TBM thrust and FPI index calculation correction method

Abstract

The application provides a TBM thrust and FPI index calculation correction method. The correction method is to establish a three-dimensional analysis model of a cutter head excavating rock mass by using ABAQUS / Explicit, study the influence of the cutter head rotating speed on the cutter head thrust and torque under different excavating rock mass and different penetration degrees, calculate the ratio of the cutter head thrust simulation value under different cutter head rotating speeds to the traditional theoretical calculation value of the cutter head thrust, and fit to obtain the influence coefficient of the cutter head rotating speed on the traditional model of the cutter head thrust; the traditional model of the total TBM thrust is corrected through the cutter head rotating speed influence coefficient, and the influence function of the penetration degree on the FPI index is obtained by eliminating the cutter head rotating speed influence coefficient, so that the calculation formula of the corrected FPI index is obtained. Compared with the measured value, the TBM thrust calculated by the corrected theoretical model in the application has a smaller error, can effectively guide the tunneling construction, and can also provide reliable data for TBM equipment selection; through the FPI index calculation correction, the change of the excavating rock mass condition can be accurately reflected.

Description

Technical Field

[0001] The present invention belongs to the field of underground construction control, and in particular relates to a TBM thrust and FPI index calculation and correction method. Background Art

[0002] With the development and utilization of underground space, TBMs (Transport Bomb Machines) (TBMs) have gradually gained widespread application in hard rock tunnel construction. TBM thrust is a critical parameter. Its theoretical determination is not only valuable for guiding excavation construction but also crucial during the TBM selection phase. Designing the appropriate thrust parameter based on the excavation geology and estimated excavation efficiency is crucial. Failure to do so can result in low excavation efficiency, prolonged construction periods, and significantly increased construction costs. However, most current theoretical models, such as the Colorado School of Mines CSM model, suffer from significant errors due to incomplete considerations or inaccurate analysis. The CSM model, developed by the Colorado School of Mines after extensive rock cutting experiments and engineering analysis, does not consider the influence of cutterhead speed. However, during actual excavation, the cutterhead and rock mass are in relative motion. Rock breaking is achieved through the revolution of the TBM cutterhead, which drives the cutterhead's rotation. TBM cutterhead thrust and torque can also be affected by cutterhead speed. This results in significant discrepancies between previous models and actual values, leading to misjudgments.

[0003] TBM construction is only suitable for hard rock formations and places high demands on excavation geological conditions. Changing geological conditions require real-time assessment. Failure to promptly identify unfavorable geological conditions, such as weak surrounding rock ahead of the tunnel face, can lead to major accidents such as landslides and machine jams. Currently, geological conditions are primarily assessed through geological surveys or geophysical exploration. However, geological surveys often provide only a partial view, making it difficult to make real-time assessments of geological changes. Geophysical exploration, on the other hand, requires significant financial and material resources. Current research suggests that the Field Depth Index (FPI), calculated by dividing the average thrust of a single cutter by its penetration, can eliminate the influence of penetration parameters and thus reflect changes in rock mass conditions in real time, enabling timely assessments. The FPI is the ratio of the average thrust of each cutter to its penetration, representing the force required for the cutter to penetrate 1 mm into the rock. This value increases when the rock mass at the excavation face is strong and well-integrated, and decreases when it is not. However, the actual FPI index is not only related to the geological conditions, but may also be affected by tunneling parameters such as cutterhead speed and penetration rate. It cannot only reflect changes in the excavated rock mass conditions, and therefore urgently needs to be corrected. Summary of the Invention

[0004] In response to the technical problems existing in the background technology, the present invention provides a method for calculating and correcting TBM thrust and FPI indicators. The TBM thrust calculated by the corrected theoretical model in the present invention has a smaller error than the measured value, which can effectively guide tunneling construction. Moreover, more accurate thrust parameters can be designed before excavation based on the excavation geological conditions and the estimated tunneling efficiency, providing reliable data for TBM equipment selection. By calculating and correcting the FPI index, changes in geological conditions can be accurately reflected and timely judgments can be made.

[0005] In order to achieve the above technical objectives, the present invention provides a TBM thrust and FPI index calculation and correction method, which is characterized by specifically comprising the following steps:

[0006] S1. Use ABAQUS / Explicit to establish a three-dimensional analysis model of cutterhead excavation rock mass, achieving a simulation state that is closest to the actual working conditions. Study the effect of cutterhead speed on cutterhead thrust and torque under different excavation rock masses and different penetration conditions.

