Determination of the constant m in the Hoek-Brown criterion based on digital drill parameters i and the intensity envelope method

Abstract

The present invention discloses a method for determining the constant m in the Hoek-Brown criterion based on digital drill parameters. i The cutting force F is obtained by using the Hoek-Brown criterion and the relationship between the digital drill parameters. t With thrust F n The relationship curve of the drill bit rake angle α and the rock contact friction angle θ between the drill bit cutting surface and the end face are calculated; the friction angle between the compression zone and the intact rock #imgabs0# and the internal friction angle of the rock #imgabs1# are calculated to draw the cutting force F t About Thrust F n The relationship curve is obtained, the curve intercept b is obtained, and the constant m in the Hoek-Brown criterion is calculated. i ; Substitute θ and #imgabs2# intercept b into the equation of rock cohesion c to calculate cohesion c, and then calculate the rock uniaxial compressive strength UCS; Substitute the calculated constant m i The uniaxial compressive strength UCS is substituted into the H-B criterion to calculate the triaxial compressive strength TCS of the rock. i The accuracy, scientificity and simplicity of the method cannot be guaranteed.

Description

Technical Field

[0001] The present invention belongs to the field of geotechnical engineering in-situ testing technology, and specifically relates to determining the constant m in the Hoek-Brown criterion based on digital drill parameters. i and intensity envelope methods. Background Art

[0002] The Hoek-Brown (HB) strength criterion is a well-known empirical formula for predicting rock failure. In the HB criterion, there are two constants: s and m. i The constant s reflects the degree of rock fragmentation, and the constant m i Reflects the hardness of rock, ranging from 0.001 to 25. From the perspective of geological information, experimental evaluation and rock properties, the constant m i There are different definitions. However, for the same rock, the measurement method is different and the constant m i The results will also vary greatly.

[0003] The earliest geological data was used to determine the constant m i However, the accuracy of the geological information obtained mainly depends on the experience of the exploration engineer; if the method recommended by ISRM is used, the constant m obtained will be affected by factors such as lack of experimental data, unsatisfactory experimental results, and differences in experimental conditions. i A certain error is generated; using statistical methods (including relevant specifications, R index method and model based on unconfined compressive strength (UCS)) to illustrate the applicability of the HB criterion is a fast and accurate way to determine the constant m i Although the above method can quickly determine the constant m according to the lithology classification and rock properties i However, there is an urgent need to establish a mechanical parameter analysis model to directly determine the constant m i Previously, scholars proposed to use the integral of triaxial compressive strength TCS and deformation modulus to determine the constant m i , but the error reached 20%; some scholars also used the constant m i It is defined as an indicator related to the micromechanics of brittle rocks. Based on linear elastic fracture mechanics, a nonlinear strength criterion is established. This nonlinear strength criterion is very similar to the HB criterion, but the nonlinear strength criterion is based on the fracture coefficient to determine the constant m. i However, in determining the constant m i There are some limitations in the calculation of fracture coefficient. Summary of the Invention

[0004] The present invention provides a method for determining the constant m in the Hoek-Brown criterion based on digital drill parameters. iand strength envelope method, the digital drilling parameters and constant m were established i The analytical relationship between the constant m is determined quickly and accurately using the digital drill parameters. i , it is possible to determine the rock strength envelope simply by conducting on-site in-situ digital drilling experiments on the rock.

[0005] The technical solution adopted by the present invention is to determine the constant m in the Hoek-Brown criterion based on the digital drill parameters. i The method of intensity envelope is implemented according to the following steps:

[0006] Step 1: Use the digital drilling equipment (DPMA) to conduct rock digital drilling experiments, and obtain the cutting force F according to the Hoek-Brown criterion and the relationship between the digital drilling parameters. t Thrust F n The relationship curve of the drill bit is obtained, and then the drill bit rake angle α and the rock contact friction angle θ between the drill bit cutting surface and the end surface are calculated;

[0007] Step 2: Based on the drill bit rake angle α and the rock contact friction angle θ between the drill bit cutting surface and the end surface calculated in step 1, the friction angle between the compression zone and the intact rock is calculated. and the internal friction angle of rock

