Method for establishing rock creep failure time prediction model under conventional triaxial compression condition

Abstract

The invention relates to a method for establishing a rock creep failure time prediction model under a conventional triaxial compression condition. The method comprises the following steps: performing conventional triaxial compression tests on a target rock under n groups of different creep stresses under preset confining pressure to obtain n creep curves; for any creep curve, acquiring creep failure time and constant-speed creep rate corresponding to the creep curve, so as to obtain a plurality of to-be-fitted points; linear fitting is carried out on the multiple to-be-fitted points to obtain a fitting curve, fitting parameters of the fitting curve are obtained, and the fitting parameters comprise the slope and the intercept; and obtaining a rock creep failure time prediction model of the target rock under the conventional triaxial compression condition according to the fitting parameters. When the model is used, only the target rock needs to be tested subsequently, and the damage time can be predicted according to the model when the creep rate is monitored, so that constructors can conveniently take protective measures in advance.

Description

Technical Field

[0001] The invention relates to the technical field of rock engineering, and in particular to a method for establishing a rock creep failure time prediction model under conventional triaxial compression conditions. Background Art

[0002] Creep characteristics are inherent properties of rock materials, which affect the safety and long-term stability of rock structures, especially soft rock tunnels and deep coal mine tunnels under high stress conditions, where creep deformation is particularly obvious, and in severe cases will directly threaten the operational safety of rock structures. It is crucial to clarify the creep law of rocks under different load disturbances, determine the long-term strength of rocks, and reveal their creep failure mechanism in order to understand the stress and deformation state of surrounding rocks, determine the type and timing of surrounding rock support, and predict the service life of structures.

[0003] At present, rock creep research mainly includes three aspects: creep model, long-term strength and creep failure time. Creep model is the theoretical basis for analyzing the law of rock stress-strain variation over time, and it is also the focus and difficulty of rock creep mechanics research. At present, rock creep model and long-term strength determination method are relatively mature, but compared with the research on these two aspects, there are few reports on rock creep failure time under conventional triaxial compression conditions.

[0004] Rock creep failure time is not only a key indicator of the long-term stability of mountain tunnels, water conservancy dam foundations, and surrounding rock chambers of deep underground projects, but also has important reference value for evaluating their full life cycle and service life. At the same time, rock creep failure time is also one of the key parameters in rock structure design. The reasonable selection of this parameter is crucial to the safe use of the structure and the protection of people's lives and property.

[0005] Therefore, it is urgent to provide a method for establishing a rock creep failure time prediction model under conventional triaxial compression conditions to obtain the rock creep failure time under conventional triaxial compression conditions. Summary of the invention

[0006] The technical problem to be solved by the present invention is to provide a method for establishing a rock creep failure time prediction model under conventional triaxial compression conditions.

[0007] To solve the above problems, the technical solution adopted by the present invention is:

[0008] A method for establishing a rock creep failure time prediction model under conventional triaxial compression conditions, the method comprising:

[0009] The target rock is subjected to n groups of conventional triaxial compression tests under different creep stresses under a predetermined confining pressure to obtain n creep curves;

[0010] For any creep curve i, obtain the creep failure time t corresponding to the creep curve iFi and constant creep rate Thus, multiple points to be fitted are obtained

[0011] For multiple points to be fitted Performing linear fitting to obtain a fitting curve, and obtaining fitting parameters of the fitting curve, wherein the fitting parameters include a slope k and an intercept b;

[0012] The rock creep failure time prediction model under conventional triaxial compression conditions of the target rock is obtained according to the fitting parameters: Among them, t F is the rock creep failure time, for

[0013] Constant creep rate.

[0014] As an implementation mode of the present invention, the target rock is subjected to n groups of conventional triaxial compression tests under different creep stresses under a predetermined confining pressure to obtain n creep curves, including:

[0015] Cut and grind the target rock to obtain n samples;

[0016] Determine the creep stress of each specimen, conduct conventional triaxial compression tests on n specimens, and obtain n creep curves;

[0017] Among them, for any sample, the creep curve corresponding to the sample is obtained in the following manner: applying a confining pressure to the predetermined confining pressure at a rate of 100 to 500 N / s, then maintaining the pressure for 30 to 90 s, then applying an axial pressure to the creep stress at a rate of 100 to 500 N / s, and then maintaining the pressure until creep failure occurs to the sample, so as to obtain the creep curve corresponding to the sample.