[0007] S2. Calculate the ratio A of the simulated cutterhead thrust value to the traditional theoretical calculated cutterhead thrust value at different cutterhead speeds, draw a graph of the cutterhead speed and multiple sets of ratio A, and fit the influence coefficient β of different cutterhead speeds on the traditional cutterhead thrust model. ω , that is, the cutter head speed influence coefficient β ω The curve formula is:

[0008] β ω =1.01596×ω 0.08926 ;

[0009] Where: ω represents the influence of the cutter head speed;

[0010] S3. The cutter head speed influence coefficient β obtained in step S2 ω The traditional TBM total thrust model is modified, and the calculation formula of the modified TBM total thrust theoretical model is as follows:

[0011] F=β ω NF n +μG ①

[0012] Where: β ω is the influence coefficient of different cutterhead speeds on the traditional cutterhead thrust model;

[0013] F is the theoretical value of the corrected model of the total thrust of the TBM; N is the total number of hobs;

[0014] F n is the vertical force on a single hob;

[0015] μ is the friction coefficient, the friction coefficient between the rigid material and rock mass is generally 0.3;

[0016] G is the weight of the TBM shield body;

[0017] S4. The cutterhead speed influence coefficient β obtained in the S2 step ω The influence function of the penetration degree on the FPI index is obtained; specifically, first, the FPI index under different tunneling penetration degrees and rock mass strength conditions is respectively divided by the cutterhead speed influence coefficient β ω to eliminate the influence of the cutterhead speed, and the curve function FPI / β ω after eliminating the influence of the cutterhead speed is obtained; then, the curve function FPI / β ω after eliminating the influence of the cutterhead speed is divided by the rock mass compressive strength to obtain a function FPI / (β ω ×σ c ) affected only by the penetration degree; through calculation, the FPI / (β ω ×σ c ) value under different penetration degrees is obtained, and the influence function of only the penetration degree on the FPI index is obtained through fitting with the penetration degree:

[0018] FPI / (β ω ×σ c ) = 0.8874h -0.6728 ②

[0019]

[0020] In the formula: F' is the actual value of the total thrust of the TBM, kN;

[0021] N is the total number of TBM cutters; h is the tunneling penetration degree, mm;

[0022] FPI is the ratio of the average thrust of a single cutter to the tunneling penetration degree;

[0023] σ c is the compressive strength of the rock mass;

[0024] S5. The FPI index correction value FPI' is obtained through the cutterhead speed influence coefficient β ω in the S2 step and the influence function of only the penetration degree on the FPI index 0.8874h -0.6728 in the S4 step, and the calculation formula of the FPI index correction value FPI' is as follows:

[0025] FPI' = FPI / (β ω × 0.8874h -0.6728 ) ④

[0026] and the above formula ③ is substituted into formula ④, and finally the calculation formula of FPI' is as follows:

[0027]

[0028] The further technical scheme of the present application: the cutter disc thrust traditional theory model in the S2 step is calculated according to the following formula:

[0029]

[0030] In the formula, F1 is the traditional theory value of the TBM cutter disc excavation; r is the roller cutter radius;

[0031] F n is the vertical force received by the single roller cutter; T is the blade width of the roller cutter;

[0032] α is the contact angle of the single roller cutter and the rock;

[0033] η is the cutter tip pressure distribution coefficient, the value is -0.2-0.2, the value is larger when the roller cutter is sharp, generally the value is 0.1;

[0034] σ c is the rock compressive strength; σ t is the rock tensile strength;

[0035] N is the total number of the roller cutters; C is a dimensionless coefficient, the value is 2.12.

[0036] S is the cutter tip spacing of the adjacent two roller cutters;

[0037] The further technical scheme of the present application: the TBM total thrust F in the S3 step and the S4 step is the sum of the cutter disc excavation thrust F1 and the friction force F2 of the shield, and the calculation formula is as follows:

[0038] F=F1+F2=F1+μG

[0039] From the above formula, the change of the cutter disc speed does not affect the size of the shield friction force F2, but affects the size of the TBM total thrust through the cutter disc thrust F1, so the friction force F2 of the shield is not considered when calculating the influence of the cutter disc speed on the cutter disc thrust.

[0040] The beneficial effects of the present application are:

[0041] (1) The present application obtains the influence law of the cutter head rotating speed on the cutter head thrust traditional theoretical model by setting various different rock mass properties, different penetration degrees and different cutter head rotating speed excavation numerical simulation, taking the ratio of the cutter head thrust simulation value and the theoretical value obtained by using the traditional model as the target, finding that the ratio basically presents power function growth with the cutter head rotating speed, obtaining the cutter head rotating speed influence function by fitting, and obtaining the corrected theoretical model; comparing the calculation value according to the corrected theoretical model with the measured value, the theoretical calculation result is greatly improved, basically consistent with the actual value, and the error is basically controlled within 10%.

