A method for measuring rock tensile strain and its mechanical parameters using the ring deformation method
The tensile strain and mechanical parameters of rocks are measured by the ring deformation method, which solves the accuracy problem of strain measurement of rock materials, and achieves high-precision mechanical parameters acquisition, simplifies sample processing and avoids stress concentration and measurement errors.
Patent Information
- Application Number
- CN202210552531.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-05-19
- Publication Date
- 2025-08-26
- Estimated Expiration
- 2042-05-19
AI Technical Summary
It is difficult to accurately measure the tensile mechanical parameters of rocks and rock-like materials, especially strain values and tensile strength, and conventional methods have problems such as stress concentration and large strain measurement errors.
The circular deformation method is used to install a deformation sensor in the circular sample to monitor the deformation amount of the inner hole diameter during radial loading, and the tensile strain, ultimate tensile fracture strain, elastic modulus and tensile strength are calculated based on the elastic beam bending theory.
It improves the accuracy of tensile strain measurement of rock and rock-like materials, avoids stress concentration and strain point measurement errors, simplifies sample processing and is suitable for unidirectional stress states.
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Figure CN114965055B_ABST
Abstract
Description
Technical Field
[0001] The invention relates to the technical field of rock mechanics testing, in particular to a method for measuring rock tensile strain and its mechanical parameters by utilizing a ring deformation method. Background Art
[0002] Materials such as rocks, concrete, and certain brittle metals are resistant to compression but not to tension. They fracture when subjected to very small deformation under tension, without significant plastic deformation. In engineering fields such as mining, tunneling, and underground spaces, the tensile mechanical properties of brittle geotechnical materials (rocks, coal, concrete, etc.) control the damage and instability of structures. The effective acquisition of their mechanical parameters is of great significance for ensuring engineering safety. For metal materials, direct tensile methods are usually used to measure their tensile mechanical parameters due to the convenience of machining and clamping with testing machine fixtures. However, for rocks and rock-like materials, it is very difficult to process them into standard tensile specimens similar to metal materials, and it is difficult to clamp them with conventional fixtures. Therefore, indirect measurement methods are usually used to obtain their tensile mechanical parameters.
[0003] The tensile and compressive mechanical strengths of rocks and rock-like materials vary widely. Tensile mechanical parameters primarily include tensile fracture strain, tensile strength, and elastic modulus. Currently, the main methods for testing the mechanical properties of brittle materials such as rocks include direct tension, Brazilian splitting, three-point bending, and hydraulic fracturing. The Brazilian disc splitting test is a standard method recommended by the ISRM (International Society for Rock Mechanics) for determining rock tensile parameters. However, it is well known that Brazilian discs generate significant stress concentrations at the loading point, making fracture initiation more likely. Even by modifying the loading method, such as using an arc-shaped splitting test apparatus or machining platforms at both ends of the disc to create a platform disc specimen, so that the specimen splits from the center unit of the disc, the tensile strength can be calculated assuming that the failure meets the maximum principal stress criterion. However, it should be noted that the stress state at the disc's center is plane stress, not unidirectional stress. A compressive stress three times the tensile stress inevitably affects rock fracture. The tensile strength of rock measured by the Brazilian splitting method is an "engineering" strength, not the "real" failure strength of the rock. The tensile failure of the Brazilian disk always occurs with the help of considerable compressive stress.
[0004] In existing technology, the most commonly used methods for measuring strain at a specific point in a rock specimen are strain gauge measurement and digital speckle pattern measurement. Digital speckle pattern measurement of rock elastic strain has significant errors, while strain gauge measurement is essentially the average strain within the area covered by the strain gauge, not the actual strain at a specific point. This leads to significant errors in strain measurement in areas with large strain variations. Therefore, further improvements are needed to existing methods for measuring rock tensile strain and its mechanical parameters. Summary of the Invention
[0005] In order to overcome the influence of large errors in plane stress state and strain point measurement data in the measurement of tensile mechanical parameters of rocks and rock-like materials, effectively utilize the advantages of circular ring specimen testing and improve measurement accuracy, the present invention provides a method for measuring rock tensile strain and its mechanical parameters using the circular ring deformation method. The specific technical solution is as follows.
