Mining Handbook. Volume 2, Blasting and Rock Support

Author: Chief Editor: Xu Xiaohuo
Publisher:
Publish Date: 1999-09-01
Features: The Mining Handbook is divided into 41 chapters and published in seven volumes:
Volume 1: Mine Geology and Mine Surveying
Volume 2: Blasting and Rock Support
Volume 3: Open-Pit Mining
Volume 4: Underground Mining
Volume 5: Mine Transport and Equipment
Volume 6: Mine Ventilation and Safety
Volume 7: Mine Management
This volume is the second one, covering six chapters: Rock Mechanics, Blasting Engineering, Rock Support and Reinforcement, Mine Haulage and Ore Dumping, Rock Support and Strengthening, and Mine Tunnel Engineering. This book is primarily intended for mining engineers but is also an important reference for researchers, designers, educators, and mine management personnel involved in mining.
Excerpt:
Core?br>6.4.2.1 Stress-Strain Relationship Curve A Experimental Curve
The mechanical properties of rock are reflected in its deformation and failure under load. Summarizing the results of a series of compression tests, the typical stress-strain and dilatancy relationship curves shown in Figure 6-8 can be obtained. For a complete rock specimen, when compressive stress is applied from zero, compressive strain occurs along the force direction, while tensile strain occurs laterally. Initially, small loads can produce significant deformation, which continues until point A. The curve in the OA segment bends downward, and if unloaded in the OA range, residual deformation is observed. This segment is known as the "compaction segment," typically attributed to crack closure. Due to the low stress level at point A, this segment is often disregarded.
Elastic Segment AB: Within this segment, there is a one-to-one correspondence between stress and strain, and AB is nearly linear. Unloading in the AB segment does not produce residual deformation, and this behavior can be described by elastic mechanics.
Yield Point B: This is an important feature point on the stress-strain curve, known as the yield point. Beyond B, the material enters the ductile or strain-hardening segment.
Ductile or Strain-Hardening Segment BC: At any point M in the BC segment, if unloaded, significant irreversible residual deformation (measured as B′M′) is observed. When a material can sustain permanent deformation without losing its load-bearing capacity, it is said to be in a ductile state or exhibit ductility [12]. If reloading begins from M, the working point moves along M"M upward, and the material regains elasticity within this segment, with M′M approximately parallel to AB. Once the stress reaches M, the material re-yields. This new yield point M is called a secondary yield point. The graph shows that the secondary yield stress is greater than the initial yield stress, a phenomenon known as strain hardening or work hardening. It is worth noting that when loading starts from O, the compressive strain is greater than the lateral extension, and the specimen volume decreases. Near point B, the lateral extension strain increases faster than the longitudinal shortening, and after B, volume shrinkage changes to volume expansion, known as dilatancy. Studies indicate that this dilatancy is due to the opening of micro-cracks parallel to the compression direction.
Ultimate Strength Point C: This is the point of maximum stress on the stress-strain curve, known as the uniaxial compressive strength σC. Research shows that at this stage, micro-cracks in the specimen begin to concentrate on inclined planes passing through its center, forming a dense fracture surface, also known as a shear plane.
Brittle or Softening Segment CD: After C, due to the formation of the shear plane, the specimen's load-bearing capacity rapidly decreases. If the maximum load is maintained or not reduced promptly, the specimen may suddenly fracture under overpressure, causing rock burst. If the load is reduced promptly and appropriately, the stress-strain relationship can follow the CD curve from C to D, where the load-bearing capacity decreases with increasing deformation, a condition known as a brittle state or brittleness. If the load is reduced rapidly at point L in the CD segment, an unloading line LL′ can be obtained. When reloading from L′, the reloading line will yield at L″, where the stress is lower than at L. This reduction in yield stress is called strain softening.
In the CD segment, the specimen undergoes significant dilatancy, which is not only due to crack opening but also to sliding along the shear plane. Since the sliding surface is rough and uneven, dilatancy accompanies the sliding.
In summary, if the load is not reduced promptly and sufficiently after C, failure will automatically develop in the specimen. Therefore, the post-C segment is a progressive failure segment and an unstable segment.
The above deformation behavior can be largely generalized to low confining stress triaxial loading conditions. As confining stress increases, compressive strength improves, and the behavior of the stress-strain curve undergoes significant changes. To understand these conditions, refer to relevant specialized literature, such as reference [12].
B Theoretical Curve Stress-Strain Relationship Experimental curves often vary depending on the specimen used and can be complex. To make the analysis more general, theoretical calculations typically employ typicalized stress-strain curve models. A simplified example is shown in Figure 6-9. Figure 6-9a shows a model where strain ε and stress σ have a linear relationship, known as the elastic model, which is widely used. Figure 6-9b shows an ideal elastoplastic model, c shows a linear strain-hardening and strain-softening elastoplastic model, d shows a viscous model, e shows an elasto-viscous model, and f shows a viscoelastic model, among others. A single elastic, plastic, or viscous body can be represented by elements such as springs, sliders, and hydraulic cylinders. Complex materials can be constructed using a combination of these elements. For example, the simplest elasto-viscous body can be composed of a series of springs and hydraulic cylinders in series, while the simplest viscoelastic body can be composed of springs and hydraulic cylinders in parallel.