Rock uniaxial compressive strength inversion method based on while-drilling parameters and Mohr-Coulomb criterion

Abstract

The invention relates to the field of rock mechanics and drilling engineering, and particularly discloses a rock uniaxial compressive strength inversion method based on while-drilling parameters and a Mohr-Coulomb criterion. The method comprises the following steps: acquiring while-drilling parameters in a drilling process in real time, wherein the while-drilling parameters at least comprise drill bit axial thrust, drill bit torque, drill bit diameter, a normal efficiency factor and a tangential efficiency factor; determining an effective normal load, and calculating the average normal pressure intensity of the contact surface of the drill bit and the rock; effective torque is determined, and the average tangential shear stress of the contact surface is deduced; correcting a result by introducing a normal efficiency factor and a tangential efficiency factor; and a rock uniaxial compressive strength inversion model based on the while-drilling parameters and the Mohr-Coulomb criterion is established, so that in-situ, continuous and mechanism-driven quantitative evaluation of the rock strength is realized. According to the method, the dependence of a traditional empirical model on the drilling working condition is overcome, and the accuracy, the stability and the engineering applicability of a strength inversion result are remarkably improved.

Description

Technical Field

[0001] This invention relates to the fields of rock mechanics and drilling technology, specifically to a method for inverting the uniaxial compressive strength of rock based on measurement-while-drilling parameters and the Mohr-Coulomb strength criterion. Background Technology

[0002] Uniaxial compressive strength of rock, as a core parameter characterizing the mechanical properties of rock, plays a decisive role in geotechnical engineering fields such as mining, tunneling, oil and gas drilling, and underground space development. This parameter directly reflects the rock's ability to resist compressive failure and is the fundamental basis for assessing formation stability, optimizing blasting design, selecting drilling techniques, and formulating support schemes. Therefore, accurately and efficiently obtaining the uniaxial compressive strength of rock is crucial for ensuring project safety, improving operational efficiency, and controlling construction costs.

[0003] Traditional methods for obtaining uniaxial compressive strength of rocks mainly rely on a combination of "core drilling and laboratory testing". This method requires drilling rock cores on-site, transporting them to the laboratory, and then performing standardized sample preparation processes such as cutting, grinding, and end face flattening. Finally, the cores are subjected to axial loading on a servo-controlled pressure testing machine until the sample fails, thereby calculating the strength value. Although this method is considered an industry benchmark, it has obvious limitations: (1) The testing cycle is long, usually taking several days or even weeks from core drilling, sample transportation, preparation to completion of the test, making it difficult to respond to the real-time decision-making needs of engineering in a timely manner; (2) It cannot reflect the actual impact of the in-situ environment (such as geostress, temperature, groundwater, etc.) on rock strength; (3) The economic cost is high, with significant costs for the entire process of core drilling, logistics, sample preparation and testing, especially in deep engineering or complex and difficult-to-sample strata; (4) The characterization ability is limited, as the discrete core test results are difficult to fully characterize the spatial heterogeneity and anisotropy of the rock mass due to the limited number and spatial distribution of sampling points. Due to the objective existence of internal structural planes, microfracture networks, and lithological gradations within rock masses, the mechanical properties of rocks often exhibit strong variability on a scale ranging from centimeters to meters. It is impossible to construct a continuous and reliable stratigraphic strength profile based solely on test data from a few discrete points.

[0004] To overcome the inherent limitations of traditional methods, measurement-while-drilling (MWD) technology has emerged and developed rapidly. This technology, through sensor arrays installed on drilling rigs or drill strings, can acquire multi-dimensional dynamic drilling parameters in real time during borehole construction, including but not limited to drill bit axial thrust, rotational torque, drilling rate, slewing speed, vibration acceleration, and mud pressure. These WWD parameters directly reflect the mechanical response of the interaction between the drill bit and the rock, providing a new technical approach for in-situ inversion of rock strength. Establishing a mapping relationship between drilling parameters and rock strength based on WWD data, and achieving continuous inversion of the uniaxial compressive strength of rock across the entire borehole depth, has become a research hotspot in the field of rock mechanics.