[0006] A method for measuring rock tensile strain and its mechanical parameters using a ring deformation method, comprising the following steps:
[0007] S1. Install a deformation sensor in the hole of the ring specimen, ensuring that the deformation sensor is in close contact with the inner wall of the hole of the specimen.
[0008] S2. Use a testing machine to radially load the ring specimen and monitor the deformation of the inner diameter of the specimen in a direction parallel to the load during compression.
[0009] S4. Determine the relationship curve between the ring specimen load and the vertical deformation in the hole of the ring specimen material;
[0010] S5. Calculate the tensile strain value, ultimate tensile fracture strain, elastic modulus, and tensile strength of the ring specimen material based on the relationship curve.
[0011] Preferably, the deformation sensor includes a fracture mechanics extensometer, an extended aluminum rod, a spring and an arc-shaped contact. Two parallel extended aluminum rods are installed at the measuring end of the fracture mechanics extensometer, and arc-shaped contacts are installed at the other ends of the extended aluminum rods. Springs are arranged between the extended aluminum rods.
[0012] Preferably, the spring sleeve is arranged on the limit screw, and the limit screw is connected to the two lengthened aluminum rods; the limit screw is provided with a thread at one end, and the threaded end is connected to the screw hole on the lengthened aluminum rod.
[0013] Preferably, in the calculation of the tensile strain value, the annular specimen in a plane stress state is formed by bending an elastic beam, and a neutral layer of the annular bending is selected, and the neutral layer is offset during the bending process.
[0014] It is also preferred that the tensile strain value is calculated as:
[0015]
[0016] Among them, ε A is the tensile strain at the intersection of the inner diameter of the ring specimen and the line of action of the radial load it is subjected to, in με; R is the outer diameter of the ring specimen, in mm; r is the inner diameter of the ring specimen, in mm; δ1 is the vertical deformation of the inner diameter of the ring, in mm; β is the comprehensive influence coefficient.
[0017] It is also preferred that in the calculation of the ultimate tensile fracture strain, the maximum load P of the ring radial compression is determined when the macro crack initiation of the brittle material is accompanied by the drop of the load. max Calculate the ultimate tensile fracture strain ε t .
[0018] It is also preferred that the ultimate tensile fracture strain is calculated as:
[0019]
[0020] Where δ is the vertical deformation of the inner diameter of the ring corresponding to the ultimate load, in mm.
[0021] More preferably, the elastic modulus is calculated as:
[0022]
[0023] Among them, k a k is the slope of the elastic stage in the relationship curve between the load of the aluminum ring specimen and the vertical deformation in the hole, r is the slope of the elastic stage in the relationship curve between the radial load of the ring specimen and the vertical deformation in the hole, E 铝 is the elastic modulus of aluminum.
[0024] It is further preferred that the tensile strength is calculated as follows:
[0025]
[0026] Among them, σ t It is the tensile strength, unit is MPa.
[0027] Further preferably, the method is applied to the measurement of tensile strain value, ultimate tensile fracture strain, elastic modulus and tensile strength of rock or rock-like material.
[0028] The method provided by the present invention for measuring rock tensile strain and its mechanical parameters using the ring deformation method has the following beneficial effects:
[0029] This method uses ring specimens. Compared with direct tensile specimens of rocks and rock-like materials, ring specimens are simple and easy to process, and overcome the disadvantage that direct tensile specimens of rocks are difficult to effectively clamp. Compared with disc specimens, ring specimens are not easy to break at the loading point, and are in a unidirectional stress state at the measuring point, avoiding the influence of the plane stress state on the fracture strain of the material.
