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The energy conversion in rocks has an important significance for evaluation of the stability and safety of rock engineering. In this paper, some uniaxial compression tests for fifteen different rocks were performed. The evolution characteristics of the total energy, elastic energy, and dissipated energy for the fifteen rocks were studied. The dissipation energy coefficient was introduced to study the evolution characteristics of rock. The evolution of the dissipation energy coefficient for different rocks was investigated. The linear interrelations of the dissipation energy coefficients and the yield strength and peak strength were explored. The method was proposed to determine the strength of rock using the dissipation energy coefficients. The results show that the evolution of the dissipation energy coefficient exhibits significant deformation properties of rock. The dissipation energy coefficients linearly increase with the compaction strength, but decrease with the yield strength and peak strength. Moreover, the dissipation energy coefficient can be used to determine the rock burst proneness and crack propagation in rocks.

Geotechnical engineering problems in civil, mining, and petroleum engineering practices [

The deformation and failure process of rock is the gradual damage evolution process driven by energy. It would be better to describe the deformation and failure of rocks from the perspective of energy [

In this work, the uniaxial compression tests were conducted for different rocks to study the energy conversion. The evolution of the total input energy, elastic energy, and dissipation energy was systematically analyzed during the deformation and failure process of rock. A new energy parameter, dissipation energy coefficient, was introduced. The purpose is to clarify the energy evolution characteristics. Besides, the linear relationship between the dissipation energy coefficient and the strength of rock was also established.

The rock specimens in this experiment were mudstone, physicochemical slate, schist, limestone, gneiss, sandstone, porphyrite, dolomite, shale, metamorphic sandstone, marble, quartz schist, quartzite, diorite, and granite. They were collected from a quarry in Shaanxi, China. All specimens were drilled and processed into

Rock types and basic parameters.

Rock types | Density | Moisture content | Water absorption | Compressive strength | Elastic modulus | Tensile strength | Poisson’s ratio |
---|---|---|---|---|---|---|---|

Mudstone | 2.50 | 2.36 | 3.30 | 32.53 | 4.21 | 4.37 | 0.24 |

Physicochemical slate | 2.72 | 0.87 | 1.28 | 32.48 | 4.06 | 4.28 | 0.24 |

Schist | 2.75 | 0.36 | 0.50 | 41.11 | 4.53 | 4.75 | 0.23 |

Limestone | 2.63 | 0.29 | 0.47 | 37.15 | 4.72 | 4.32 | 0.24 |

Gneiss | 2.72 | 0.22 | 0.74 | 38.52 | 4.81 | 4.25 | 0.24 |

Sandstone | 2.67 | 1.89 | 2.73 | 55.64 | 6.75 | 6.24 | 0.23 |

Porphyrite | 2.60 | 1.57 | 2.35 | 65.77 | 7.46 | 6.87 | 0.22 |

Dolomites | 2.70 | 0.35 | 0.71 | 91.57 | 10.35 | 8.79 | 0.21 |

Shale | 2.68 | 0.52 | 1.12 | 90.03 | 9.78 | 8.63 | 0.20 |

Metamorphic sandstone | 2.74 | 0.03 | 0.73 | 99.66 | 11.64 | 9.73 | 0.20 |

Marble | 2.68 | 0.04 | 0.75 | 105.95 | 12.25 | 10.54 | 0.19 |

Quartz schist | 2.76 | 0.14 | 0.72 | 127.03 | 14.95 | 11.83 | 0.19 |

Quartzite | 2.81 | 0.08 | 0.70 | 164.36 | 19.29 | 12.56 | 0.18 |

Diorite | 2.80 | 0.11 | 0.71 | 207.44 | 24.75 | 14.28 | 0.17 |

Granite | 2.85 | 0.05 | 0.35 | 261.58 | 29.65 | 15.36 | 0.16 |

The uniaxial compression tests were conducted on the WDT-1500 testing system (Figure

The WDT-1500 multifunctional material testing machine.