[0042] (2) The present application obtains the influence function of the penetration degree on the FPI index, and after the FPI index is eliminated by the influence function of the cutter head rotating speed and the penetration degree by using the ratio method, only the excavation rock mass condition can be reflected; through theoretical test, under different penetration degrees and cutter head rotating speeds, the corrected FPI index is related to the rock mass compressive strength, and is irrelevant to the cutter head rotating speed and the penetration degree. By comparing with the actual tunnel advanced geological prediction result, it is found that the FPI index obviously increases in the place where the rock mass strength is high and the broken zone is less, and vice versa, which shows that the FPI index can only characterize the real-time geological condition. BRIEF DESCRIPTION OF DRAWINGS

[0043] Figure 1 is a force analysis schematic diagram of a cutter when excavating a rock mass;

[0044] Figure 2 is a CSM model schematic diagram;

[0045] Figure 3-a 、 Figure 3-b and Figure 3-c are comparison schematic diagrams of the theoretical torque value and the actual torque average value of three tunnels in the embodiment according to the traditional method;

[0046] Figure 4-a and Figure 4-b are respectively a single-blade cutter physical model and a numerical model schematic diagram in the embodiment;

[0047] Figure 4-c and Figure 4-d are respectively a double-blade cutter physical model and a numerical model schematic diagram in the embodiment;

[0048] Figure 5-a and Figure 5-b are respectively a cutter head cutter plan view and a solid modeling schematic diagram in the embodiment;

[0049] Figure 6 is a cutter head rotating numerical simulation schematic diagram in the embodiment;

[0050] Figure 7 is a cutter head thrust time history curve comparison diagram of different cutter head rotating speeds in the embodiment;

[0051] Figure 8 3. A comparison diagram of time history curves of cutter head torque at different cutter head speeds in the embodiment;

[0052] Figure 9 : is a fitting curve diagram of the influence coefficient of different cutter head rotation speeds on the cutter head thrust in the embodiment;

[0053] Figure 10-a 、 Figure 10-b and Figure 10-c Schematic diagram showing the comparison between the theoretical torque values ​​calculated according to the revised method and the average actual torque values ​​for the three tunnels in the embodiment;

[0054] Figure 11 Schematic diagram of the ratio curve of the traditional FPI theoretical value and the cutterhead speed influence coefficient in the embodiment;

[0055] Figure 12 Schematic diagram of the ratio curve of the traditional FPI to the rock mass strength after eliminating the influence of the rotation speed in the embodiment;

[0056] Figure 13 Schematic diagram of the effect of the cutter head rotation speed on the corrected FPI in the embodiment;

[0057] Figure 14 Schematic diagram of the effect of penetration on the corrected FPI in the embodiment;

[0058] Figure 15 Schematic diagram showing the comparison between the modified FPI index and the advanced geological prediction in a TBM tunnel in the embodiment. DETAILED DESCRIPTION

[0059] The present invention will be further described below with reference to the accompanying drawings and embodiments. The accompanying drawings are all drawings of the embodiments, which are drawn in a simplified manner and are only used to clearly and concisely illustrate the embodiments of the present invention. The technical solutions shown in the accompanying drawings are specific solutions of the embodiments of the present invention and are not intended to limit the scope of the invention to be protected. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0060] The specific derivation process of the TBM thrust and FPI index calculation and correction method provided in the embodiment is as follows:

[0061] The inventors provide a detailed explanation of the traditional TBM thrust and field depth index (FPI) calculation process, and analyze and verify the existing problems:

[0062] (1) Traditional calculation methods of TBM thrust and torque and their defects

[0063] The cutter is mainly subjected to two forces when excavating rock mass, namely vertical force F n and rolling force F t ,like Figure 1 As shown in the figure, the vertical force and rolling force on each disc cutter are the reasons for the cutter head thrust and cutter head torque. The CSM model is traditionally used for calculation. The CSM model was proposed by the Colorado Institute of Mining after a large number of rock cutting tests and engineering analysis. The schematic diagram of the CSM model is shown in the figure. Figure 2 As shown; the contact stress calculation formula of the CSM model is:

[0064]

[0065] Where: p 0 is the basic pressure in the crushing zone directly below the cutter; α is the contact angle between a single cutter and the rock;

[0066] θ is the angle between a rock breaking point A and the center line of the hob, and its value is 0~α;

[0067] η is the tool tip pressure distribution coefficient, ranging from -0.2 to 0.2. It takes a larger value when the hob is sharp, and is generally 0.1;

[0068] σ c is the compressive strength of rock mass; t is the tensile strength of the rock mass; S is the distance between the tips of two adjacent roller cutters;

[0069] r is the radius of the hob; T is the blade width of the hob;

[0070] h is the penetration depth, mm; the penetration depth h can be calculated by dividing the TBM excavation speed by the cutterhead speed.