[0030] Furthermore, this method eliminates the influence of systematic errors and human error in point-of-strain measurement by measuring the relative change in displacement and then converting it into a strain value at a specific point. Rocks and rock-like materials are granular cemented materials, and the stress and strain values obtained using tensile stress or strain at a specific point have a large data dispersion. BRIEF DESCRIPTION OF THE DRAWINGS
[0031] Figure 1 This is a schematic diagram of the measurement of the vertical deformation of the inner diameter of a brittle material ring specimen under radial compression;
[0032] Figure 2 It is a schematic diagram of the radial compression deformation and principle analysis of a brittle material ring specimen;
[0033] Figure 3 is the P-δ experimental curve of the mortar specimen;
[0034] Figure 4 It is the P-δ experimental curve of aluminum alloy sample.
[0035] In the figure: 1- ring specimen; 2- pressure plate of testing machine; 3- fracture mechanics extensometer; 4- extension rod; 5- limit screw; 6- spring. DETAILED DESCRIPTION
[0036] Combine Figures 1 to 4 As shown, a specific implementation of a method for measuring rock tensile strain and its mechanical parameters using a ring deformation method provided by the present invention is described.
[0037] Example 1
[0038] A method for measuring rock tensile strain and its mechanical parameters using the ring deformation method. This method is based on the tensile strain analysis of the ring deformation. Under the assumption that the rock material is brittle and obeys the maximum principal strain fracture criterion, the tensile strength and other parameters of the material are further analyzed. The specific steps include:
[0039] S1. Install a deformation sensor in the hole of the ring specimen, and ensure that the deformation sensor is in close contact with the inner wall of the hole of the specimen.
[0040] The deformation sensor includes a fracture mechanics extensometer, an extended aluminum rod, a spring, and an arc-shaped contact. The measuring end of the fracture mechanics extensometer is installed with two parallel extended aluminum rods, and the other ends of the extended aluminum rods are respectively installed with arc-shaped contacts, and a spring is set between the extended aluminum rods. The spring is mounted on a limit screw, and the limit screw connects the two extended aluminum rods. The limit screw is threaded at one end and not at the other end. One end with the thread is connected to the screw hole on the extended aluminum rod, and the other end passes through the extended aluminum rod. There is a gap between the screw and the through hole of the aluminum rod, and the smooth section of the screw can move along the through hole of the extended aluminum rod. This structure ensures that the sensor is in close point contact with the inner hole wall of the specimen.
[0041] S2. Use a testing machine to radially load the ring specimen and monitor the deformation of the inner diameter of the specimen in a direction parallel to the load during compression.
[0042] S3. Determine the relationship curve between the ring specimen load and the vertical deformation in the hole of the ring specimen material.
[0043] During the experiment, the deformation of the hole diameter in the direction parallel to the load during the ring compression process was monitored, and the relationship curve between the load P of the rock and rock-like material ring specimen and the vertical deformation δ in the hole (i.e., the P-δ experimental curve) was obtained, as shown in Figure 2. Figure 3 As shown. Finally, according to the P-δ curve, combined with further theoretical analysis and calculation, the real-time tensile strain value, ultimate tensile fracture strain, elastic modulus, tensile strength and other parameters of the material are obtained. In order to facilitate the comparative calibration of material parameters, the ring deformation method is first used to obtain the relationship curve between the load and the deformation in the hole of the aluminum alloy ring specimen, as shown in Figure 4 As shown in the figure, since the elastic modulus and other parameters of aluminum alloy materials are known, the experimental results have small dispersion, so the aluminum alloy ring experiment can be used as a calibration experiment for rock and rock-like rings.
[0044] S4. Calculate the tensile strain value, ultimate tensile fracture strain, elastic modulus and tensile strength of the ring specimen material based on the above relationship curve.