[0008] Step 3: Draw the cutting force F t About Thrust F n The relationship curve is obtained, and the curve intercept b is obtained. The α, θ and Substitute m i The constant m in the Hoek-Brown criterion is then calculated from the equation i ;

[0009] Step 4: The rock contact friction angle θ and internal friction angle of the drill bit cutting surface and end face calculated in steps 1, 2, and 3 are Friction angle of intact rock Substitute the intercept b into the equation of rock cohesion c to calculate the cohesion c, and then calculate the rock uniaxial compressive strength UCS;

[0010] Step 5: The constant m calculated in step 3 i , the uniaxial compressive strength UCS calculated in step 4 is substituted into the HB failure criterion to calculate the triaxial compressive strength TCS of the rock.

[0011] The present invention is also characterized in that:

[0012] When conducting the rock digital drilling experiment in step 1, it is divided into two stages according to the dominant force: cutting and friction stage. When the cutting force is greater than the thrust force, the cutting force is dominant; when the cutting force is less than the thrust force, the thrust force is dominant.

[0013] When the cutting force is greater than the thrust force, the relationship between the cutting force and the thrust force is:

[0014]

[0015] In formula (1), F t is the cutting force, F n is the thrust, α is the drill rake angle, and θ' is the contact friction angle of the cutting surface

[0016] When the cutting force is less than the thrust force, the relationship between the cutting force and the thrust force is:

[0017]

[0018] In formula (2), π·(R 2 -r 2 ) is the cross-sectional area of ​​the drill bit, R is the outer diameter of the drill bit, r is the inner diameter of the drill bit, θ is the rock contact friction angle between the cutting surface and the end face of the drill bit, is the internal friction angle of the rock;

[0019] According to the relationship curve when the cutting force is less than the thrust force, the slope is calculated to obtain θ. Then, according to the relationship curve when the cutting force is greater than the thrust force, the slope is calculated to obtain α+θ'. Since θ is approximately equal to θ', α is obtained.

[0020] The friction angle between the compression zone and the intact rock in step 2 and rock internal friction angle The calculation formula is:

[0021]

[0022] Cutting force F in step 3 t With thrust F n The intercept of the relationship curve is represented by a constant b, and the calculation formula of b is:

[0023]

[0024] Then we get the constant m in the Hoek-Brown criterion i The calculation formula is:

[0025]

[0026] The calculation formulas for the uniaxial compressive strength UCS and cohesion c of rock in step 4 are:

[0027]

[0028]

[0029] The HB failure criterion in step 5 is:

[0030]

[0031] σ c is the uniaxial compressive strength UCS of rock, σ1 and σ3 are the two components of σ, where σ1 is the triaxial compressive strength TCS, and s is a constant, and s for intact rock is taken as 1.0;

[0032] The calculation formula of rock triaxial compressive strength TCS is:

[0033]

[0034] The beneficial effect of the present invention is that the present invention determines the constant m in the Hoek-Brown criterion based on the digital drill parameters. i The method of strength envelope only requires on-site digital drilling experiments to obtain digital drilling parameters, and then a series of theoretical calculations can directly determine the constant m in the HB criterion. i , uniaxial compressive strength (UCS), cohesion (c), and triaxial compressive strength (TCS). This avoids the inaccurate experimental results caused by the impact of traditional sampling and transportation on the rock. The method of the present invention is simple, fast, cost-effective, highly accurate, and has broad application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 It is a diagram of the digital drilling equipment (DPMA) and its system components;

[0036] Figure 2 This is a diagram of the WDT-1500 multifunctional rock material compression testing machine;

[0037] Figure 3 is the relationship curve between different rock cutting forces and thrust, among which, Figure 3 (a) is the relationship curve between shale cutting force and thrust, Figure 3 (b) is the relationship curve between slate cutting force and thrust, Figure 3 (c) is the relationship curve between granite cutting force and thrust, Figure 3 (d) is the relationship curve between marble cutting force and thrust, Figure 3 (e) is the relationship curve between limestone cutting force and thrust, Figure 3 (f) is the relationship curve between cutting force and thrust force of diorite;

