده است. مسئله موردنظر پیش‌ازاین توسط محققی دیگر به‌صورت تجربی و با استفاده از یک روش عددی حل شده است. نتایج این تحقیق در قالب حداکثر سرعت ذره‌ای در هر دو روش عددی و داده‌های برداشت‌شده از یک انفجار واقعی با یکدیگر مقایسه شده‌اند. درنهایت نتایج حاصل از پژوهش حاضر با نتایج مطالعه مذکور و در قالب همان حداکثر سرعت ذره‌ای مقایسه شده است. این مقایسه نشان داده است که حداکثر سرعت ذره‌ای حاصل‌شده از روش پژوهش حاضر تطابق خوبی با واقعیت دارد.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

Analytical solution of the explosion-induced wave propagation in rock using elastodynamic theory

نویسندگان [English]

  • Meysam Lak 1
  • Mohammad Fatehi Marji 1
  • Alireza Yarahmadi Bafghi 1
  • Abolfazl Abdollahipour 2
  • mehdi pourghasemi sagand 1
1 Dept. of Mining and Metallurgy Engineering, Yazd University, Yazd, Iran
2 Dept. of Mining Engineering, University of Tehran, Tehran, Iran
چکیده [English]

Summary
In this study, an analytical solution has been introduced to solve the explosion-induced wave propagation phenomenon in rock using elastodynamic theory.
Introduction
The explosion of explosives in the blast-hole can apply very high pressure to the surrounding rock media. The pressure can cause to propagate cracks and fractures and eventually fragment and destroy them. Rock blasting, like other dynamic phenomena, needs to propagate waves and dynamic stresses through the body. Therefore, the study of the propagation of waves is of great importance in understanding the subsequent effects of rock blasting. For this purpose, an analytical algorithm is used to obtain the appropriate Green functions to achieve the best description of the problem. To solve the blast-induced wave propagation problem.
Methodology and Approaches
A two-dimensional elastodynamic Green's function has been analytically derived. Firstly, Navier's equations of motion and explosion equations have been used as governing equations. Then, using the Helmholtz theory, the Navier equations have been separated into two scleral and vector fields in terms of displacement. Explosion pressure as a body force has been added to the equations using the Poisson function. After performing the relevant calculations and solving the above equations, the corresponding Green function in terms of displacement is obtained. Moreover, a time-dependent green function is developed for the particle velocity using the basic functions and the resulting green function. After finding the appropriate Green functions, a typical problem consisting of a blast-hole in an elastic homogenous isotropic infinite rock media has been investigated and modeled. Finally, to validate, a real problem has been analytically modeled and solved using the proposed solution.
Results and Conclusions
Its results have been compared with results from a finite element-discrete element numerical method and the explosion reality results. Based on the results of the comparison, there is a good agreement between the analytical, experimental, and numerical results at different distances from the blast-hole. A good match between the analytical results of this study and the experimental and numerical results of previous studies shows the validity of the proposed method and confirms the Green function obtained in this study. In general, it can be said that this method can be used to study the propagation of elastic waves in rock and rock-like materials. Also, it can be utilized from the resulting Green functions in other methods for different purposes as an input dynamic function.

کلیدواژه‌ها [English]

  • Blasting
  • Green&rsquo
  • s function
  • Analytical solution
  • Wave propagation
  • Rock Dynamics

مراجع

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  • تاریخ دریافت: 07 آبان 1400
  • تاریخ بازنگری: 01 دی 1401
  • تاریخ پذیرش: 20 بهمن 1401

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