Method for estimating the fracture propagation rate based on changes in rock humidity

Abstract

To predict the progress rate of cracks in rock and thereby predict rockfall occurrence period from base rock to prevent a disaster event.SOLUTION: A method for estimating the progress rate of cracks due to the change of humidity in rock comprises the steps of: preparing a sample from sampled rock; providing the change of relative humidity to the sample on the condition of constant temperature to measure the strain of the sample; calculating the constant value of a formula representing the change rate of the strain by fitting the strain measurement result of the sample; obtaining far stress in the rock from the formula representing the change rate of the strain and a formula representing a relation between stress and strain in isotropic rock; obtaining a stress intensity factor related to the cracks in the rock from the far stress; and estimating the progress rate of the cracks by the Paris rule from the stress intensity factor.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] This disclosure relates to a method for estimating the fracture propagation rate due to changes in the humidity of rock. [Background technology]

[0002] Conventionally, various techniques have been proposed to obtain information about cracks and voids in rocks that make up bedrock, etc. (see, for example, Patent Documents 1 to 3).

[0003] For example, the technology described in Patent Document 1 can obtain information about cracks and voids in the bedrock underground. Furthermore, the technology described in Patent Document 2 can explore the crack distribution within the bedrock at the back of the tunnel face. Additionally, the technology described in Patent Document 3 can visualize a crack network in relation to rock fracturing, including crack propagation. [Prior art documents] [Patent Documents]

[0004] [Patent Document 1] Japanese Patent Application Publication No. 05-247920 [Patent Document 2] Japanese Patent Application Publication No. 04-190187 [Patent Document 3] Patent No. 6926352 [Overview of the Initiative] [Problems that the invention aims to solve]

[0005] However, while the aforementioned conventional technology can provide information about existing cracks, it cannot provide information about the conditions that contribute to crack propagation, and therefore cannot estimate the rate of crack propagation in rocks within bedrock.

[0006] If we can estimate the rate of fracture propagation in rocks, it will contribute to predicting the timing of rockfalls from the rock mass caused by the propagation of fractures, thereby enabling us to avoid or reduce damage to infrastructure such as railways caused by rockfalls.

[0007] Furthermore, various natural phenomena contribute to the propagation of rock fractures, including repeated drying and wetting, stress generation due to temperature changes, freezing and expansion of water within the fracture, and growth of tree roots that penetrate the fracture. Comparing these natural phenomena, the strain generated by repeated drying and wetting contributes more to the propagation of rock fractures than temperature changes. Also, while freezing and expansion of water within the fracture is important in cold regions, it can be ignored in areas other than cold regions where freezing does not occur. In addition, tree roots that penetrate the fracture impart load to the fracture, especially during strong winds, but disaster events can be prevented by taking measures such as shutting down infrastructure use and inspecting infrastructure during strong winds.

[0008] The objective here is to provide a method for estimating the rate of fracture propagation due to changes in rock humidity, which can prevent disasters by solving the problems of the conventional technology described above, making it possible to predict the rate of fracture propagation in rocks, and by using the results to predict the timing of rockfalls from the bedrock. [Means for solving the problem]

[0009] Therefore, in the method for estimating the crack propagation rate due to the humidity change of rock, the steps include: preparing a specimen from the sampled rock; applying a change in relative humidity to the specimen under the condition of constant temperature and measuring the strain of the specimen; obtaining the value of a constant in an equation representing the strain change rate by fitting the measurement results of the strain of the specimen; obtaining the far-field stress in the rock from the equation representing the strain change rate and the equation representing the relationship between stress and strain in isotropic rock; obtaining the stress intensity factor related to the crack in the rock from the far-field stress; and estimating the crack propagation rate according to the Paris law from the stress intensity factor. The equation representing the strain change rate is proportional to the difference between the current strain and the strain in the equilibrium state, and the strain in the equilibrium state changes linearly with respect to the relative humidity, and can be written as the following equation. TIFF0007872726000001.tif12167 ε: Strain t: Time H: Relative humidity k, a, b: Constants obtained by fitting

[0010] The fitting is performed on the measurement results obtained by repeatedly changing the relative humidity stepwise and measuring the strain until the strain of the specimen reaches a constant value a plurality of times.