It is assumed that the deformation and failure process of rock under the external load is no heat loss [

Relationship between the elastic strain energy and dissipated energy of rock under uniaxial compression [

The deformation and failure process of rock involves the complex energy conversion. To analyze the process of the energy evolution, the dissipation energy coefficient was introduced, which is the ratio of the dissipated energy to the elastic energy at any time during the deformation process of rock [

The deformation and failure process of rock has four stages: the compaction stage, elastic deformation stage, yield stage, and failure stage [

Compaction stage: the stress-strain curve is nonlinear, which results from the closure of some primary microcracks and pores under the action of initial pressure [

Elastic deformation stage: the stress-strain curve is linear, and the slope of linear portions is the elastic modulus.

Yield stage: as the stress increases, the stress-strain curves gradually depart from the linear. It is due to the fact that the sample gradually transformed from elastic deformation to elastic-plastic deformation.

Failure stage: when the peak strength is reached, the sample shows macroscopic fracture. Moreover, the postpeak curves present two different failure characteristics (Figure

Stress-strain curves for different rocks under the uniaxial compression condition.

The deformation and failure process of rock also is the process of the generation, expansion, connection, and slip of the microcracks. The generation of new cracks needs absorption of energy, and the friction between the crack surfaces dissipate energy. Actually, the process of rock deformation and failure is the process of energy accumulation and dissipation [

Figure

Variation of total energy with stress for different rocks.

Figure ^{3} and 20 kJ/m^{3}, respectively (Figures ^{3} and 430 kJ/m^{3}, respectively (Figures

Variation of elastic energy with stress for different rocks.

The energy dissipation is the main factor leading to the internal damage of rocks [^{3} and 15 kJ/m^{3}, respectively (Figures

Variation of dissipated energy with stress for different rocks.

The dissipation energy coefficient

Variation of the dissipation energy coefficient with stress for different rocks.

The compaction stage (OA): the point A is called the compaction point, which also is the first characteristic point of the curve. The stress of point A is defined as compaction strength. The dissipation energy coefficient

The elastic deformation stage (AB): the point B is called the yield point, which is the second characteristic point of the curve. The dissipation energy coefficient

The yield stage (BC): the point C is called the peak point, which is the third characteristic point of the curve. The dissipation energy coefficient

The failure stage (CD): the dissipation energy coefficient

It can also be seen that the primary and secondary status of elastic energy and dissipated energy vary during the four stages. In the initial stage of loading,

According to Table ^{2}), respectively. The correlation coefficient ^{2} is 0.97, 0.94, and 0.94, respectively. It shows that there is a strong linear relationship between the dissipation energy coefficients and strength in three different characteristic points.

Strength and dissipation energy coefficients at three different characteristic points.

Rock types | Compaction point | Yield point | Peak point | |||
---|---|---|---|---|---|---|

Mudstone | 1.06 | 1.40 | 31.77 | 0.41 | 32.53 | 0.54 |

Physicochemical slate | 1.03 | 1.31 | 31.01 | 0.39 | 32.48 | 0.55 |

Schist | 1.15 | 1.76 | 34.59 | 0.31 | 41.11 | 0.53 |

Limestone | 1.09 | 1.43 | 32.74 | 0.32 | 37.15 | 0.54 |

Gneiss | 1.51 | 1.93 | 35.22 | 0.35 | 38.52 | 0.53 |

Sandstone | 1.65 | 2.03 | 49.60 | 0.32 | 55.64 | 0.51 |

Porphyrite | 1.85 | 2.23 | 55.59 | 0.29 | 65.77 | 0.48 |

Dolomites | 2.89 | 2.77 | 86.70 | 0.25 | 91.57 | 0.35 |

Shale | 2.81 | 2.65 | 84.44 | 0.28 | 90.03 | 0.39 |

Metamorphic sandstone | 3.06 | 2.88 | 91.66 | 0.22 | 99.66 | 0.33 |

Marble | 3.35 | 3.14 | 100.40 | 0.21 | 105.95 | 0.29 |

Quartz schist | 4.09 | 3.58 | 122.84 | 0.17 | 127.03 | 0.22 |

Quartzite | 5.23 | 4.05 | 156.79 | 0.12 | 164.36 | 0.16 |

Diorite | 6.44 | 4.54 | 193.18 | 0.07 | 207.44 | 0.1 |

Granite | 7.66 | 4.98 | 229.70 | 0.03 | 261.58 | 0.05 |

Relationships between stress and the dissipation energy coefficients at three different characteristic points. (a) Curve of the dissipation energy coefficients for the compaction point. (b) Curve of the dissipation energy coefficients for the yield point. (c) Curve of the dissipation energy coefficients for the peak point.