[0071] Therefore, the vertical force and rolling force of the cutter are the resultant forces of the contact stress between the cutter and the rock in the axial and tangential directions, respectively:

[0072]

[0073] Where: F n and F t are the vertical force and rolling force on a single hob respectively;

[0074] r is the radius of the hob; T is the blade width of the hob;

[0075] α is the contact angle between a single roller cutter and the rock;

[0076] η is the tool tip pressure distribution coefficient, ranging from -0.2 to 0.2. It takes a larger value when the hob is sharp, and is generally 0.1;

[0077] σ cσ is the compressive strength of rock mass; t σt is the tensile strength of rock mass;

[0078] C is a dimensionless coefficient, and the value is 2.12.

[0079] S is the distance between the cutting edges of two adjacent cutters.

[0080] Considering that the double-shield TBM overcomes the thrust F1 of the cutter head in breaking rock and the friction force F2 of the shield body when excavating in hard rock stratum, the total thrust theoretical calculation formula of the TBM can be obtained as follows:

[0081] F=F1+F2=F1+μG (6)

[0082] In the formula, F1 is the conventional theoretical value of the TBM cutter head excavation; the conventional calculation of the TBM cutter head thrust is mostly determined according to the product of the CSM force calculation result of a single cutter and the number of cutters, that is, F1=NF n ;

[0083] μ is the friction coefficient, and the friction coefficient of the rigid material and the rock mass is generally 0.3; G is the weight of the TBM shield body.

[0084] For the cutter head torque, the main source is the torque of the cutter rolling force on the center of the cutter head, and the calculation formula is shown in formula (7):

[0085]

[0086] In the formula, F t is the rolling force of a single cutter, R i is the installation radius of the i-th cutter.

[0087] However, in actual excavation, the cutter and the rock mass are in a relative motion state, and the cutter is driven to rotate by the revolution of the TBM cutter head to break the rock, and the TBM cutter head thrust and torque may also be affected by the rotation speed of the cutter head, which leads to a large error between the previous model and the actual value.

[0088] Therefore, the inventors of the present application verify the defects of the traditional calculation method of the TBM cutter head thrust:

[0089] In order to verify the applicability of the traditional theoretical model, the inventors of the present application verify the TBM total thrust and cutter head torque parameters of three tunnels of Qingdao subway. In actual engineering, there is a certain interval distance between the drill holes, and there is no accurate rock mass parameter at each position, and meanwhile, due to the unevenness of the geological properties, it is difficult to calculate the total thrust and torque at each position according to the geological survey data. It can be known from formulas (4) and (5) that the same rock mass parameters are contained in the calculation formulas of both. Therefore, the real-time parameters of rock mass can be inversed by using the actual total thrust of TBM Then, the calculated theoretical value is compared with the actual value to verify the applicability of the traditional theoretical model. If the two values are consistent, it is considered that the traditional theoretical model is applicable. If the two values are significantly different, it means that the theoretical model is unreasonable. The calculation formula is shown in formula (8), and the parameters in formula (8) are the same as those in the above formula:

[0090]

[0091] The theoretical torque of the cutter head can be calculated by substituting it into formulas (5) and (7). The comparison between the average actual torque and the theoretical torque of three tunnels is shown in Figure 3-a 、 Figure 3-b and Figure 3-c respectively. Figure 3-a is the comparison curve of the average actual torque and the theoretical torque of the right line of Li-Lao section; Figure 3-b is the comparison curve of the average actual torque and the theoretical torque of the left line of Li-Lao section; Figure 3-c is the comparison curve of the average actual torque and the theoretical torque of the right line of Lao-Zhang section. Figure 3-a 、 Figure 3-b and Figure 3-c It can be found that although the change trend of the theoretical value of the TBM cutter head torque is similar to that of the actual value, the numerical value is significantly different, and most of the errors are more than 20%, with the maximum error reaching 44.26%, indicating that there are still some factors that need to be corrected in the theoretical model. From a theoretical point of view, when the penetration depth of the cutter is constant, the faster the cutter head speed, the higher the efficiency of rock breaking by the cutter, which should lead to changes in dynamic parameters, indicating that the cutter head speed also has an important influence on the theoretical model.

[0092] (2) The traditional calculation method of FPI index and its defects;

[0093] Currently, most studies commonly use the change of the field penetration index FPI to represent the change of the excavation geological conditions. FPI refers to the ratio of the average thrust of a single cutter to the penetration depth, which represents the force required by the cutter to penetrate the rock per unit distance. The traditional theoretical calculation is shown in formula (9).

[0094]

[0095] In the formula, F' is the actual value of the total thrust of TBM, kN;

[0096] N is the total number of TBM cutters, and h is the penetration depth, mm.