[0011] Furthermore, when there are unstable rock blocks bounded by cracks, based on the estimated crack propagation rate, the occurrence time of rockfall can be estimated by calculating the time until the bearing capacity of the remaining part of the crack is lower than the tensile force caused by the load of the rock block.

Advantages of the Invention

[0012] According to the present disclosure, it is possible to predict the crack propagation rate of rock, and thereby it is also possible to predict the occurrence time of rockfall from the rock mass, and prevent disaster events.

Brief Description of the Drawings

[0013] [Figure 1]This is a diagram for explaining an example of exfoliation-type rockfall in the present embodiment. [Figure 2] This is a schematic diagram showing an experiment of applying humidity change to a rock specimen in the present embodiment. [Figure 3] This is a photograph showing a rock specimen in the present embodiment. [Figure 4] This is a graph showing changes in temperature and humidity in an experiment of applying humidity change to a rock specimen in the present embodiment. [Figure 5] This is a graph showing the results of an experiment of applying humidity change to a rock specimen in the present embodiment. [Figure 6] This is a conceptual diagram of the strain of a rock in an equilibrium state in the present embodiment. [Figure 7] This is a graph showing the relationship between the strain and humidity of a rock obtained based on the results of an experiment of applying humidity change to a rock specimen in the present embodiment. [Figure 8] This is a schematic diagram showing the stress distribution within a rock of a rock mass in the present embodiment. [Figure 9] This is a schematic diagram showing a rock mass including unstable rock blocks in the present embodiment. [Figure 10] This is a flowchart for explaining the operation of a method for estimating the occurrence time of rockfall in the present embodiment.

Embodiments for Carrying Out the Invention

[0014] Hereinafter, the embodiments will be described in detail with reference to the drawings.

[0015] FIG. 1 is a diagram for explaining an example of exfoliation-type rockfall in the present embodiment. In the figure, (a) is a photograph showing an example of a rock mass slope, and (b) is a schematic diagram showing the state of a crack in a part of (a) and the state where a rock block separates and falls along the crack.

[0016] In a slope of bedrock 10 as shown in the figure, unstable rock masses 12 bounded by cracks 11 undergo the propagation of cracks 11 due to temperature changes, repeated drying and wetting, etc., causing them to separate at the cracks 11 and fall as rockfalls 12a. In other words, rockfalls occur. In order to efficiently implement hard measures on slopes of bedrock 10 distributed along railway lines, which are an important part of infrastructure, it is desirable to be able to predict the location, timing, and scale of rockfalls.

[0017] Therefore, in this embodiment, we will describe a method for estimating the crack propagation rate due to changes in the humidity of rocks, which can be used to predict the timing of rockfalls.

[0018] It should be noted that infrastructure damaged by rockfalls is not limited to railways, but for the sake of explanation, we will describe the case of railways. Also, the slopes of bedrock 10 may be distributed in any location, but for the sake of explanation, we will describe them as being distributed along railway tracks.

[0019] Furthermore, while various natural phenomena other than changes in rock humidity contribute to the propagation of rock cracks 11, temperature changes and the freezing and expansion of water within the cracks are excluded from consideration in this embodiment for the reasons explained in the section on "Problems to be Solved by the Invention." In addition, during heavy rain, strong winds, and earthquakes, measures such as slowing down trains or suspending operations are taken when predetermined regulatory values ​​are exceeded to ensure railway safety; therefore, heavy rain, strong winds, and earthquakes are also excluded from consideration in this embodiment.

[0020] Next, we will describe an experiment to measure the rate of change in rock strain in this embodiment.

[0021] Figure 2 is a schematic diagram showing an experiment in which humidity changes are applied to a rock specimen in this embodiment, Figure 3 is a photograph showing the rock specimen in this embodiment, Figure 4 is a graph showing the changes in temperature and humidity in an experiment in which humidity changes are applied to a rock specimen in this embodiment, Figure 5 is a graph showing the results of an experiment in which humidity changes are applied to a rock specimen in this embodiment, Figure 6 is a conceptual diagram of the strain of rock in equilibrium state in this embodiment, and Figure 7 is a graph showing the relationship between rock strain and humidity obtained based on the results of an experiment in which humidity changes are applied to a rock specimen in this embodiment.

[0022] Generally, porous materials undergo strain due to changes in temperature and moisture content. Specifically, with respect to temperature changes, porous materials expand when heated and contract when cooled. Similarly, with respect to changes in moisture content, porous materials expand when they absorb water and contract when they dry.