[0005] Various technical solutions have been proposed by scholars both domestically and internationally regarding the correlation modeling between drilling parameters and rock strength. One type of method is based on the principle of energy conservation, using mechanical specific energy as the core indicator. This indicator is defined as the energy consumed in breaking a unit volume of rock, obtained through coupled calculations of drill bit torque, axial force, drilling rate, and rotational speed. It is assumed that mechanical specific energy is positively correlated with the uniaxial compressive strength of the rock. Another type of technical solution starts from the theory of ultimate cutting equilibrium, considering the frictional energy dissipation mechanism at the drill bit-rock interface, establishing a unit volume cutting energy model, and introducing weighting coefficients for axial force and torque to correct the energy distribution ratio under different drilling conditions. Other studies have employed dimensional analysis and multiple regression methods to construct a drillability index model, achieving strength inversion by fitting the statistical relationship between drilling parameters and laboratory test data. These models utilize drilling information to a certain extent, partially solving the timeliness problem of traditional methods.

[0006] However, the aforementioned existing technical solutions generally share a common deficiency: model construction is mainly based on macroscopic energy balance or statistical correlation analysis, lacking in-depth consideration of the mechanical mechanism of drill bit rock breaking, resulting in a disconnect between model parameters and physical processes. More critically, these technologies fail to effectively handle the inherent coupling relationship between drilling parameters, making the inversion results susceptible to interference from dynamic changes in drilling conditions. In actual engineering practice, operators adjust drilling process parameters according to formation changes. For example, increasing the axial thrust of the drill bit in the same rock formation will change the drill bit torque, drilling rate, and cuttings particle size distribution; changing to drill bits with different tooth shapes, diameters, or wear resistance will also significantly change the contact stress distribution characteristics between the drill bit and the rock. These adjustments to working conditions fall within the normal scope of construction processes, and the inherent strength properties of the rock itself should not fluctuate as a result. However, existing models, because they do not distinguish between the influence of working conditions and the inherent properties of the rock, often directly transmit changes in process parameters to the strength inversion results, resulting in significantly different strength estimates for the same rock formation under different combinations of drilling parameters, with large dispersion and poor repeatability of predicted values.

[0007] Furthermore, existing technologies lack a quantitative correction mechanism for the load transfer efficiency at the drill bit-rock interface. Due to factors such as the cuttings cushion at the bottom of the borehole, unevenness of the contact surface, drill bit wear, and vibration, the axial thrust and torque measured by sensors cannot be fully and effectively applied to rock breaking; some energy is dissipated in the form of friction, heat, and vibration. Existing models typically directly substitute measured values ​​into calculations without considering the attenuation and variation of load transfer efficiency, further amplifying the disturbance effect of changes in operating conditions on the inversion results. As drilling depth increases, formation conditions become more complex, or drill bit conditions change, the model inversion deviation increases accordingly, even leading to physical paradoxes in areas of stress concentration or interbedded soft and hard layers, severely limiting its practical engineering application value.

[0008] In summary, while existing inversion techniques have made progress in terms of timeliness and economy compared to traditional methods, their neglect of the physical coupling mechanism of drilling parameters in the model principle fails to effectively eliminate interference caused by changes in drilling conditions. This results in insufficient reliability and stability of the inversion results, making it difficult to meet the technical requirements of continuous and accurate assessment of rock strength in practical engineering. Therefore, there is an urgent need to develop a new method for inverting the uniaxial compressive strength of rock based on rock breaking mechanics, considering load transfer efficiency correction, and reducing dependence on drilling conditions, in order to improve inversion accuracy and adaptability to different drilling conditions. Summary of the Invention

[0009] To address the shortcomings of existing technologies, this invention provides a method for inverting the uniaxial compressive strength of rocks based on drilling parameters and the Mohr-Coulomb criterion, thus solving the problems mentioned in the background section.

[0010] To achieve the above objectives, the present invention provides a method for inverting the uniaxial compressive strength of rock based on drilling parameters and the Mohr-Coulomb criterion, comprising the following steps:

[0011] Obtain drilling parameters during the drilling process, which include at least the drill bit axial thrust, drill bit torque, drill bit diameter, normal efficiency factor, and tangential efficiency factor.