[0018] As an implementation mode of the present invention, it is characterized in that n≥5; when n is 5, the creep stresses of the five samples are respectively 75%, 80%, 85%, 90% and 95% of the target rock compressive strength.

[0019] As an embodiment of the present invention, the target rock compressive strength is obtained by:

[0020] Cut and grind the target rock to obtain m samples;

[0021] After conventional triaxial compression tests are performed on m specimens, the compressive strengths corresponding to the m specimens are averaged and obtained;

[0022] Among them, for any sample, the following method is used to obtain the compressive strength corresponding to the sample: apply confining pressure at a rate of 100 to 500 N / s to the predetermined confining pressure, then stabilize the pressure for 30 to 90 seconds, and then apply axial pressure at a rate of 100 to 500 N / s until the sample is destroyed, and the corresponding creep stress when the sample is destroyed is used as the compressive strength corresponding to the sample.

[0023] As an implementation mode of the present invention, m≥5.

[0024] As an implementation mode of the present invention, the predetermined confining pressure is related to the actual ground stress of the target rock; when the target rock is sandy mudstone on the coal roof, the predetermined confining pressure is 5 MPa.

[0025] As an implementation manner of the present invention, the preset axial pressure is equal to the sum of the creep stress and the predetermined confining pressure.

[0026] As an embodiment of the present invention, the sample is a standard cylindrical sample with a diameter of 50 mm and a height of 100 mm;

[0027] The angles between the normal lines of the upper and lower end surfaces of the sample and their axis are within the range of ±0.25°, and the unevenness deviations of the upper and lower end surfaces are within the range of ±0.05mm.

[0028] The beneficial effects of adopting the above technical solution are:

[0029] The method for establishing a rock creep failure time prediction model under conventional triaxial compression conditions provided by the present invention can establish an accurate rock creep failure time prediction model based on numerical values ​​by performing conventional triaxial compression tests on multiple target rock samples. In this way, it is only necessary to conduct tests on the target rock in the future, and the failure time can be predicted based on the model after monitoring the creep rate (the rock has not been destroyed at this time), thereby making it convenient for construction personnel to take protective measures in advance.

[0030] The prediction model provided by the present invention cleverly avoids the shortcomings of the Innocente prediction model, replaces the creep stress with a constant creep rate function, and establishes a new prediction model, which can reduce the adverse effects of the inhomogeneity and non-homogeneity between samples on the prediction results, and has high accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 It is the relationship curve between creep stress and failure time.

[0032] Figure 2 It is the curve of damage variable evolution.

[0033] Figure 3 This is a picture of sandy mudstone sample.

[0034] Figure 4 This is the MTS816 test system. (a) is the overall diagram of the system, and (b) is a partial diagram.

[0035] Figure 5 is the stress-strain curve.

[0036] Figure 6 It is the creep curve of sandy mudstone.

[0037] Figure 7 It is the fitting curve of the creep failure time prediction model.

[0038] Figure 8 These are the fitting curves of the test data of five types of rocks and the prediction model.

[0039] Fig. 9 1 is a comparison chart of different models and experimental data, (a) comparison of predicted values ​​of the Innocente model with experimental data; (b) comparison of predicted values ​​of the Charles model with experimental data; (c) comparison of predicted values ​​of the model of the present invention with experimental data. DETAILED DESCRIPTION

[0040] In order to make the objectives, technical solutions and advantages of the present invention more clear, the present invention is clearly and completely described below in conjunction with specific embodiments.

[0041] An embodiment of the present invention provides a method for establishing a rock creep failure time prediction model under conventional triaxial compression conditions. The present invention first describes the expression form of the rock creep failure time prediction model under conventional triaxial compression conditions.

[0042] Figure 1 This is a schematic diagram of the general law of rock creep stress and failure time. Figure 1 It can be seen that when creep stress σ1>σ2>σ3, the relationship between creep failure time of rock under three stress levels is t F1 <t F2 <t F3 , while from Figure 1 It can also be found that the greater the creep stress, the greater the creep rate of the rock in the isokinetic creep stage, that is, According to the above relationship, we try to replace the creep stress in the stress method prediction model based on some intrinsic connection between creep stress and constant creep rate, and then establish a functional relationship between creep failure time and constant creep rate to eliminate the influence of creep stress and uniaxial compressive strength.