[0023] Therefore, when the rocks were subjected to temperature and humidity changes and their strain was measured, it was found that at room temperature, strain was mainly caused by changes in humidity. Room temperature is defined in JIS Z 8703 as 20°C ± 15°C (5°C to 35°C). Furthermore, when the temperature was changed, the rocks contracted when heated and expanded when cooled. It was determined that this is because when heated, the moisture evaporates and dries, resulting in contraction.

[0024] For these reasons, in this embodiment, a rock specimen 13 was prepared, and as shown in Figure 2, the specimen 13 was placed in a constant temperature and humidity chamber 15, and the humidity of the specimen 13 was changed by repeatedly humidifying and dehumidifying, and the relationship between relative humidity and strain was measured.

[0025] The aforementioned specimen 13 is, specifically, a plate-shaped member made from blocks of Kimachi sandstone and Tashimo tuff, as shown in Figure 3. Its dimensions are 15 mm thick, 30 mm wide, and 130 mm long. Strain gauges are attached to the center of the two sides, 30 mm wide and 130 mm long. The average grain size in the rocks is 0.60 mm for Kimachi sandstone and 0.49 mm for Tashimo tuff. The gauge length of the strain gauge is 10 mm, which is more than 10 times the average grain size.

[0026] The experiment was conducted while keeping the ambient temperature (air temperature) constant and only varying the relative humidity. Specifically, two specimens each of Kimachi sandstone 13 and Tashimo tuff 13 were placed in a constant temperature and humidity chamber 15. As shown in Figure 4, the air temperature was kept constant at 35°C, and the relative humidity was varied within the range of 40% to 85%. The strain of each specimen 13 was measured using a strain gauge. In Figure 4, the horizontal axis represents elapsed time [hours], the left vertical axis represents relative humidity [%], and the right vertical axis represents temperature [°C].

[0027] The results of the experiment are shown in Figure 5. In Figure 5, the horizontal axis represents the elapsed time [hours] from the start of the experiment, and the left vertical axis represents the strain [10 -6 The right vertical axis shows relative humidity [%].

[0028] As shown in Figure 5, when a step function-like humidity change is applied to the specimen 13, (A) the strain responds to the humidity change with a delay, and the equilibrium strain ε eq It exhibits behavior that asymptotically approaches (B) the strain ε of the equilibrium state. eq It can be seen that increases when humidity is increased and decreases when humidity is decreased. Figure 6 shows the strain ε in equilibrium state. eq The concept is shown. In Figure 6, the horizontal axis represents elapsed time, and the vertical axis represents relative humidity in the upper graph and strain in the lower graph.

[0029] From this, assuming relative humidity is H, under constant temperature conditions, (C) the rate of change of strain ε is the current strain ε and the equilibrium strain ε. eq , that is, the final strain ε eq It is proportional to the difference between and (D) the final strain ε eq It can be seen that it changes linearly with respect to relative humidity H.

[0030] The above (C) and (D) can be expressed using the constants k, a, and b determined by experiment as shown in the following equations (1) and (2).

[0031]

number

[0032] Then, from equations (1) and (2) above, we can obtain the following equation (3).

[0033]

number

[0034] Here, the values ​​of the constants k, a, and b can be obtained by fitting them to experimental results (measurement results) as shown in Figure 5. An example of the fitting is shown in Figure 7. In Figure 7, the horizontal axis represents time [minutes], and the left vertical axis represents strain [10 -6 The right vertical axis shows relative humidity [%].

[0035] When actually performing fitting, a thermo-hygrostat 15 or a furnace capable of changing the relative humidity at a constant temperature is prepared. Also, a rock specimen 13 as shown in FIG. 3 is fabricated, and strain gauges are attached to both sides thereof. Then, the specimen 13 is placed in the thermo-hygrostat 15 or the furnace, the relative humidity is changed, and the strain is recorded. At this time, as shown in FIG. 6, the relative humidity is changed stepwise. Also, the strain is measured until it reaches a constant value. By repeatedly conducting such tests, the accuracy of the values of the constants k, a, and b obtained by fitting can be enhanced.

[0036] Next, a method for estimating the propagation rate of the crack 11 in the rock based on the findings obtained from the above experiment will be described.