[0045] Its calculation principle, combined with Figure 2 As shown in Figure 1, assuming the plane stress ring is formed by bending an ideal elastic beam, the circle passing through point B is the neutral layer of the ring. During the bending process, the neutral layer is not always located at the centroid of the bent part and will shift during the bending process. Assuming the displacement coefficient of the neutral layer of the ring is k, the distance from the circle where the neutral layer is located to the innermost circle, that is, the distance from point B to point A, is h:
[0046] h=k(Rr)
[0047] Where h is the distance from the neutral layer to the inner ring, R is the outer diameter of the ring, and r is the inner diameter of the ring.
[0048] As shown in the figure, the ring is compressed diametrically, and the inner circle outside a certain range of the loading area becomes an ideal ellipse. If the ring is made of brittle material, it will fail if the deformation is not large. The transformation from a circular ring to an elliptical ring conforms to the small deformation assumption. Assuming that the distance h between points A and B remains unchanged, the radius of curvature of the neutral layer of the ring in the figure is ρ1:
[0049] ρ1=r+h
[0050] After the circular ring specimen is compressed, the curvature radius of the neutral layer of the elliptical ring is ρ2:
[0051]
[0052] Where a is Figure 2 After the middle ring specimen is compressed, the short semi-axis of the ellipse passing through point A; b is Figure 2 The major semi-axis of the ellipse passing through point A after the middle ring specimen is compressed.
[0053] Assuming the vertical deformation of the inner diameter d of the ring is δ1 and the lateral deformation is δ2, we have:
[0054]
[0055]
[0056] The change in curvature produces strain. According to the relationship between curvature and strain, we can get:
[0057]
[0058]
[0059] Where, ε A1 , ε A1 are the tensile strains at point A of the circular ring and the elliptical ring, respectively.
[0060] ε A1 , ε A1 The difference is equal to the tensile strain ε generated at point A by the ring under radial compression A , so we get:
[0061]
[0062] To calculate the tensile strain at point A, we need to measure the vertical deformation δ1 and lateral deformation δ2 of the ring's inner diameter d. To simplify the experiment, we assume that under small deformation, the circumference of the ring's inner diameter remains unchanged as it transforms from a circle to an ellipse. Numerical simulations confirm that this assumption is consistent with the finite element calculation results.
[0063] The circumference of the ellipse l2 is calculated using the approximate formula:
[0064] l2=2πa+4(ba)
[0065] The circumference of the circle is l1:
[0066] l1=2πr
[0067] Among them, the relationship between the vertical deformation δ1 and the lateral deformation δ2 is:
[0068]
[0069] Therefore, the tensile strain ε generated at point A by the radial compression of the ring is A for:
[0070]
[0071] The value of the neutral layer displacement coefficient k is determined by assuming that the curvature radius ρ1 of the neutral layer of the ring is approximately related to the inner radius r and the outer radius R of the ring as follows:
[0072]
[0073] Calculation can be obtained:
[0074]
[0075] In reality, since the ring used in the experiment is a three-dimensional model with defined structural dimensions, the value of the neutral layer displacement coefficient, k, is closely related not only to the ring's inner and outer radii (R and r), the difference between the inner and outer radii (Rr), and their ratio (R / r), but also to the ring's thickness t, the Poisson's ratio μ of the ring material, and the experimental boundary conditions. During the bending deformation of a ring (or other curved component), k is not a constant but rather a variable. However, under small deformation perturbations, the circle deforms slightly to an ellipse, and k and h can be considered constant. Despite this, the specific value of k remains difficult to determine, and actual strain is expected to have errors.
[0076] It can be further assumed that the comprehensive influence coefficient of the neutral layer displacement coefficient k on the strain is β. The size of β can be calibrated through corresponding numerical experiments, and at the same time, the errors caused by the assumption of constant circumference of the ring and the assumption of plane stress state in the above derivation process can be eliminated.
[0077] In the calculation of tensile strain value, the circular ring specimen in plane stress state is formed by bending the elastic beam. The neutral layer of the circular ring bending is selected, and the neutral layer shifts during the bending process.