[0043] Based on this, the material creep damage rate theory proposed by Soviet scholar Kachanov shows that the greater the rock creep stress, the faster the damage rate develops. The relationship between stress level and damage rate is established as follows:

[0044]

[0045] Where D is the damage variable, is the damage rate, σ a =σ1-σ3 is the creep stress, σ1 and σ3 are the maximum and minimum principal stresses respectively, and C and n are material constants.

[0046] Integrating both sides of formula (1) with respect to time yields:

[0047]

[0048] Where A is the integration constant.

[0049] Assuming that the damage of rock is 0 before creep loading, and the damage variable is 1 when creep failure occurs, the evolution rule of damage variable with time is Figure 2 shown.

[0050] according to Figure 2 With t = 0, D = 0, substituting it into equation (2), we get the integral constant:

[0051]

[0052] When t = t F , D = 1, and substituting (3) into (2), the function expression of the rock creep failure time prediction model based on Kachanov damage rate theory is obtained as follows:

[0053]

[0054] This model does not consider the influence of rock uniaxial compressive strength and rock instantaneous failure time, and believes that rock creep failure time is only related to creep stress.

[0055] In 1929, Norton conducted a large number of rock creep tests under different stress levels and summarized the constitutive relationship between creep stress and constant creep rate:

[0056]

[0057] In the formula, is the constant creep rate, δ is the rock material constant, and ω is the creep exponent.

[0058] Substituting equation (5) into equation (4) to eliminate the influence of creep stress, we can obtain the rock creep failure time expression expressed by constant creep rate:

[0059]

[0060] Taking the logarithm of both sides of the above equation gives:

[0061]

[0062] make:

[0063]

[0064] Substituting formula (8) into formula (7), we get:

[0065]

[0066] Formula (9) is the creep failure time prediction model established based on the constant creep rate of rock.

[0067] In view of this, the method for establishing a rock creep failure time prediction model under conventional triaxial compression conditions provided by the present invention includes:

[0068] Step 1: subject the target rock to n groups of conventional triaxial compression tests under a predetermined confining pressure and different creep stresses to obtain n creep curves;

[0069] This step specifically includes:

[0070] Step S101, obtaining target rock compressive strength, this step includes:

[0071] Cut and grind the target rock to obtain m samples, where m≥5;

[0072] After conventional triaxial compression tests are performed on m specimens, the compressive strengths corresponding to the m specimens are averaged and obtained;

[0073] Among them, for any sample, the following method is used to obtain the compressive strength corresponding to the sample: apply confining pressure at a rate of 100 to 500 N / s to the predetermined confining pressure, then stabilize the pressure for 30 to 90 seconds, and then apply axial pressure at a rate of 100 to 500 N / s until the sample is destroyed, and use the corresponding creep stress when the sample is destroyed as the compressive strength corresponding to the sample.

[0074] Among them, the predetermined confining pressure is related to the actual ground stress of the target rock; the pressure increase rate of the confining pressure and the pressure increase rate of the axial pressure can be determined according to the predetermined confining pressure, which is a parameter that can be obtained by technical personnel in this field according to the prior art, and the present invention does not make specific limitations on this. For example: when the target rock is sandy mudstone on the coal roof, the predetermined confining pressure is 5MPa, the pressure increase rate is 200N / s; the axial pressure increase rate is 0.06mm / min.

[0075] In the present invention, according to the Standard for Engineering Rock Mass Test Methods (GB / T 50266-2013), the sandy mudstone of the 9th coal roof of a mine in the Lianghuai mining area was cut and polished into a standard cylindrical specimen with a diameter of 50 mm and a height of 100 mm ( Figure 3), the angle between the normal line of the upper and lower end faces of the sample and its axis is within the range of ±0.25°, and the unevenness deviation of the upper and lower end faces is within the range of ±0.05mm. The wave velocity of each specimen is measured using a rock ultrasonic instrument, and samples with large wave velocity differences are eliminated, and 5 samples are selected.