[0012] The effective normal load is determined based on the drill bit's axial thrust and normal efficiency factor, and the average normal pressure at the contact surface between the drill bit and the rock is calculated in conjunction with the drill bit's diameter.

[0013] The effective torque is determined based on the drill bit torque and tangential efficiency factor, and the average tangential shear stress at the contact surface between the drill bit and the rock is calculated in combination with the drill bit diameter; the in-situ horizontal stress and internal friction angle of the rock are obtained.

[0014] The uniaxial compressive strength of rock is calculated using the Mohr-Coulomb failure criterion based on the average normal pressure, average tangential shear stress, in-situ horizontal stress, and rock internal friction angle.

[0015] Preferably, the calculation process of the average normal pressure includes: multiplying the axial thrust of the drill bit by the normal efficiency factor to obtain the effective normal load; determining the contact area between the drill bit and the rock, which is calculated based on the drill bit diameter; and dividing the effective normal load by the contact area to obtain the average normal pressure.

[0016] Preferably, the contact area between the drill bit and the rock is calculated as a circular region, the area of ​​which is equal to the product of pi and the square of the drill bit diameter divided by 4.

[0017] Preferably, the calculation process of the average tangential shear stress includes: multiplying the drill bit torque by the tangential efficiency factor to obtain the effective torque; integrating the shear stress uniformly distributed on the contact surface based on the torque balance principle to establish the relationship between the effective torque and the average tangential shear stress, thereby solving for the average tangential shear stress.

[0018] Preferably, in the calculation of the average tangential shear stress, the relationship between the effective torque and the average tangential shear stress is established through the following integration process: the product of shear stress, the area of ​​the infinitesimal element, and the lever arm is integrated over a radius from 0 to the drill bit radius, and the integration result is equal to the effective torque.

[0019] Preferably, the process of calculating the uniaxial compressive strength of rock using the Mohr-Coulomb failure criterion includes: determining the maximum and minimum principal stresses of the local stress state of the rock through stress analysis based on the average normal pressure, average tangential shear stress, and in-situ horizontal stress; and substituting the maximum and minimum principal stresses into the Mohr-Coulomb failure criterion relationship to solve for the uniaxial compressive strength of the rock.

[0020] Preferably, the process of determining the maximum principal stress and the minimum principal stress includes: calculating the sum and difference of the average normal pressure and the in-situ horizontal stress; squaring half of the difference and adding it to the square of the average tangential shear stress, and then taking the square root of the sum to obtain the principal stress difference component; the maximum principal stress is equal to half of the above sum plus the principal stress difference component, and the minimum principal stress is equal to half of the above sum minus the principal stress difference component.

[0021] Preferably, when the in-situ horizontal stress value is negligible relative to the average normal pressure, the in-situ horizontal stress is set to 0, and the calculation of the uniaxial compressive strength of the rock is simplified to be based only on the average normal pressure, the average tangential shear stress, and the internal friction angle of the rock.

[0022] Preferably, when the average tangential shear stress is negligible relative to the average normal pressure, the average tangential shear stress is set to 0, and the calculation of the uniaxial compressive strength of the rock is simplified to the average normal pressure minus the product of the coefficient related to the internal friction angle of the rock and the in-situ horizontal stress.

[0023] This invention provides a method for inverting the uniaxial compressive strength of rock based on drilling parameters and the Mohr-Coulomb criterion. It has the following advantages:

[0024] 1. This invention corrects the axial thrust and torque of the drill bit by introducing normal efficiency factors and tangential efficiency factors. It obtains the average normal pressure and average tangential shear stress at the contact surface between the drill bit and the rock by combining contact mechanics analysis. Furthermore, it establishes an inversion model of the uniaxial compressive strength of the rock using the Mohr-Coulomb failure criterion, clarifies the physical mechanism of rock breaking, avoids the fluctuation of inversion results caused by changes in drilling conditions in purely empirical models, and significantly improves the accuracy and stability of rock strength inversion.