[0078] By adding the comprehensive influence coefficient β, the tensile strain value can be calculated as:
[0079]
[0080] Among them, ε A is the tensile strain at the intersection of the inner diameter of the ring specimen and the line of action of the radial load it is subjected to, in με; R is the outer diameter of the ring specimen, in mm; r is the inner diameter of the ring specimen, in mm; δ1 is the vertical deformation of the inner diameter of the ring, in mm; β is the comprehensive influence coefficient.
[0081] In the calculation of the ultimate tensile fracture strain, the macro crack initiation of brittle materials is accompanied by the drop of load. The maximum load P of the radial compression of the ring is determined. max Calculate the ultimate tensile fracture strain ε t The ultimate tensile fracture strain is calculated as:
[0082]
[0083] Where δ is the vertical deformation of the inner diameter of the ring corresponding to the ultimate load, in mm.
[0084] The elastic modulus is calculated as:
[0085]
[0086] Among them, k a k is the slope of the elastic stage in the relationship curve between the load of the aluminum ring specimen and the vertical deformation in the hole, r is the slope of the elastic stage in the relationship curve between the radial load of the ring specimen and the vertical deformation in the hole, E 铝 is the elastic modulus of aluminum.
[0087] The tensile strength is calculated as:
[0088]
[0089] Among them, σ t It is the tensile strength, unit is MPa.
[0090] This method can be applied to the measurement of tensile strain value, ultimate tensile fracture strain, elastic modulus and tensile strength of rocks or rock-like materials.
[0091] Example 2
[0092] Based on Example 1, the following experiment was conducted to obtain the parameters of the mortar specimens.
[0093] The outer diameter of the ring used is R = 25 mm and the inner diameter is r = 10 mm. Figure 3 is the P-δ experimental curve of the mortar specimen obtained according to the above experimental method; Figure 4 The P-δ experimental curve of the aluminum alloy material specimen obtained according to the above experimental method; the following calculation and analysis methods are all analyzed based on this experimental result as an example.
[0094] Substituting the ring parameters of this experimental example into the tensile strain value calculation formula, we can obtain:
[0095]
[0096] Under ideal conditions, taking β = 1, when the deformation of the inner diameter d of the ring is measured at δ1 = 0.01 mm, the tensile strain (first principal strain) at point A is calculated to be 254.5 με; when the deformation δ1 = 0.1 mm, the tensile strain (first principal strain) at point A is calculated to be 2537.7 με. In the small deformation range ε A It is linear with δ1.
[0097] Based on the above analysis, the tensile mechanical parameters of the experimental mortar materials were obtained respectively.
[0098] Calculation of tensile fracture strain: When the macro crack of brittle material is initiated, the load is dropped. The relationship curve between the load P and the inner diameter deformation δ (i.e., P-δ curve) is obtained through the radial compression test of the ring. max The strain ε obtained by calculating the corresponding δ A , which is the ultimate tensile fracture strain ε of the material t
[0099]
[0100] Among them Figure 3 The δ corresponding to the first peak point of the load is 0.04 mm, and the ultimate tensile fracture strain ε of the experimental mortar material is obtained t is 700 microstrain.
[0101] Elastic modulus calculation: The tensile elastic modulus of brittle materials is obtained using the aluminum ring calibration method. The elastic modulus of aluminum is known to be 70 GPa. A radial compression test is performed on the aluminum ring to obtain the P-δ curve of the aluminum ring, as shown in the following example: Figure 4 , assuming that the slope of the elastic stage of the aluminum ring radial compression P-δ curve is k a , the P-δ curve of the radial compression of the brittle material ring of the mortar is as follows: Figure 3 The slope of the elastic phase is k r , then the elastic modulus E of the measured mortar material is obtained as:
[0102]
[0103] Combined with the P-δ curve, the elastic modulus E of the experimental mortar material was obtained to be 4.65 GPa.
