This paper presents a chance-constrained integer programming approach based on the linear method to solve the longterm open pit mine production scheduling problem. Specifically, a single stockpile ...has been addressed for storing excess low-grade material based on the availability of processing capacity and for possible future processing. The proposed scheduling model maximizes the project NPV while respecting a series of physical and economic constraints. Differently from common practice, where deterministic models are used to calculate the average grade for material in the stockpiles, in this work a stochastic approach was performed, starting from the time of planning before the stockpile realization. By performing a probability analysis on two case studies (on iron and gold deposits), it was proven that the stockpile attributes can be treated as normally distributed random variables. Afterwards, the stochastic programming model was formulated in an open pit gold mine in order to determine the optimum amount of ore dispatched from different bench levels in the open pit and at the same time a low-grade stockpile to the mill. The chance-constrained programming was finally applied to obtain the equivalent deterministic solution of the primary model. The obtained results have shown a better feed grade for the processing plant with a higher NPV and probability of grade blending constraint satisfaction, with respect to using the traditional stockpile deterministic model.
The higher order displacement discontinuity method (HODDM) utilizing special crack tip elements has been used in the solution of linear elastic fracture mechanics (LEFM) problems. The paper has ...selected several example problems from the fracture mechanics literature (with available analytical solutions) including center slant crack in an infinite and finite body, single and double edge cracks, cracks emanating from a circular hole. The numerical values of Mode I and Mode II SIFs for these problems using HODDM are in excellent agreement with analytical results (reaching up to 0.001% deviation from their analytical results). The HODDM is also compared with the XFEM and a modified XFEM results. The results show that the HODDM needs a considerably lower computational effort (with less than 400 nodes) than the XFEM and the modified XFEM (which needs more than 10000 nodes) to reach a much higher accuracy. The proposed HODDM offers higher accuracy and lower computation effort for a wide range of problems in LEFM.
Slope stability estimation is an engineering problem that involves several parameters. The interactions between factors that affect slope instability are complex and multi-factorial, so often it is ...difficult to describe the slope stability mathematically. This paper, proposes the use of a genetic algorithm (GA) as a heuristic search method to find a regression model for analyzing the slope stability. For this purpose, an evolutionary algorithm based on GA was used to develop a regression model for prediction of factor of safety (FS) for circular mode failure. The proposed GA uses the root mean squared error as the fitness function and searches among a large number of possible regression models to choose the best for estimation of FS from six geotechnical and geometrical parameters. For validation of the model and checking its efficiency, a validation dataset was used to evaluate FS using the proposed model and a previously developed mathematical GA based model in the literature. Results have shown that the presented model in this study was capable of evaluating FS at a higher level of confidence regarding the other model (R = 0.89 for presented model in this study comparing R = 0.78 for the other model) and can be efficient enough to be used as a simple mathematical tool for evaluation of factor of safety for circular mode failure especially in preliminary stages of the designing phase.
Production planning of an open pit mine is defined as determining the extraction sequence of blocks in the final pit limit with the goal of maximizing Net Present Value (NPV) while considering the ...constraints imposed on the mining system. Mathematical programming models are used to optimize long-term open pit production planning problems. In real mines with several thousands of blocks and several scheduling periods, however, these methods lose their efficiency by increasing the number of decision variables, and it is almost impossible to solve and obtain a solution in a reasonable time using current solvers. In this paper, a new method based on block clustering was proposed to reduce the model size. In the first step, blocks are aggregated in clusters called "mother clusters" using the concept of clustering as a mathematical programming problem and solved using Genetic Algorithm (GA). In the second step, the mother clusters are converted to the mining clusters considering the practicality issues. The results of implementing the proposed method on a real deposit showed that block clustering could decrease the number of binary variables from 476,100 to 5,652. This led to a significant reduction in solution time from 372 hours to 23.4 seconds compared to the original block model. The clustering strategy was also able to realize more than 82% of the NPV obtained from scheduling original blocks.
Many problems in subsurface rocks which are naturally filled with saturated cracks and pores (with one or more fluid phases) are better understood in a poroelastic framework. Displacement ...discontinuity method (
DDM
) is particularly ideal for problems involving fractures and discontinuities. However, the
DDM
in its original form is limited to elastic problems. The paper derives fundamental solutions of a poroelastic
DDM
. Then introduces a numerical formulation and implementation for the poroelastic
DDM
in a code named constant element poroelastic
DDM
(
CEP-DDM
). The accuracy and validity of the proposed solution and the newly developed code is verified by an analytical solution at short-time and long-time. Numerical results showed good agreement with analytical results at short time (undrained response) and long time (
t
=
8000
s) (drained response). A crack propagation scheme for crack propagation problems is introduced and demonstrated in an example which enables the code to follow crack propagation in time and space.