[0097] Similarly, the FPI index is determined based on the TBM thrust value, and when the TBM thrust traditional theoretical model is inaccurate, the traditional FPI index calculation is also inaccurate, such as not considering the influence of cutterhead speed, and the traditional FPI index assumes that the cutterhead thrust and the penetration degree are in a linear relationship, so as to directly divide to eliminate the influence of the penetration degree, but the actual situation may not be in a linear relationship, if it is not in a linear relationship, directly dividing is difficult to completely eliminate the influence of the penetration degree, that is, the size of the traditional FPI index is also related to the penetration degree.

[0098] Embodiment one: the traditional cutterhead thrust and torque theoretical model is modified as follows: from equation (6), the change of cutterhead speed does not affect the size of shield friction F2, but affects the size of TBM total thrust through the influence of cutterhead thrust F1, so it is necessary to study the influence of cutterhead speed on cutterhead thrust and cutterhead torque. Field test is difficult to obtain accurate geological parameters, and it is difficult to obtain theoretical calculation value by using traditional model, and it is impossible to accurately modify the model according to the comparison between actual value and theoretical value. Indoor test cannot comprehensively and truly restore the cutterhead structure and excavation state.

[0099] A three-dimensional analysis model of cutterhead excavation rock mass is established by using ABAQUS / Explicit to achieve the most similar simulation state to the actual working condition, and then the influence of cutterhead speed on cutterhead thrust and torque under different excavation rock masses and different penetration degrees is studied.

[0100] (1) Rock mass material parameters: in order to reduce the calculation time and consider the calculation accuracy, the rock mass is selected within 2m around the tunnel and in the excavation direction, the grid elements of the nearby rock mass directly cut are refined, and the grid elements of the remote part are appropriately increased, and the rock mass is divided into 410000 grid elements. According to the simulation needs, three kinds of strength rock masses of 30MPa, 60MPa and 90MPa are set, and the physical and mechanical parameters of each rock mass are set according to the data given in the geological prospecting report, as shown in table 1.

[0101] Table 1 Physical and mechanical parameters of rock mass model

[0102]

[0103] (2) Cutterhead model and parameter setting

[0104] The cutter model of the cutter head is established according to the entity size of the TBM tunnel cutter head in Qingdao subway. The cutter head is arranged with 39 19-inch cutters, 43 cutting edges, a diameter of 482.6 mm, and a cutting edge width of 20 mm. Considering the wear during tunneling, the width is widened to 22 mm during modeling. Among them, 23 are single-edge cutters on the front face, 12 are single-edge cutters on the edge, and 4 are double-edge cutters at the center. When dividing the grid, the grid in direct contact between the cutter and the rock is encrypted, and the remote part is appropriately increased. Each single-edge cutter is divided into 14474 grids, with 0 errors and 19 warning units, accounting for 0.13% of the total number of units; each double-edge cutter is divided into 17713 grids, with 0 error grids and 249 warning units, accounting for 1.41% of the total number of units; the cutter grid type is set to tetrahedron C3D10M. The actual cutter and the model are shown in FIG. 4, wherein Figure 4-a and Figure 4-b are respectively the single-edge cutter actual and numerical model schematic diagram in the example; Figure 4-c and Figure 4-d are respectively the double-edge cutter actual and numerical model schematic diagram in the example.

[0105] The actual cutter head excavation diameter is 6300 mm, and the basic components also include a slag scraping plate and an observation hole structure. In order to save modeling and calculation time, the part that does not affect the rock breaking of the cutter head cutter is omitted during modeling. The 39 cutters are installed on the cutter head according to the given installation radius, azimuth angle and installation inclination angle, etc. Since the cutter head cutter is made of high-strength Q345 steel, the elastic modulus is much larger than the elastic modulus of the rock mass, and the deformation of the cutter head cutter is not the focus of this study, therefore the cutter head cutter is set as a rigid body attribute. The cutter head is divided into 6316 grids, with 0 error grids and 269 warning units, accounting for 4.26% of the total number of units. The plan view of the cutter head is shown in Figure 5-a and the model comparison is shown in FIG. (5-b).