[0038] Figure 4 Constant m for different types of rocks i , cohesion c, internal friction angle The comparison chart of the predicted value and the measured value, where Figure 4 (a) is the constant m i The comparison chart of predicted value and measured value, Figure 4 (b) is the internal friction angle The comparison chart of predicted value and measured value, Figure 4 (c) is a comparison chart of the predicted and measured values ​​of cohesion c;

[0039] Figure 5 Comparison of failure envelope diagrams of MC criterion and HB criterion based on digital drilling experiment and laboratory method, Figure 5 (a) is the failure envelope diagram based on the MC criterion, Figure 5 (b) is the failure envelope diagram based on the HB criterion. DETAILED DESCRIPTION

[0040] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0041] The present invention determines the constant m in the Hoek-Brown criterion based on the digital drill parameters i The method of intensity envelope is implemented according to the following steps:

[0042] Step 1: First, use the digital drilling equipment (DPMA) as Figure 1 As shown in the figure, a rock digital drilling experiment was conducted, and the cutting force F was obtained according to the Hoek-Brown criterion and the relationship between the digital drilling parameters. t Thrust F n The relationship between the drill bit rake angle α and the rock contact friction angle θ between the drill bit cutting surface and the end face is then calculated.

[0043] When conducting the rock digital drilling experiment in step 1, it is divided into two stages according to the dominant force: cutting and friction stage. When the cutting force is greater than the thrust force, the cutting force is dominant; when the cutting force is less than the thrust force, the thrust force is dominant.

[0044] When the cutting force is greater than the thrust force, the relationship between the cutting force and the thrust force is:

[0045]

[0046] Among them, F t is the cutting force, F n is the thrust force, α is the drill rake angle, and θ' is the contact friction angle of the cutting surface. When the cutting force is less than the thrust force, the relationship between the cutting force and the thrust force is:

[0047]

[0048] Among them, π·(R 2 -r 2) is the cross-sectional area of ​​the drill bit, R is the outer diameter of the drill bit, r is the inner diameter of the drill bit, θ is the rock contact friction angle between the cutting surface and the end face of the drill bit, is the internal friction angle of the rock;

[0049] According to the relationship curve when the cutting force is less than the thrust force, the slope is calculated to obtain θ. Then, according to the relationship curve when the cutting force is greater than the thrust force, the slope is calculated to obtain α+θ'. Since θ is approximately equal to θ', α is obtained.

[0050] Step 2: Based on the α and θ calculated in step 1, calculate the friction angle between the compression zone and the intact rock. and the rock internal friction angle

[0051] The friction angle between the compression zone and the intact rock in step 2 Internal friction angle with rock The calculation formula is:

[0052]

[0053] Step 3: Draw the cutting force F t About Thrust F n The relationship curve is obtained, and the curve intercept b is obtained. The α, θ and Substitute m i The constant m in the Hoek-Brown criterion is then calculated from the equation i ;

[0054] F t With F n The intercept in the relationship curve is represented by a constant b, and the calculation formula for b is:

[0055]

[0056] Then we get the constant m in the Hoek-Brown criterion i The calculation formula is:

[0057]

[0058] Step 4: The rock contact friction angle θ and internal friction angle of the drill bit cutting surface and end face calculated in steps 1, 2, and 3 are Friction angle of intact rock Substitute the intercept b into the equation of rock cohesion c to calculate the cohesion c, and then calculate the rock uniaxial compressive strength UCS;

[0059] The calculation formulas for rock uniaxial compressive strength UCS and cohesion c are:

[0060]

[0061] Step 5: The constant m calculated in step 3 i , the uniaxial compressive strength UCS calculated in step 4 is substituted into the HB failure criterion to calculate the triaxial compressive strength TCS of the rock;

[0062] The HB failure criterion is:

[0063]

[0064] σ c is the uniaxial compressive strength UCS of rock, σ1 and σ3 are the two components of σ, where σ1 is the triaxial compressive strength TCS, s is a constant, and s for intact rock is taken as 1.0.