Hydraulic fracturing as applied to well stimulation is analyzed. Propagation of one or more hydraulic fractures from a wellbore that is oriented with either the maximum or intermediate principal in ...situ stress is studied. A Higher Order Displacement Discontinuity Method (HODDM) with special crack tip elements is used for achieving higher accuracy in simulation of the process. The effect of fluid pressure inside pre-existing fractures is considered. A uniformly distributed internal pressure, which implies injection of a fluid with a very low viscosity is assumed. On the onset of initiation, the crack may reorient itself as it extends from the wellbore, until it becomes aligned with the preferred direction for crack propagation relative to the far-field stresses. Propagation of multiple cracks has been considered to study their interaction. In such cases, some cracks are unable to extend at all, or they arrest after limited propagation, but others can propagate in length relative to earlier developed fractures and even may intersect each other. Also two common perforation phases are studied and best orientations for each one is determined.
•Higher order DDM with four special crack tip elements is used for more accuracy.•Hydraulic fracturing as applied to well stimulation is analyzed.•Interaction of several pre-existing fractures starting from a wellbore is studied.•Propagation, arrest and interference of pre-existing fractures have been observed.•Critical inclination angles are suggested for better results in hydraulic fracturing.
Rate of penetration of a Tunnel Boring Machine（TBM） in a rock environment is generally a key parameter for the successful accomplishment of a tunneling project.This paper presents the results of a ...study into the application of an Artificial Neural Network（ANN） technique for modeling the penetration rate of tunnel boring machines.A database,including actual,measured TBM penetration rates,uniaxial compressive strengths of the rock,the distance between planes of weakness in the rock mass and rock quality designation was established.Data collected from three different TBM projects（the Queens Water Tunnel,USA,the Karaj-Tehran water transfer tunnel,Iran,and the Gilgel Gibe II hydroelectric project,Ethiopia）.A five-layer ANN was found to be optimum,with an architecture of three neurons in the input layer,9,7 and 3 neurons in the first,second and third hidden layers,respectively,and one neuron in the output layer.The correlation coefficient determined for penetration rate predicted by the ANN was 0.94.
Rad prikazuje uporabu vjerojatnosnoga cjelobrojnog programiranja, temeljenoga na linearnome algoritmu, za dugoročno rješavanje proizvodnje u rudniku otvorenoga kopa. Obrađeno je jedno odlagalište ...jalovine sa „siromašnom” koncentracijom rude u cilju aktiviranja toga materijala u budućoj preradbi korisne sirovine. Takav projekt maksimizira trenutačnu vrijednost rudarenja uzimajući u obzir niz fizičkih i ekonomskih varijabli. Posebnost u odnosu na determinističke modele koji se danas uglavnom koriste za izračun granične prosječne vrijednosti koncentracije rude prije odlaganja kao jalovine izražena je stohastikom. Ona je uključila vjerojatnosnu analizu dvaju slučajeva, tj. za ležište željeza i zlata. U obama je dokazano kako se varijable određene na odlagalištu mogu opisati normalnom razdiobom. Stohastički model programiran je za rudnik zlata te je uzeta u obzir optimalna vrijednost rude razvrstane na različitim rudničkim razinama, a prije slanja na obradbu (mljevenje). Optimizirani model zatim je primijenjen za dobivanje usporednoga determinističkog modela. Rezultati su upozorili na to da je konačno rješenje pokazalo znatno bolji odabir granične koncentracije rude koja se mogla poslati na daljnju obradbu. Time je uvećana i ukupna vrijednost rudnika/ležišta.
Rocks are naturally filled with cracks and pores that are saturated with one or more fluid phases. Many problems in rock mechanics, petroleum engineering, geophysics, etc. deal with cracks and ...discontinuities in rock formations. These problems should consider effects of a porous medium. Displacement discontinuity method (DDM) as an indirect boundary element method is particularly ideal for problems involving fractures and discontinuities. However, the DDM in its original form is limited to elastic problems. The paper uses a fundamental solution of a point displacement discontinuity in poroelastic medium to obtain the solution for a poroelastic DDM. Then it introduces a numerical formulation and implementation for the poroelastic DDM in a code named CEP-DDM (Constant Element Poroelastic DDM). The accuracy and validity of the proposed solution and the newly developed code are verified by two analytical solutions, another numerical solution, and some field measurements. These results showed good agreement between CEP-DDM and other methods’ results. The verifications prove the accuracy and applicability of the proposed numerical model in a wide range of real-world problems.
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