[0104] Calculation of tensile strength: Assuming that the brittle rock material meets the maximum principal stress (tensile stress) fracture criterion, and the stress-strain curve maintains a linear relationship before the crack occurs, showing obvious elastic-brittle fracture characteristics, its tensile strength σ can be inferred. t (MPa) is:
[0105]
[0106] According to the fracture strain and elastic modulus, the tensile strength σ of the experimental mortar material is obtained. t It is 3.255MPa.
[0107] This method measures the relative change in displacement and converts it into a strain value at a specific point, eliminating the influence of systematic errors and human error in strain point measurement. Rocks and rock-like materials are granular cemented materials, and the stress and strain values obtained using tensile stress or strain at a specific point have a large data dispersion.
[0108] Of course, the above description is not a limitation of the present invention, and the present invention is not limited to the above examples. Changes, modifications, additions or substitutions made by technicians in this technical field within the essential scope of the present invention should also fall within the scope of protection of the present invention.
Claims
1. A method for measuring rock tensile strain and its mechanical parameters using a circular deformation method, characterized in that the steps include: S1. Install a deformation sensor in the hole of the ring specimen, ensuring that the deformation sensor is in close contact with the inner wall of the hole of the specimen. S2. Use a testing machine to radially load the ring specimen and monitor the deformation of the inner diameter of the specimen in a direction parallel to the load during compression. S3. Determine the relationship curve between the ring specimen load and the vertical deformation in the hole of the ring specimen material; S4. Calculate the tensile strain value, ultimate tensile fracture strain, elastic modulus, and tensile strength of the ring specimen material based on the relationship curve; The tensile strain value is calculated as follows: Among them, ε A is the tensile strain at the intersection of the inner diameter of the ring specimen and the line of action of the radial load, in με; R is the outer diameter of the ring specimen, in mm; r is the inner diameter of the ring specimen, in mm; δ1 is the vertical deformation of the inner diameter of the ring, in mm; β is the comprehensive influence coefficient; In the calculation of the ultimate tensile fracture strain, the brittle material is accompanied by the drop of load when the macro crack is initiated, and the maximum load P of the radial compression of the ring is determined. max Calculate the ultimate tensile fracture strain ε t ; The ultimate tensile fracture strain is calculated as follows: Wherein, δ is the vertical deformation of the inner diameter of the ring corresponding to the maximum load, in mm; The elastic modulus is calculated as follows: Among them, k a k is the slope of the elastic stage in the relationship curve between the load of the aluminum ring specimen and the vertical deformation in the hole, r is the slope of the elastic stage in the relationship curve between the load of the ring specimen and the vertical deformation in the hole, E 铝 is the elastic modulus of aluminum; The tensile strength is calculated as follows: Among them, σ t It is the tensile strength, unit is MPa.
2. The method for measuring rock tensile strain and its mechanical parameters using the ring deformation method according to claim 1, characterized in that: The deformation sensor includes a fracture mechanics extensometer, an extended aluminum rod, a spring and an arc contact. The measuring end of the fracture mechanics extensometer is equipped with two parallel extended aluminum rods, the other ends of the extended aluminum rods are respectively equipped with arc contacts, and a spring is arranged between the extended aluminum rods.
3. The method for measuring rock tensile strain and its mechanical parameters using the ring deformation method according to claim 2, characterized in that: The spring sleeve is arranged on the limit screw, and the limit screw is connected to the two lengthened aluminum rods; the limit screw is provided with a thread at one end, and the threaded end is connected with the screw hole on the lengthened aluminum rod.
4. The method for measuring rock tensile strain and its mechanical parameters using the ring deformation method according to claim 1, characterized in that: In the calculation of the tensile strain value, the circular ring specimen in a plane stress state is formed by bending an elastic beam, and the neutral layer of the circular ring bending is selected, and the neutral layer is offset during the bending process.
5. The method for measuring rock tensile strain and its mechanical parameters using the ring deformation method according to any one of claims 1 to 4, characterized in that: It is used to measure the tensile strain value, ultimate tensile fracture strain, elastic modulus and tensile strength of rocks or rock-like materials.