[0065] The calculation formula of rock triaxial compressive strength TCS is:

[0066] The present invention is a method for determining the constant m in the rock Hoek-Brown (HB) criterion based on digital drilling parameters. i The method is verified as follows:

[0067] 1) Digital drill experiment

[0068] like Figure 1 As shown, the Digital Drilling Machine (DPMA) is used for in-situ digital drilling experiments. The equipment includes an electronic control system, hydraulic system, oil pump transmission system, real-time monitoring system, data acquisition system, and diamond drill bit. During the experiment, a specific rotational speed and drilling rate are set. The data acquisition system automatically collects the digital drilling parameters and saves them to an Excel spreadsheet. The diamond drill bit used in this equipment is a hollow drill bit with an outer diameter of 70 mm and an inner diameter of 60 mm. Before the experiment begins, to ensure the equipment is functioning properly, 3-5 pre-drilling runs should be performed to verify that the data are within the normal range. During the experiment, at least five tests are conducted on the same rock type to ensure the accuracy of the experimental data. This experiment selected six rock types from the Weihe River Basin Project in Shaanxi Province for in-situ digital drilling experiments: limestone (low strength), shale (normal strength), slate (medium-high strength), granite (medium-high strength), diorite (high strength), and marble (extremely high strength). During the experiment, the DPMA speed was set to 500-800 rpm and the drilling speed was set to 0.2-2.3 cm / min. The digital drilling parameters for different types of rock were obtained as shown in Table 1:

[0069] Table 1 Average values ​​of digital drilling parameters for different types of rocks measured by DPMA

[0070]

[0071] 2) Conventional triaxial test

[0072] like Figure 2 As shown, conventional triaxial compression tests were conducted on a WDT-1500 multifunctional rock material compression testing machine controlled by a digital DOLI device. The experimental equipment consists of an electrical control system, an acoustic detection system, and a loading system. The equipment has a maximum axial load of 1800 kN and a maximum confining pressure of 80 MPa. To ensure consistency between laboratory experiments and in-situ digital drilling test specimens, samples were collected from the digital drilling test site. According to ISRM recommended standard specimens, the specimens were manufactured as standard cylinders with a height of 100 mm and a diameter of 50 mm. The bottom and top of the specimens must be completely flat to ensure uniform loading during the experiment. The specimen size and flatness tolerance were controlled within ±0.02 mm. During the experiment, the specimens were wrapped with a flexible rubber membrane to prevent pressurized oil penetration. A spherical valve seat was used at the top to minimize errors caused by unevenness of the sample bottom. To reduce friction, two heat-treated, hardened smooth plates were placed at each end of the specimen during the unconfined and triaxial compression tests. To eliminate variability due to rock heterogeneity, three tests were conducted for each rock type, and the average value was calculated. The cohesion c and internal friction angle of the rock were obtained by laboratory experiments using the method recommended by ISRM. Uniaxial compressive strength UCS, triaxial compressive strength TCS and constant m i The results are shown in Table 2:

[0073] Table 2 ISRM recommended method for obtaining rock strength

[0074]

[0075]

[0076] 3) Calculate the drill bit rake angle α and the contact friction angle θ' of the cutting surface

[0077] When conducting rock drilling experiments, it is divided into two stages according to the dominant force: cutting and friction stages. When the cutting force is greater than the thrust force, the cutting force is dominant; when the cutting force is less than the thrust force, the thrust force is dominant.

[0078] When the cutting force is greater than the thrust force, the relationship between the cutting force and the thrust force is:

[0079]

[0080] Among them, F t Cutting force, F n is the thrust, α is the drill rake angle, and θ' is the contact friction angle of the cutting surface

[0081] When the cutting force is less than the thrust force, the relationship between the cutting force and the thrust force is:

[0082]

[0083] Among them, π·(R 2 -r 2 ) is the cross-sectional area of ​​the drill bit, R is the outer diameter of the drill bit, r is the inner diameter of the drill bit, θ is the rock contact friction angle between the cutting surface and the end face of the drill bit, is the internal friction angle of rock.

[0084] According to the relationship curve when the cutting force is less than the thrust force, the slope is calculated to obtain θ. Then, according to the relationship curve when the cutting force is greater than the thrust force, the slope is calculated to obtain α+θ'. Since θ is approximately equal to θ', α is calculated.