[0025] 2. This method only requires obtaining the axial thrust, torque, drill bit diameter, and efficiency factor obtained through on-site calibration during the drilling process. It eliminates the need for core sampling and laboratory testing, enabling real-time continuous inversion of the uniaxial compressive strength of rock throughout the drilling process. This significantly shortens the testing cycle and reduces testing costs, providing timely and reliable technical support for the evaluation of formation hardness and engineering decisions in fields such as mining and tunnel construction. Attached Figure Description

[0026] Figure 1 This is a schematic diagram showing the forces acting on the drill bit of the present invention in contact with the rock;

[0027] Figure 2 This is a schematic diagram of the Mohr's circle representing the local stress state of rock according to the present invention;

[0028] Figure 3 This is a scatter plot comparing the UCS predictions of this model with the uniaxial compression test values. Detailed Implementation

[0029] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other methods obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0030] Please see the appendix Figure 1 -Appendix Figure 3 The present invention provides step one, attached... Figure 1 The diagram illustrates the forces acting on the drill bit in contact with the rock. The drill bit has a diameter of D and a radius of R = D / 2. Assuming the contact surface between the drill bit and the rock is a circular region, the contact area A is the area of ​​the circular disk.

[0031]

[0032] Step two: Since the axial thrust F does not act 100% on the rock during actual drilling (due to uneven contact, cuttings pads, etc.), a normal contact efficiency factor η is introduced. n To correct the effective normal load to η nF. The average normal pressure is defined as the effective normal load divided by the contact area, from which the average normal pressure p0 of the contact surface can be obtained:

[0033]

[0034] In the formula, the unit of p0 is Pascal (Pa), which is consistent with the dimension of pressure. Physically, p0 represents the average positive compressive stress exerted by the drill bit on the rock. Its magnitude is directly proportional to the drilling pressure F and inversely proportional to the cross-sectional area of ​​the drill bit (that is, the larger the drill bit diameter, the smaller the p0 generated under the same F).

[0035] Step three: Next, calculate the average tangential shear stress τ0 at the contact surface. During drilling, part of the torque is used to break the rock, and the remainder may be lost due to friction and other factors. Therefore, a tangential contact efficiency factor η is introduced. t The corrected effective torque is η t M. Assuming the shear stress distribution on the contact surface is uniform with a value of τ0, as shown in the attached figure. Figure 1 As shown, consider a tiny ring element with radius r and thickness dr on the contact disk. The area of ​​this ring element is dA = 2πrdr, and it bears a tangential force dF. t =τ0dA, generating a small torque dM=dF t ·r. dF t Substituting and integrating the total contact area (0 ≤ r ≤ R), we obtain the effective torque η. t M, after transformation, yields the average tangential stress:

[0036]

[0037] In the above formula, τ0 is in Pascals (Pa). The formulas for calculating contact stresses p0 and τ0 based on drilling parameters were given earlier, where the efficiency factor η... n η t Depending on the interaction between the drill bit and the rock formation, this can be obtained through experimental calibration or field calibration. Under the action of the drill bit, the rock contact surface is subjected to normal compressive stress p0 (perpendicular to the contact surface) and tangential shear stress τ0 (tangential along the contact surface). The surrounding rock mass may also have an initial horizontal stress σ. h (Minimum principal stress in the far field parallel to the contact surface).

[0038] Step four, plane stress analysis based on elasticity mechanics, as shown in the appendix. Figure 2 As shown, this local stress state can be abstracted as σ = p0 and σ acting in two orthogonal directions, perpendicular and parallel to the contact surface. h There exists a shear stress τ0 between the two. The resulting Mohr stress circle can be used to solve for the principal stresses within the rock. The local maximum principal stress σ1 (compressive stress is taken as positive) and minimum principal stress σ3 can be calculated using the following formula:

[0039]

[0040] In the above formula, The average of the normal stress and the horizontal stress is expressed as the square root of the expression. It is half of the difference between the principal stresses.

[0041] When p0 is greater than σ h hour, The maximum principal stress required to crush rock, The corresponding minimum principal stress (generally close to the in-situ horizontal stress σ) h ).