[0106] (3) Cutter head excavation and rock mass interaction setting

[0107] Before the cutter disc rotates to break the rock, all the surfaces of the cutters and the rock mass surface are set to surface-to-surface contact in the interaction module, each surface of the cutters is an active surface, and the surface of the rock mass is a driven surface. The tangential behavior of the contact attribute adopts a penalty contact, and the friction coefficient is 0.2, and the normal behavior adopts a "hard" contact. Since there is a large displacement of the cutter disc relative to the surface of the rock mass during excavation rotation, a finite slip formula is adopted. In the load setting module, the part except the excavation surface is set to a completely fixed mode, and the excavation surface is in a free state. When the cutter disc excavates the rock mass, the cutters penetrate the rock under the action of the disc thrust and cut the rock under the action of the disc rotation. When modeling, this process can be simplified into two parts, one is that the cutters first penetrate the rock, and the other is that the cutters begin to rotate and cut the rock. This paper mainly studies the relationship between the disc thrust and torque and the disc rotation speed in the stable excavation stage, so only the disc thrust and torque when the disc rotates to cut the rock mass under different penetration degrees are studied. When the load is applied, the reference point is set and rigidly constrained with the disc, and the disc rotation load is applied through the reference point, as shown in Figure 6 Fig. 1, the analysis time is set to 20s from the initial analysis step.

[0108] (4) Numerical simulation results: taking the numerical model with a penetration degree of 10mm, a rock mass strength of 30MPa, a disc rotation speed of 1r / min, 3r / min and 6r / min as an example, the time history curves of the disc thrust and torque are shown in Figure 7 and Figure 8 respectively. The average values of the disc thrust and torque are calculated, and the results are shown in Table 2.

[0109] Table 2 Numerical simulation results of the average values of the disc thrust and torque

[0110]

[0111] According to the numerical simulation results, the rotation speed has a significant effect on the disc thrust, the higher the disc rotation speed, the greater the thrust F1, and it also has an effect on the torque, but the effect is small and can be ignored. Therefore, the disc thrust theoretical calculation model needs to be modified with respect to the disc rotation speed, and the original calculation model is still used for the disc torque.

[0112] Using numerical simulation, 96 groups of numerical simulation are set with rock mass properties of 30MPa, 60MPa and 90MPa, penetration degrees of 10mm, 15mm, 20mm and 25mm, and disc rotation speeds of 1r / min-8r / min. The ratio of the disc thrust simulation value to the traditional theoretical calculation value F1 of the disc thrust is taken as the target to analyze the influence law of the disc rotation speed on the traditional theoretical model of the disc thrust. The traditional theoretical calculation value of the disc thrust is calculated according to the following formula:

[0113] F1=NF n

[0114]

[0115] Where: F1 is the traditional theoretical value of the excavation load on the TBM cutterhead; r is the cutter radius;

[0116] F n is the vertical force on a single hob; T is the blade width of the hob;

[0117] α is the contact angle between a single roller cutter and the rock;

[0118] η is the tool tip pressure distribution coefficient, ranging from -0.2 to 0.2. It takes a larger value when the hob is sharp, and is generally 0.1;

[0119] σ c is the compressive strength of rock mass; t is the tensile strength of rock mass;

[0120] N is the total number of hobs; C is the dimensionless coefficient, which is 2.12.

[0121] α is the contact angle between any roller cutter and the rock;

[0122] S is the distance between the cutting edges of two adjacent hobs.

[0123] The simulated values ​​of the cutterhead thrust of the above 96 simulation tests and the traditional theoretical calculated values ​​of the cutterhead thrust are shown in Table 3 below.

[0124] Table 3 Simulated and theoretical calculated values ​​of cutterhead thrust

[0125]

[0126]

[0127] The ratio of the cutterhead thrust simulation value to the traditional theoretical calculated value is plotted as a scatter plot according to different cutterhead speeds. Figure 9 As shown in the figure, it can be seen that as the cutter head speed increases, the ratio increases, but the rate of increase gradually slows down. After fitting, the ratio of the two basically shows a power function growth with the cutter head speed.

[0128] Therefore, the modified theoretical model of TBM actual thrust can be set as shown in the following equations (10) and (11):

[0129] F=β ω NF n +μG (10)

[0130] β ω =1.01596×ω 0.08926 (11)

[0131] Where: β ωThe influence coefficient of different cutterhead rotating speed on cutterhead thrust.

[0132] The inventor of the present application verifies the application effect of the above modified model, as follows: the real-time parameters of the rock mass are calculated according to the modified thrust model Then, the theoretical value is compared with the actual value by substituting it into the torque theoretical calculation formula, The calculation is shown in formula (12).

[0133]

[0134] The theoretical cutterhead torque can be calculated by substituting it into formula (5) and (7). The comparison between the actual torque value and the theoretical torque value of the three tunnels after calculation is shown in Figure 10-a 、 Figure 10-b and Figure 10-c From Figure 10-a 、 Figure 10-b and Figure 10-c , it can be seen that after the modification of the cutterhead thrust theoretical model, the cutterhead torque theoretical calculation result has been greatly improved, and is basically consistent with the actual value, with the relative error basically controlled within 10%. It is considered that the modified cutterhead thrust theoretical calculation value meets the engineering requirements.