[0076] The MTS816 rock test system of Anhui University ( Figure 4 ) Five groups of conventional triaxial compression tests were carried out on the samples. The confining pressure was applied at a rate of 200 N / s to a predetermined value of 5 MPa, then the pressure was stabilized for 60 seconds, and then the axial pressure was applied at a rate of 200 N / s until the sample was destroyed. The stress-strain curve of sandy mudstone under a confining pressure of 5 MPa was obtained according to the test results. The results are shown in Figure 5 As shown in Table 1, the basic mechanical parameters of sandy mudstone are obtained according to the test curve.

[0077] Table 1 Mechanical parameters of sandy mudstone

[0078]

[0079] The average value of the compressive strength of sandy mudstone under five groups of conventional triaxial compression conditions was rounded to an integer of 80 MPa after removing decimal places, which was taken as the compressive strength of sandy mudstone.

[0080] Step S102: obtaining a creep curve:

[0081] This step includes:

[0082] Cut and grind the target rock to obtain n samples;

[0083] Determine the creep stress of each specimen, conduct conventional triaxial compression tests on n specimens, and obtain n creep curves;

[0084] Among them, for any sample, the creep curve corresponding to the sample is obtained in the following manner: applying a confining pressure to the predetermined confining pressure at a rate of 100 to 500 N / s, then stabilizing the pressure for 30 to 90 seconds, and then applying an axial pressure to the preset axial pressure at a rate of 100 to 500 N / s, and then stabilizing the pressure until the sample undergoes creep failure, so as to obtain the creep curve corresponding to the sample; wherein the preset axial pressure value is equal to the sum of the creep stress and the predetermined confining pressure.

[0085] Similarly, when the target rock is sandy mudstone with coal roof, the predetermined confining pressure is 5 MPa, the pressure increase rate is 200 N / s; the pressure is maintained for 60 s; and the axial pressure increase rate is 200 N / s.

[0086] In order to ensure the accuracy of subsequent results, n in the present invention is ≥5. When n is 5, the creep stresses of the five samples are 75% (60MPa), 80% (64MPa), 85% (68MPa), 90% (72MPa) and 95% (76MPa) of the compressive strength of the target rock, respectively.

[0087] The test first applied a confining pressure of 5 MPa at a rate of 200 N / s, then maintained the pressure for 60 s, and then applied an axial pressure at a rate of 200 N / s to a preset axial pressure (for sample A, when the selected creep stress is 60 MPa, the corresponding preset axial pressure is 5 MPa + 60 MPa = 65 MPa). After reaching the predetermined stress state, the pressure was maintained until the sample was creep-damaged. Finally, five groups of creep curves of sandy mudstone under different stress states were obtained as follows: Figure 6 shown.

[0088] Step 2: For any creep curve i, obtain the creep failure time t corresponding to the creep curve i Fi and constant creep rate Thus, multiple points to be fitted are obtained

[0089] Depend on Figure 6 The creep failure time and constant creep rate of sandy mudstone under different creep stress conditions are shown in Table 2 (where σ1 represents axial pressure, σ3 represents the predetermined confining pressure, and σ a represents creep stress).

[0090] Table 2 Creep failure time and constant creep rate

[0091]

[0092] This gives us 5 points to be fitted:

[0093] Step 3: Multiple points to be fitted A linear fit is performed to obtain a fitting curve, and fitting parameters of the fitting curve are obtained, wherein the fitting parameters include a slope k and an intercept b.

[0094] Linear fitting is performed on the five points to be fitted obtained from Table 2 to obtain the fitting curve as shown in Figure 7 As shown, the slope k of the obtained fitting curve is -0.96 and the intercept b is -8.45.

[0095] Step 4: Obtain a rock creep failure time prediction model under conventional triaxial compression conditions of the target rock according to the fitting parameters: Among them, t F is the rock creep failure time, for

[0096] Constant creep rate.

[0097] In the above case, the rock creep failure time prediction model under conventional triaxial compression conditions of sandy mudstone is obtained as follows: Among them, t F is the rock creep failure time, for

[0098] Constant creep rate.

[0099] By adopting the method for establishing a rock creep failure time prediction model under conventional triaxial compression conditions provided by the present invention, an accurate rock creep failure time prediction model can be established based on numerical values ​​by performing conventional triaxial compression tests on multiple target rock samples. In this way, it is only necessary to conduct tests on the target rock in the future, and the failure time can be predicted based on the model after monitoring the creep rate (the rock has not been destroyed at this time), thereby making it convenient for construction personnel to take protective measures in advance.