[0042] Step 5: The Mohr-Coulomb criterion can be used to determine the strength failure of the rock. The Mohr-Coulomb criterion states that when the maximum principal stress σ1 and the minimum principal stress σ3 satisfy a linear relationship... When the rock fails under uniaxial compression (σ3=0), σ1 is the uniaxial compressive strength σ of the rock. c At this point, the relation becomes Therefore, the cohesion term can be... Equivalent replacement with σ c Therefore, the Mohr-Coulomb violation criterion can be rewritten as:

[0043]

[0044] In the above formula, φ is the internal friction angle of the rock, and σ c This is equivalent to the ultimate strength (UCS) of the rock when σ³ = 0. The uniaxial compressive strength σ of the rock can then be calculated. c The expression. Substituting it, we get:

[0045]

[0046] This is the inversion of the uniaxial compressive strength σ of rock based on drilling parameters. c The general formula. All the quantities included can be obtained through drilling measurements and known parameters: σ h σ is the in-situ horizontal stress of the rock stratum where the borehole is located (which can be obtained through in-situ stress testing or empirical estimation), and φ is the internal friction angle of the rock (which can be determined experimentally or obtained from literature). From formula (6), it can be seen that σ c It increases with increasing p0 (contact stress generated by drilling pressure) and τ0 (drill bit shearing action), while σ h The presence of [something] increases the rock's strength threshold against damage.

[0047] Step six: For the above formula, we can analyze its expression under different simplification conditions. When the in-situ horizontal stress σ in the rock strata... hWhen the stress is much smaller than the drill bit contact stress (e.g., in shallow drilling or when the confining pressure effect is ignored), σ can be approximated. h =0, at this time formula (6) simplifies to:

[0048]

[0049] As can be seen from the above formula, the UCS of a rock under no confining pressure is mainly determined by the contact normal stress p0 and the tangential stress τ0: the larger p0 and τ0 are, the greater σ becomes. c The higher.

[0050] Step 7: If we further assume that the tangential component during drilling can be neglected (e.g., in some pure indentation rock breaking cases, τ0→0), then the stress state at the contact surface approaches uniaxial compression. Substituting τ0=0 into equation (6), we get:

[0051] σ c =p0-Kσ h ;

[0052] It is evident that for pure indentation (no cutting), the predicted uniaxial compressive strength of the rock is equal to the contact normal pressure p0 minus K times the confining pressure σh; when σh = 0 simultaneously, then σc ≈ p0, meaning the average normal stress applied by the drill bit is directly equal to the rock's UCS. These results are consistent with intuitive engineering understanding, verifying the model's rationality. In summary, the method provided by this invention calculates contact stress using drilling parameters and derives the inversion formula for rock UCS using the Mohr-Coulomb criterion. When implementing this method, the rock strength can be evaluated in real time using measured parameters during drilling, thus providing a reliable basis for drilling process control and formation hardness identification. To verify the model's reliability, the Teale model and its improved models were selected for comparison. Figure 3 As shown in the figure, the horizontal axis represents the uniaxial compression test value of UCS, with the same horizontal axis representing the same type of rock, and the vertical axis represents the UCS predicted value calculated using the strength model. From existing models ( Figure 3 The results show that the UCS prediction results (vertical axis) for the same type of rock (same horizontal axis) vary significantly under different drilling conditions, while the model in this paper... Figure 3 The predicted UCS values ​​under different drilling conditions are quite similar with small differences, indicating a stronger adaptability to changes in drilling conditions. Furthermore, from... Figure 3 It can be seen that the fitting curve of this model is closer to the 1:1 line and has the highest coefficient of determination, which means that the UCS predicted value and the experimental value are closer.

[0053] Teale model formula

[0054]

[0055] Teale Improved Model

[0056]

[0057] The detailed data is shown in Table 1:

[0058] Table 1 Comparison of errors of different models

[0059]

[0060] In summary, this invention corrects the axial thrust and torque of the drill bit by introducing normal and tangential efficiency factors, obtains the average normal pressure and average tangential shear stress at the contact surface between the drill bit and the rock by combining contact mechanics analysis, and further establishes a rock uniaxial compressive strength inversion model using the Mohr-Coulomb failure criterion. This clarifies the physical mechanism of rock breaking and avoids the fluctuations in prediction results caused by changes in drilling conditions in purely empirical models, significantly improving the accuracy and stability of rock strength inversion.