[0037] FIG. 8 is a schematic diagram showing the stress distribution in the rock of the rock mass in the present embodiment. In the figure, (a) is a diagram showing an isotropic rock without cracks, and (b) is a diagram showing a rock with cracks.

[0038] The relationship between the stress σ and the strain ε in the rock of the isotropic rock mass 10 as shown in FIG. 8(a) can generally be obtained by the following formula (4) where i and j = x, y, z. σ ij =2Gε ij +2Gν / (1 - 2ν)ε kk δ ij ··· Formula (4)

[0039] Here, G is the shear modulus, ν is the Poisson's ratio, and δ ij is the Kronecker delta (δ), which is δ ij = 1 when i = j and δ ij = 0 when i ≠ j. Also, ε kk is the volumetric strain, and ε kk = ε xx + ε yy + ε zz is.

[0040] From equations (3) and (4) above, the stress distribution within the fracture-free rock under appropriate boundary conditions can be determined. In the case of the actual rock mass 10, the relative humidity H substituted into equation (3) above is the relative humidity measured on-site.

[0041] Now, considering the rock mass 10 containing a crack 11 of length w as shown in Figure 8(b), the stress at a point at a distance r from the tip of the crack 11 (where r ≪ w) is expressed by the following equation (5). Stress at a distance r from the tip of the crack = K / sqrt(2πr) ...Equation (5)

[0042] Here, K is the stress intensity factor for a mode I crack (crack 11), and is expressed by the following equation (6). K∝σ0sqrt(πw) ···Equation (6)

[0043] Note that σ0 is the stress at a distance and is calculated from equations (3) and (4) above.

[0044] Applying Paris's law to the perspective of fatigue under repeated cycles, the rate at which crack 11 propagates is given by equation (7) below. Fracture propagation rate due to fatigue = C(ΔK) m ...Equation (7)

[0045] ΔK is the stress intensity factor range, and is the difference between the maximum and minimum values ​​of K. C and m are constants determined by the material. The values ​​of C and m can be those listed in the literature; if not listed, they can be determined experimentally.

[0046] Assuming that the stress is positive when it is a tensile stress, the maximum and minimum values ​​of K are determined from equation (6) above (when a compressive stress is acting, the minimum value of K is 0).

[0047] Based on the above, the fatigue crack propagation rate can be determined from equation (7).

[0048] In other words, the fracture propagation rate due to changes in the humidity of the rock can be estimated by performing the following steps: preparing a specimen 13 from a sampled rock; applying a change in relative humidity to the specimen 13 under constant temperature conditions and measuring the strain ε of the specimen 13; determining the values ​​of the constants k, a, and b in equation (3), which represents the rate of change of strain ε, by fitting the measurement results of strain ε of the specimen 13; obtaining the far-field stress σ0 within the rock from equation (3), which represents the rate of change of strain ε, and equation (4), which represents the relationship between stress σ and strain ε within an isotropic rock; obtaining the stress intensity factor K related to the fracture 11 within the rock from the far-field stress σ0; and estimating the fracture propagation rate according to Paris's law from the stress intensity factor K.

[0049] Next, we will explain how to estimate the timing of rockfalls.

[0050] Figure 9 is a schematic diagram showing the rock mass containing unstable rock fragments in this embodiment.

[0051] Several methods can be considered for estimating the timing of rockfalls using crack propagation rates. By using the shortest rockfall timing among those obtained and utilizing it in planning the installation of countermeasures, an engineering-based conservative evaluation can be achieved.

[0052] If the time at which the length of the crack (fissure 11) diverges to infinity is considered the time of rockfall occurrence, then, for example, the tf obtained by solving Paris's law as a time evolution equation can be considered as the time of rockfall occurrence (see, for example, Non-Patent Document 1). tf is expressed by the following equation (8).

[0053]

number

[0054] Here, w0 is the length of the crack at time 0.

[0055] [Non-Patent Document 1] Yoshitaka Nara et al., "Subcritical crack propagation and long-term strength in rocks and high-strength, high-density concrete," The Materials Society of Japan (ed.), Materials, Vol. 58, No. 6, pp. 525-532, June 2009.