[0135] Example Two: Modification of the Traditional FPI Index Theoretical Model

[0136] (1) Elimination of the influence function of cutterhead rotating speed and penetration by using the ratio method

[0137] The cutterhead rotating speed, penetration and rock mass condition all have an influence on the traditional FPI index, and the cutterhead rotating speed influence coefficient has been obtained. In order to make the FPI index only reflect the change of the rock mass condition, the influence function of the penetration on the FPI index needs to be derived. In order to make the modified geological index be able to characterize the geological conditions and not be disturbed by other factors, the influence of the cutterhead rotating speed and the penetration change needs to be eliminated. From formula (9) and formula (10) in Example One, it can be seen that the influence of the cutterhead rotating speed can be eliminated by making the FPI index and the cutterhead rotating speed influence coefficient into a ratio, and after the elimination, it is shown in Figure 11 After the elimination of the cutterhead rotating speed influence coefficient, the FPI / β ω is only related to the rock mass condition and the penetration. However, when eliminating the influence of the penetration, it is not easy to find the function relationship between the FPI index and the penetration, so the formula after the elimination of the influence of the cutterhead rotating speed is made into a ratio with the rock mass compressive strength, and the influence of the penetration is derived, which is shown in Figure 12 Finally, the influence function of the penetration is eliminated by using the ratio method. From Figure 12 , it can be seen that after the elimination of the rock mass compressive strength, the curves of different strengths coincide, that is, the FPI / (β ω ×σc ) becomes a curve affected only by penetration, and the fitting function of its value and penetration is shown in formula (13):

[0138] FPI / (β ω ×σ c )=0.8874h -0.6728 (13)

[0139] Therefore, the traditional FPI index can only reflect the excavation rock mass condition after eliminating the influence function of cutterhead speed and penetration using the ratio method. This process is based on the TBM thrust theory model to correct the influence of cutterhead speed and penetration on FPI. The value is theoretically equal to the rock mass strength value, but when applied, the thrust measurement value can be used for real-time calculation. By eliminating the influence coefficient β of cutterhead speed from the FPI index, the ω And the impact function of penetration only on FPI index is 0.8874h -0.6728 , the calculation formula for the revised value FPI' of the FPI indicator is as follows:

[0140] FPI'=FPI / (β ω ×0.8874h -0.6728 ) (14)

[0141] Substituting formula (9) into formula (14), the final calculation formula for FPI' is as follows:

[0142]

[0143] The factors affecting the cutterhead speed and penetration rate of the modified value FPI' of the FPI index in Example 2 are tested as follows:

[0144] The influencing factors of the modified value FPI' of the FPI index were tested. When the rock mass strength was set to 30, 60, and 90 MPa, the modified FPI index FPI' of different cutterhead speeds and penetrations was calculated. The influence of cutterhead speed and penetration on the modified FPI index FPI' was studied. Figure 13 and Figure 14 As shown in Figure 2, the modified FPI index FPI' is only related to the rock mass conditions, but has nothing to do with the changes in cutterhead speed and penetration rate, that is, the influence of cutterhead speed and penetration rate has been eliminated.

[0145] The verification of the modified FPI index FPI' model in Example 2 is as follows: the excavation parameters of a TBM tunnel in Qingdao Metro are used to calculate the modified FPI index FPI', and the modified FPI index FPI' is compared with the advanced geological forecast. Figure 15 As shown. Figure 15It can be seen that the change of the modified FPI index FPI' is basically similar to the change of the superposition geological prediction, that is, the FPI index FPI' increases in the stratum with high strength, and the FPI index FPI' obviously decreases in the stratum with low strength and fracture, which conforms to the actual situation and can represent the change of the excavation geological condition.

[0146] The tunnel superposition geological prediction system TST (Tunnel Seismic Tomography) technology generates seismic waves by using an electric spark or an impact seismic source, and receives the seismic waves by a geophone, and the excitation and receiving devices are installed on both sides of the tunnel surrounding rock far away from the working face, and are in contact with the surrounding rock through the segment hole. The TST technology can simultaneously provide the wave velocity and the geological interface position image of the surrounding rock in front of the working face, the wave velocity provides the basis for the high and low strength of the rock mass and the engineering classification, and the geological interface is used for the interpretation of the completeness of the surrounding rock. As shown in the figure, the horizontal line represents the propagation velocity of the wave, the high wave velocity represents the higher strength of the rock mass, and the staggered strips represent the geological joints and fractures, and the more staggered strips indicate that the stratum is more broken.