[0061] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A rock uniaxial compressive strength inversion method based on a while-drilling parameter and a Mohr-Coulomb criterion, characterized in that, The method comprises the following steps: obtaining drilling parameters during drilling, the drilling parameters comprising at least bit axial thrust, bit torque, bit diameter, normal efficiency factor and tangential efficiency factor; determining effective normal load according to the bit axial thrust and the normal efficiency factor, and calculating average normal pressure of a bit-rock contact surface in combination with the bit diameter; determining effective torque according to the bit torque and the tangential efficiency factor, and calculating average tangential shear stress of the bit-rock contact surface in combination with the bit diameter; obtaining in-situ horizontal stress and internal friction angle of the rock; and 2. The rock uniaxial compressive strength inversion method based on the while-drilling parameters and the Mohr-Coulomb criterion according to claim 1, characterized in that, calculating uniaxial compressive strength of the rock based on the average normal pressure, the average tangential shear stress, the in-situ horizontal stress and the internal friction angle of the rock by using the Mohr-Coulomb failure criterion.

3. The rock uniaxial compressive strength inversion method based on the while-drilling parameters and the Mohr-Coulomb criterion according to claim 2, characterized in that, The average normal pressure is calculated by multiplying the bit axial thrust by the normal efficiency factor to obtain the effective normal load, determining the contact area of the bit and the rock based on the bit diameter, and dividing the effective normal load by the contact area to obtain the average normal pressure.

4. The rock uniaxial compressive strength inversion method based on the while-drilling parameters and the Mohr-Coulomb criterion according to claim 1, characterized in that, The contact area of the bit and the rock is calculated as a circular area, and the area of the circular area is equal to the product of pi and the square of the bit diameter divided by 4.

5. The rock uniaxial compressive strength inversion method based on the while-drilling parameters and the Mohr-Coulomb criterion according to claim 4, characterized in that, The average tangential shear stress is calculated by multiplying the bit torque by the tangential efficiency factor to obtain the effective torque, and integrating shear stress uniformly distributed on the contact surface based on the principle of moment balance to establish the relationship between the effective torque and the average tangential shear stress, and then solving the average tangential shear stress.

6. The rock uniaxial compressive strength inversion method based on while-drilling parameters and Mohr-Coulomb criterion of claim 1, wherein, In the calculation of the average tangential shear stress, the relationship between the effective torque and the average tangential shear stress is established by integrating the product of shear stress, infinitesimal area and force arm within the range of radius from 0 to the radius of the bit, and the integration result is equal to the effective torque.

7. The rock uniaxial compressive strength inversion method based on while-drilling parameters and Mohr-Coulomb criterion according to claim 6, characterized in that, The process of calculating the uniaxial compressive strength of the rock by using the Mohr-Coulomb failure criterion comprises the following steps: determining the maximum principal stress and the minimum principal stress of the local stress state of the rock based on the average normal pressure, the average tangential shear stress and the in-situ horizontal stress by stress analysis; and substituting the maximum principal stress and the minimum principal stress into the Mohr-Coulomb failure criterion relationship to obtain the uniaxial compressive strength of the rock.

8. The rock uniaxial compressive strength inversion method based on while-drilling parameters and Mohr-Coulomb criterion of claim 1, wherein, The determination process of the maximum principal stress and the minimum principal stress comprises the following steps: calculating the sum and the difference of the average normal pressure and the in-situ horizontal stress; adding the square of half of the difference to the square of the average tangential shear stress, and then taking the square root of the added result to obtain the principal stress difference component; the maximum principal stress is equal to half of the sum plus the principal stress difference component, and the minimum principal stress is equal to half of the sum minus the principal stress difference component.

9. The rock uniaxial compressive strength inversion method based on while-drilling parameters and Mohr-Coulomb criterion of claim 1, wherein, When the in-situ horizontal stress value is negligible relative to the average normal pressure, the in-situ horizontal stress is set to 0, and the calculation of the uniaxial compressive strength of the rock is simplified to be based only on the average normal pressure, the average tangential shear stress and the internal friction angle of the rock. When the average tangential shear stress is negligible relative to the average normal pressure, the average tangential shear stress is set to 0, and the calculation of the uniaxial compressive strength of the rock is simplified to be the average normal pressure minus the product of a coefficient related to the internal friction angle of the rock and the in-situ horizontal stress.

Images