[0056] Furthermore, as shown in Figure 9, if there is an unstable rock mass 12 bounded by a crack 11 within a rock mass 14 of the bedrock 10, fracture will occur when the bearing capacity of the remaining crack portion falls below the tensile force due to the load on the rock mass 14. In other words, it can be considered that fracture will occur when the following equation (9) is true. St(Lw)<ρghcosθ ···Equation (9)

[0057] Here, St is the tensile strength, L is the width of the unstable rock mass 12, w is the length of the crack 11, ρ is the density of the unstable rock mass 12, g is the acceleration due to gravity, h is the height from the bottom of the unstable rock mass 12 to the crack 11, and θ is the angle between gravity and the direction in which the tensile force acts.

[0058] The values ​​of L and h are obtained by measuring the surface of the rock mass 10. The value of w is used if it can be measured by viewing the rock mass 10 from the side; however, if it cannot be measured visually and the depth of the crack 11 is unknown, it can be estimated by vibration measurement (see, for example, Non-Patent Document 2).

[0059] The dominant frequency f of the unstable rock mass 12 is given by the following equation (10).

[0060]

number

[0061] Here, E is the Young's modulus of the unstable rock mass 12, and d is the opening width of the crack 11. The center of gravity of the unstable rock mass 12 is assumed to be at a position h / 2 from the crack 11.

[0062] By measuring the dominant frequency f, the length (depth) w of the crack 11 can be obtained from equation (10).

[0063] [Non-Patent Document 2] Kamihan et al., "Examination of a quantitative evaluation method for rock collapse risk using non-contact vibration measurement," Railway Technical Research Institute Report, Vol. 26, No. 8, pp. 47-52, 2012.

[0064] Furthermore, as mentioned above, the propagation rate of the length w of the crack 11 can be determined by equation (7), so the time it takes for equation (9) to hold true can be determined. This allows us to estimate the timing of the rockfall.

[0065] Furthermore, when considering tf, expressed by equation (8), as the timing of the rockfall, and when estimating the timing of the rockfall based on the time it takes for equation (9) to be true, the latter provides a more conservative assessment. However, the latter requires acquiring more parameters.

[0066] Next, the overall operation of the method for estimating the timing of rockfalls in this embodiment will be described.

[0067] Figure 10 is a flowchart illustrating the operation of the method for estimating the timing of rockfalls in this embodiment.

[0068] First, in step S1, rock samples are taken from the site. Here, rock samples are taken from bedrock 10 distributed along the railway line.

[0069] Next, in step S2, plate-shaped specimens are prepared from the rock. Specifically, plate-shaped members as shown in Figure 3 are prepared from the rock collected in step S1, and these are designated as specimens 13. Then, strain gauges are attached to the center of both sides of each specimen 13.

[0070] Next, in step S3, the strain is measured while keeping the temperature constant and only changing the humidity. Specifically, the test specimen 13 prepared in step S2 is placed in a constant temperature and humidity chamber 15, as shown in Figure 2, the ambient temperature (air temperature) is kept constant, and only the relative humidity is changed, and the strain of the test specimen 13 is measured.

[0071] Next, in step S4, the constants k, a, and b are determined by fitting to reproduce the strain. Specifically, the relative humidity is changed in a stepwise manner as shown in Figure 6, and the strain is measured until it reaches a constant value. By repeating this test and taking the average of the fitting results, the values ​​of the constants k, a, and b in equation (3), which represents the rate of strain change, are determined.

[0072] Next, in step S5, the crack propagation rate is estimated. Specifically, equation (7), which represents the propagation rate of crack 11, is obtained using equation (3), which includes the constants k, a, and b defined in step S4, along with equations (4) to (6).

[0073] Finally, in step S6, the timing of the rockfall is estimated. Specifically, the timing of the rockfall is estimated by the time it takes from equation (7), obtained in step S5, until equation (9) is satisfied, or by considering tf, expressed by equation (8), as the timing of the rockfall.

[0074] Next, I will explain flowcharts. Step S1: Sample rocks from the site. Step S2: Prepare plate-shaped specimens from rock. Step S3: While keeping the temperature constant, apply only a change in humidity and measure the strain. Step S4: Fit the constants k, a, and b to reproduce the strain. Step S5: Estimate the crack propagation rate. Step S6: Estimate the timing of the rockfall.

[0075] In this way, by performing the operations in steps S1 to S5, it is possible to estimate the fracture propagation rate due to changes in the humidity of the rocks in the bedrock 10 distributed along the railway line. Based on the estimated fracture propagation rate, it is possible to predict when rockfalls will occur from the bedrock 10 distributed along the railway line, thereby preventing disaster events.