Relationships between the characteristic stress and the characteristic dissipation energy coefficient.

The correlation coefficient ^{2} of the fitting functions is 0.91. It shows there is a strong linear relationship between the characteristic stress and the characteristic dissipation energy coefficient.

The stress-strain relationship can describe the deformation and failure processes of rocks, but it also has certain limitations in some aspects [

It is a difficult task to accurately determine yield strength of rocks. Usually, this value can only be approximated, which is typically 0.85∼0.9 of the peak strength [

The yield strength of rocks can be obtained, which is based on equations (

The ratio of the total energy of the prepeak to the elastic energy at the peak is defined as the modified brittleness index [

The judging for rock burst using the BIM value.

BIM value | Rock burst tendency |
---|---|

BIM > 1.5 | Weak rock burst |

1.2 < BIM ≤ 1.5 | Medium rock burst |

1.0 ≤ BIM ≤ 1.2 | Strong rock burst |

A new criterion for rock burst proneness with index

The rock burst proneness can be divided into three categories according to a new criterion (Equation (

The rate of change of the dissipation energy coefficient (

The curve of the rate of change of the dissipation energy coefficient (

In this paper, the conventional uniaxial compression tests for 15 different rocks were conducted. The evolution laws of the elastic properties, dissipative energy, and dissipative energy coefficient were studied. The innovation of this paper is to put forward a new calculation method of rock strength (yield strength) and to investigate the relationship between strength and the dissipation energy coefficient. Moreover, rock is a collection of minerals. The connection between mineral composition and particles is closely related to the mechanical properties and energy characteristics of rock [

According to the energy principle, the energy characteristics and evolution of the dissipation energy coefficient for different rocks under the uniaxial compression condition were investigated. The main conclusions are as follows:

The energy evolution characteristics of different rocks are basically similar at the prepeak, but have significant differences at the postpeak.

Energy evolution provides a good reflection of the rock deformation and failure process, especially the dissipation energy coefficient. It increases at first, then decreases to a minimum value, increases slowly, and finally, increases rapidly. Its evolution stage corresponds closely to the deformation stages of rocks under the uniaxial compression condition.

The dissipation energy coefficients linearly increase with the compaction strength, but decrease with the yield strength and peak strength.

The characteristic dissipation energy coefficients linearly increase with the characteristic stress.

The dissipation energy coefficient can be used not only to accurately divide the rock deformation stage and calculate the yield strength of rocks but also as a new rock burst tendency criterion.

The rate of change of the dissipation energy coefficient shows the mutation E and the mutation F, respectively. The mutations indicate the initial pore closure and new crack propagation of the rock sample, respectively. The mutation E and the mutation F are used as the initial pore closure and new crack propagation criterion.

The data used to support the findings of this study are included within the article.

The authors declare that they have no conflicts of interest.

MM carried out the lab work, participated in data analysis, carried out sequence alignments, participated in the design of the study, and drafted the manuscript; F Pang carried out the statistical analyses and critically revised the manuscript; H Wang and Y Chen collected field data and critically revised the manuscript; and J Zhu conceived the study, designed the study, and helped draft the manuscript. All authors gave final approval for publication and agreed to be held accountable for the work performed therein.

The financial support provided by the National Natural Science Foundation of China (Grants nos. 11902249 and 11872301) is greatly appreciated. This study is sponsored by the Natural Science Basic Research Plan in Shaanxi Province of China (2019JQ-395 and 17JS091).