[0085] 4) Calculate the friction angle of rock and the internal friction angle of rock

[0086] Substitute the drill bit rake angle α and the rock contact friction angle θ between the drill bit cutting surface and the end surface calculated in 3) into the friction angle Angle of internal friction In the calculation formula, the friction angle is calculated and internal friction angle

[0087] Friction angle of intact rock and rock internal friction angle The calculation formula is:

[0088]

[0089] 5) Calculate the constant m in the Hoek-Brown criterion for rocks i .

[0090] Plotting the cutting force F t About Thrust F n The relationship curve is as follows Figure 3 (a)- Figure 3 As shown in (f), the curve intercept b is obtained by substituting the α, θ and Substitute the constant m i The constant m in the Hoek-Brown criterion is then calculated from the equation i ;

[0091] 3) The calculation formula for b is:

[0092]

[0093] The constant m in the Hoek-Brown criterion i The calculation formula is:

[0094]

[0095] 6) Calculate the rock's cohesion c and uniaxial compressive strength UCS

[0096] θ calculated in 1), 2), and 3) Substitute b into the rock cohesion calculation formula to obtain the cohesion c, and then calculate the rock uniaxial compressive strength UCS.

[0097] The calculation formulas for rock uniaxial compressive strength UCS and cohesion c are:

[0098]

[0099] 7) Calculate the triaxial compressive strength TCS of rock

[0100] The constant m calculated in 5) i The uniaxial compressive strength UCS calculated in 6) is substituted into the HB failure criterion to calculate the triaxial compressive strength TCS of the rock.

[0101] The HB failure criterion is:

[0102]

[0103] σ c is the uniaxial compressive strength UCS of rock, σ1 and σ3 are the two components of σ, where σ1 is the triaxial compressive strength TCS, s is a constant, and s for intact rock is taken as 1.0.

[0104] The calculation formula of rock triaxial compressive strength TCS is:

[0105]

[0106] The strength of different types of rocks predicted by digital drilling experiments are shown in Table 3:

[0107] Table 3 Prediction of the strength of different rocks using rock digital drilling experiments

[0108]

[0109]

[0110] The rock cohesion c and internal friction angle predicted by in-situ digital drilling experiment are Constant m i Compared with the laboratory measured values, the results are as follows Figure 4 As shown in Figure 2. The comparison between the predicted value and the measured value of rock cohesion is shown in Figure 2. Figure 4 As shown in (c), the predicted values ​​of cohesion c of slate, granite and marble are about 10% smaller than the measured values. However, the predicted values ​​of cohesion c of shale, limestone and diorite are smaller than the measured values. Figure 4 In (a), the constant m iThere is a similar trend. The laboratory measured constant m of limestone and slate i Value ratio prediction constant m i The predicted m is about 8% larger. However, the laboratory measured values ​​for granite and marble are about 5% larger than the predicted values. This phenomenon can be explained by the difference in the dominant forces during the rock digital drilling process. Hard rock has high compressive strength, while soft rock is easily damaged when compressed. Therefore, cutting hard rock requires more torque, while cutting soft rock requires more pressure. Therefore, the predicted m is i The TCS envelope diagrams of the six types of rocks predicted by the HB criterion and the MC criterion and the measured TCS envelope diagrams are shown in Figure 2. Figure 5 Compared with the triaxial compressive strength TCS envelope obtained in the laboratory, the predicted triaxial compressive strength TCS envelope accurately describes the rock failure (the error bar is less than 13.5%). The comparison results show that the constant m in the HB criterion is determined based on the digital drilling parameters. i The method is effective.