[0100] The present invention also verifies the accuracy of the rock creep failure time prediction model established under conventional triaxial compression conditions.

[0101] First, the present invention adopts Figure 7 The prediction model formula in is used to obtain the predicted value of the failure time of sandy mudstone under different creep stresses. At the same time, the predicted value of the creep failure time based on the Kachanov damage rate theory is obtained according to formula (4) and compared with the test data. The results are shown in Table 3.

[0102] Table 3 Prediction and test values ​​of creep failure time

[0103]

[0104]

[0105] As shown in Table 3, the creep failure time of sandy mudstone predicted by Kachanov is quite different from the test results, with a minimum of 10.9h and a maximum of 54.8h, and the mean absolute error (MAE) and root mean square error (RMSE) as high as 26.7 and 30.8 respectively; while the prediction results of the theoretical model established in this paper are basically consistent with the test results, with a minimum error of only 1.4h, and MAE and RMSE are only 14.4 and 21.4 respectively, which are lower than the error of the Kachanov prediction model. On the one hand, it is due to the error of the test system itself, and on the other hand, the prediction model established in this paper does not consider the differences between samples, avoiding the error caused by the different compressive strengths of different samples. Therefore, the rock creep failure time prediction model under conventional triaxial compression conditions established in this paper has higher accuracy than the prediction model based on Kachanov damage rate theory.

[0106] In order to further verify the applicability and accuracy of the rock creep failure time prediction model in this paper, 42 sets of rock creep failure time test data of five types of rocks, including Inada granite, green sandstone, Ohya rock, mudstone and Gosford sandstone, under conventional triaxial compression conditions were statistically analyzed. The theoretical model of this paper, the Innocente model and the Charles model were used to predict the rock creep failure time under 42 sets of stress conditions. The results are shown in Table 4. The results of the theoretical model fitting test data of this invention are shown in Table 4. Figure 8 The comparison results between the experimental data and the predictions of the three models are shown in Fig. 9 .

[0107] Table 4 Prediction and test values ​​of creep failure time

[0108]

[0109]

[0110] Depend on Figure 8 It can be seen that under conventional triaxial compression conditions, the logarithm of the constant creep rate and the logarithm of the creep failure time of five types of rocks, including Inada granite, green sandstone, Ohya rock, mudstone and Gosford sandstone, show an obvious linear relationship. The experimental data are basically consistent with the fitting curve, indicating that the idea of ​​replacing creep stress with constant creep rate to establish a rock creep failure time prediction model is feasible. It also shows that the prediction model has high accuracy and strong applicability, and can be used to predict the creep failure time of different types of rocks under different stress states.

[0111] Depend on Fig. 9(a) It can be seen that the creep failure time of green sandstone predicted by the Innocente model is highly consistent with the test results, with MAE and RMSE of 0.67h and 0.91h respectively, indicating that the model is relatively accurate in predicting the creep failure time of green sandstone; however, the prediction results of Inada granite, Ohya rock, mudstone and Gosford sandstone are quite different from the test results, with MAE and RMSE as high as 219.76h and 1032.27h respectively, indicating that the Innocente model is suitable for predicting the creep failure time of specific types of rocks under specific stress conditions, but not for the other four types of rocks. Therefore, the use conditions of this type of model are limited and its applicability is not wide.

[0112] Depend on Fig. 9 (b) It can be seen that the creep failure time predicted by the Charles model for Inada granite and green sandstone is relatively consistent with the test results. The MAE and RMSE of the predicted value of Inada granite and the test value are 2.86h and 4.92h respectively, and the MAE and RMSE of the predicted value of green sandstone and the test value are 0.04h and 0.04h respectively, indicating that the model is relatively accurate in predicting the creep failure time of Inada granite and green sandstone; however, the results of predicting Ohya rock, mudstone and Gosford sandstone are quite different from the test results, with MAE and RMSE as high as 13.95h and 47.65h respectively, indicating that the Charles model is more applicable than the Innocente model, but is not applicable to the other three types of rocks. Therefore, the applicability of this model is still not wide.