[0076] Thus, in this embodiment, the method for estimating the crack propagation rate due to changes in the humidity of rock comprises the steps of: preparing a specimen 13 from a sampled rock; applying a change in relative humidity to the specimen 13 under constant temperature conditions using a constant temperature chamber 15 or furnace and measuring the strain ε of the specimen 13; determining the values ​​of the constants k, a, and b of equation (3) which represents the rate of change of strain ε by fitting to the measurement result of strain ε of the specimen 13; obtaining the far-field stress σ0 in the rock from equation (3) which represents the rate of change of strain ε and equation (4) which represents the relationship between stress σ and strain ε in an isotropic rock; obtaining the stress intensity factor K related to the crack 11 in the rock from the far-field stress σ0; and estimating the crack propagation rate according to Paris's law from the stress intensity factor K. Equation (3) which represents the rate of change of strain ε is the current strain ε and the strain ε in equilibrium state. eq The strain ε in equilibrium is proportional to the difference between the two. eq This indicates that it changes linearly with respect to relative humidity H.

[0077] This made it possible to predict the fracture propagation rate due to humidity changes, which are the main cause of rock strain ε in the room temperature range.

[0078] Furthermore, if there is an unstable rock mass 12 bounded by a crack 11, the timing of rockfall can be estimated by calculating the time until the bearing capacity of the remaining crack falls below the tensile force due to the load on the rock mass 14, based on the estimated crack propagation rate. Therefore, it becomes possible to predict the timing of rockfall from the bedrock 10 due to the propagation of the crack 11, and disaster events can be prevented.

[0079] Furthermore, the fitting is performed on measurement results obtained by repeatedly changing the relative humidity in a stepwise manner and measuring the strain ε of the test specimen 13 until the strain ε reaches a constant value. This improves the accuracy of the constant values ​​k, a, and b obtained through fitting.

[0080] Furthermore, the rock samples are taken from bedrock 10 distributed along the railway tracks. Therefore, railway safety is more reliably ensured.

[0081] This specification describes features relating to preferred and exemplary embodiments. Various other embodiments, modifications, and variations within the scope and spirit of the claims attached herein will be readily apparent to those skilled in the art by reviewing this specification. [Industrial applicability]

[0082] This disclosure can be applied to a method for estimating the fracture propagation rate due to changes in the humidity of rock. [Explanation of symbols]

[0083] 10 Bedrock 11 cracks 12 Unstable rock mass 13 Specimen 14 Rock fragments 15 Constant temperature and humidity chamber

Claims

1. The process of preparing test specimens from sampled rocks, The process involves applying a change in relative humidity to the specimen under constant temperature conditions and measuring the strain of the specimen. The process involves fitting the measured strain results of the aforementioned specimen to determine the value of the constant in the equation representing the rate of change of strain, The process of obtaining the remote stress within the rock from the equation representing the rate of change of strain and the equation representing the relationship between stress and strain within an isotropic rock, The process of obtaining the stress intensity factor related to fractures in the rock from the aforementioned distant stress, The process includes estimating the crack propagation rate according to Paris's law from the stress intensity factor, A method for estimating the crack propagation rate due to humidity changes in rock, characterized in that the formula representing the rate of change of strain is proportional to the difference between the current strain and the equilibrium strain, and the equilibrium strain changes linearly with respect to relative humidity.

2. A method for estimating the crack propagation rate due to changes in the humidity of a rock, according to claim 1, wherein, in the case of an unstable rock mass bounded by a crack, the timing of a rockfall can be estimated by calculating the time until the bearing capacity of the remaining crack falls below the tensile force due to the load of the rock mass, based on the estimated crack propagation rate.

3. The fitting is performed on the measurement results obtained by repeatedly changing the relative humidity in a stepwise manner and measuring the strain of the specimen until the strain reaches a constant value, as described in claim 1, for estimating the crack propagation rate of rock due to humidity changes.

4. The method for estimating the fracture propagation rate of rock due to changes in humidity, according to claim 1, wherein the rock is sampled from bedrock distributed along a railway line.

5. The formula for representing the rate of change in strain is as follows, the method for estimating the crack propagation rate due to changes in the humidity of rock according to claim 1. ε: Distortion t: time H: Relative humidity k, a, b: Constants obtained by performing fitting.

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