[0111] In order to evaluate the parameters of the digital drill, a constant m is determined. i To improve the accuracy of the method, we introduce the constant m i The fracture mechanics solution is the ratio of the uniaxial compressive strength UCS to the tensile strength TS and the coefficient ratio μ / β, where the coefficient β is (1-ν / 2)κ, ν is the Poisson's ratio, and κ is the proportional factor of the mixed fracture criterion. According to the maximum energy release rate criterion, the proportional factor κ of the mixed fracture criterion is 1.0. The friction coefficient μ is related to the brittleness of the rock and ranges from 0.2 to 0.8. According to previous studies, the friction coefficient μ is equal to the formula (4) Therefore, the friction coefficients of granite, shale, slate, marble, limestone, and diorite are 0.65, 0.37, 0.56, 0.67, 0.46, and 0.78, respectively. Substituting the friction coefficients and Poisson's ratio of these six rocks into the constant m i The fracture mechanics equations of the six rocks were obtained. The fracture mechanics solutions were compared with the constant m predicted by the digital drilling parameters. i The results of the two methods are compared and it is found that the difference between the results of the same rock is about 9.5%. i The value is less than the fracture mechanics m i Value, granite, diorite and other rocks with higher strength are predicted to have m i The value is greater than the fracture mechanics m i The m values ​​measured by the two methods for slate are i This result also proves that the constant m in the HB criterion is determined based on the digital drill parameters. i Accuracy of the method.

Claims

1. Determine the constant m in the Hoek-Brown criterion based on digital drill parameters i and the intensity envelope method, characterized in that Please follow the steps below to implement it: Step 1: Use digital drilling equipment to conduct rock digital drilling experiments, and obtain the cutting force F according to the Hoek-Brown criterion and the relationship between drilling parameters. t With thrust F n The relationship curve of the drill bit is obtained, and then the drill bit rake angle α and the rock contact friction angle θ between the drill bit cutting surface and the end surface are calculated; When performing the digital drilling experiment in step 1, the experiment is divided into two stages according to the dominant force: the cutting stage and the friction stage. When the cutting force is greater than the thrust force, the cutting force is dominant; when the cutting force is less than the thrust force, the thrust force is dominant. When the cutting force is greater than the thrust force, the relationship between the cutting force and the thrust force is: In formula (1), F t is the cutting force, F n is the thrust, α is the drill rake angle, and θ' is the contact friction angle of the cutting surface When the cutting force is less than the thrust force, the relationship between the cutting force and the thrust force is: In formula (2), π·(R 2 -r 2 ) is the cross-sectional area of ​​the drill bit, R is the outer diameter of the drill bit, r is the inner diameter of the drill bit; θ is the rock contact friction angle between the cutting surface and the end face of the drill bit, is the internal friction angle of the rock; According to the relationship curve when the cutting force is less than the thrust, the slope is calculated to obtain θ. Then, according to the relationship line when the cutting force is greater than the thrust, the slope is calculated to obtain α+θ'. Since θ is approximately equal to θ', the drill rake angle α is obtained. Step 2: Based on the drill bit rake angle α and the rock contact friction angle θ between the drill bit cutting surface and the end surface calculated in step 1, the friction angle between the compression zone and the intact rock is calculated. and the internal friction angle of rock The friction angle between the compression zone and the intact rock in step 2 Angle of internal friction with rock The calculation formula is: Step 3: Draw the cutting force F t About Thrust F n The curve intercept b is obtained by calculating the relationship curve of the drill bit cutting surface and the end surface, and the front angle α, the rock contact friction angle θ and the internal friction angle obtained in steps 1 and 2 are used. Substitute the constant m i The constant m in the Hoek-Brown criterion is calculated from the equation i ; The cutting force F in step 3 t With thrust F n The intercept of the relationship curve is represented by a constant b, and the calculation formula of b is: Then we get the constant m in the Hoek-Brown criterion i The calculation formula is: Step 4: Substitute the rock contact friction angle θ between the drill bit cutting surface and the end surface, and the friction angle between the compression zone and the intact rock calculated in steps 1, 2, and 3. Angle of internal friction of rock Substitute the intercept b into the calculation formula of rock cohesion c to obtain cohesion c, and then calculate the rock uniaxial compressive strength UCS; The calculation formulas for the uniaxial compressive strength UCS and cohesion c of rock in step 4 are: Step 5: The constant m calculated in step 3 i , the uniaxial compressive strength UCS calculated in step 4 is substituted into the HB failure criterion to calculate the triaxial compressive strength TCS of the rock; The HB failure criterion in step 5 is: σ c is the uniaxial compressive strength UCS of rock, σ1 and σ3 are the two components of σ, where σ1 is the triaxial compressive strength TCS, s is a constant, and s for intact rock is taken as 1.0; The calculation formula of rock triaxial compressive strength TCS is:

Images