[0113] Depend on Fig. 9 (c) It can be seen that the creep failure time of the five types of rocks predicted in this paper is highly consistent with the experimental results. The predicted results are basically consistent with the experimental results. The MAE and RMSE of the two are only 3.36h and 11.74h, respectively. This shows that the theoretical prediction model established in this paper is not only more accurate than the Innocente model and the Charles model, but also has a wider range of applicability.

[0114] Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art may still modify the technical solutions described in the aforementioned embodiments, or make equivalent substitutions for some of the technical features therein; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for establishing a rock creep failure time prediction model under conventional triaxial compression conditions, characterized in that: The method comprises: The target rock is subjected to n groups of conventional triaxial compression tests under different creep stresses under a predetermined confining pressure to obtain n creep curves; For any creep curve i, obtain the creep failure time t corresponding to the creep curve i Fi and constant creep rate Thus, multiple points to be fitted are obtained For multiple points to be fitted Performing linear fitting to obtain a fitting curve, and obtaining fitting parameters of the fitting curve, wherein the fitting parameters include a slope k and an intercept b; The rock creep failure time prediction model under conventional triaxial compression conditions of the target rock is obtained according to the fitting parameters: Among them, t F is the rock creep failure time, is the constant creep rate.

2. The method for establishing a rock creep failure time prediction model under conventional triaxial compression conditions according to claim 1 is characterized in that: The target rock is subjected to n groups of conventional triaxial compression tests under a predetermined confining pressure and different creep stresses to obtain n creep curves, including: Cut and grind the target rock to obtain n specimens; Determine the creep stress of each specimen, conduct conventional triaxial compression tests on n specimens, and obtain n creep curves; Among them, for any sample, the creep curve corresponding to the sample is obtained in the following manner: the creep stress of the sample is determined, a confining pressure is applied to the predetermined confining pressure at a rate of 100 to 500 N / s, and then the pressure is stabilized for 30 to 90 seconds, and then an axial pressure is applied to the preset axial pressure at a rate of 100 to 500 N / s, and then the pressure is stabilized until the sample undergoes creep failure, so as to obtain the creep curve corresponding to the sample; wherein the preset axial pressure value is obtained through the creep stress and the predetermined confining pressure.

3. The method for establishing a rock creep failure time prediction model under conventional triaxial compression conditions according to claim 2 is characterized in that: n≥5; when n is 5, the creep stresses of the five specimens are respectively 75%, 80%, 85%, 90% and 95% of the target rock compressive strength.

4. The method for establishing a rock creep failure time prediction model under conventional triaxial compression conditions according to claim 3 is characterized in that: The target rock compressive strength is obtained by: Cut and grind the target rock to obtain m samples; After conventional triaxial compression tests are performed on m specimens, the compressive strengths corresponding to the m specimens are averaged and obtained; Among them, for any sample, the compressive strength corresponding to the sample is obtained in the following manner: applying confining pressure at a rate of 100 to 500 N / s to the predetermined confining pressure, then maintaining the pressure for 30 to 90 seconds, and then applying axial pressure at a rate of 100 to 500 N / s until the sample is destroyed, and taking the creep stress corresponding to the destruction of the sample as the compressive strength corresponding to the sample.

5. The method for establishing a rock creep failure time prediction model under conventional triaxial compression conditions according to claim 4 is characterized in that: m≥5。 6. The method for establishing a rock creep failure time prediction model under conventional triaxial compression conditions according to claim 2 is characterized in that: The predetermined confining pressure is related to the actual ground stress of the target rock; when the target rock is sandy mudstone on the coal roof, the predetermined confining pressure is 5 MPa.

7. The method for establishing a rock creep failure time prediction model under conventional triaxial compression conditions according to claim 6 is characterized in that: The preset axial pressure is equal to the sum of the creep stress and the predetermined confining pressure.

8. The method for establishing a rock creep failure time prediction model under conventional triaxial compression conditions according to claim 2 or 4, characterized in that: The sample is a standard cylindrical sample with a diameter of 50 mm and a height of 100 mm; The angles between the normal lines of the upper and lower end surfaces of the sample and their axis are within the range of ±0.25°, and the unevenness deviations of the upper and lower end surfaces are within the range of ±0.05mm.

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