[0147] The present application sets 30MPa, 60MPa, 90MPa three kinds of rock mass properties, 10mm, 15mm, 20mm, 25mm four kinds of penetration, 1r / min-8r / min eight kinds of cutter head rotating speed, a total of 96 groups of cutter head excavation numerical simulation, taking the ratio of the cutter head thrust simulation value and the theoretical value obtained by using the traditional model as the target, the influence law of the cutter head rotating speed on the cutter head thrust traditional theoretical model is obtained, it is found that the ratio of the two increases with the cutter head rotating speed basically presents a power function, the cutter head rotating speed influence function is obtained by fitting, and the modified theoretical model is obtained. The calculated value according to the modified theoretical model is compared with the measured value, the theoretical calculation result is greatly improved, and is basically consistent with the actual value, and the error is basically controlled within 10%.

[0148] Meanwhile, the present application studies the influence function of the penetration on the modified FPI index FPI', and the modified FPI index FPI' is eliminated by using the ratio method to eliminate the influence function of the cutter head rotating speed and the penetration, so that only the excavation rock mass condition can be reflected. Through testing, under different penetrations and cutter head rotating speeds, the modified FPI index FPI' is only related to the rock mass condition. By comparing with the actual tunnel superposition geological prediction result, it is found that the modified FPI index FPI' obviously increases in the stratum with high rock mass strength, and vice versa, which shows that the modified FPI index FPI' can only represent the real-time rock mass condition.

Claims

1. A TBM thrust and FPI index calculation and correction method, characterized in that: The specific steps include: S1. Use ABAQUS / Explicit to establish a three-dimensional analysis model of cutterhead excavation rock mass, achieving a simulation state that is closest to the actual working conditions. Study the effect of cutterhead speed on cutterhead thrust and torque under different excavation rock masses and different penetration conditions. S2. Calculate the ratio A of the simulated cutterhead thrust value to the traditional theoretical calculated cutterhead thrust value at different cutterhead speeds, draw a graph of the cutterhead speed and multiple sets of ratio A, and fit the influence coefficient β of different cutterhead speeds on the traditional cutterhead thrust model. ω , that is, the cutter head speed influence coefficient β ω The curve formula is: b ω =1.01596×ω 0.08926 ; Where: ω represents the influence of the cutter head speed; S3. The cutter head speed influence coefficient β obtained in step S2 ω The traditional TBM total thrust model is modified, and the calculation formula of the modified TBM total thrust theoretical model is as follows: F=β ω NF n +μG① Where: β ω is the influence coefficient of different cutterhead speeds on the traditional cutterhead thrust model; F is the theoretical value of the corrected model of the total thrust of the TBM; N is the total number of hobs; F n is the vertical force on a single hob; μ is the friction coefficient, and the friction coefficient between the rigid material and the rock mass is generally taken as 0.3; G is the weight of the TBM shield; S4. The cutter head speed influence coefficient β obtained in step S2 ω The influence function of penetration on FPI index is obtained; specifically, the FPI index under different excavation penetration and rock strength conditions is firstly combined with the cutter head speed influence coefficient β ω Make a ratio to eliminate the influence of the cutter head speed, and get the curve function FPI / β after eliminating the influence of the cutter head speed ω ; Then eliminate the influence of cutter head speed curve function FPI / β ω Comparing with the rock mass compressive strength, we can get the function FPI / (β ω ×σ c ); The FPI / (β ω ×σ c ) value, and fitted with the penetration to obtain the impact function of only the penetration on the FPI index: FPI / (β ω ×s c )=0.8874h -0.6728 ② Where: F' is the actual value of the total thrust of the TBM, kN; N is the total number of TBM cutters; h is the tunnel penetration, mm; FPI is the ratio of the average thrust of a single disc cutter to the penetration rate; σ c is the compressive strength of rock mass; S5. Eliminate the cutterhead speed influence coefficient β in step S2 by adjusting the FPI index ω And the impact function of only penetration on FPI index in step S4 is 0.8874h -0.6728 , the calculation formula for the revised value FPI' of the FPI indicator is as follows: FPI’=FPI / (β ω ×0.8874h -0.6728 ) ④ Substituting the above formula ③ into formula ④, the final calculation formula for FPI' is as follows:

2. A TBM thrust and FPI index calculation and correction method according to claim 1, characterized in that: The traditional theoretical model of the cutterhead thrust in step S2 is calculated according to the following formula: F1=NF n Where: F1 is the traditional theoretical value of the excavation load on the TBM cutterhead; r is the cutter radius; F n is the vertical force on a single hob; T is the blade width of the hob; α is the contact angle between a single roller cutter and the rock; η is the tool tip pressure distribution coefficient, ranging from -0.2 to 0.

2. It takes a larger value when the hob is sharp, and is generally 0.1; σ c is the compressive strength of rock mass; σ t is the tensile strength of rock mass; N is the total number of hobs; C is the dimensionless coefficient, which is 2.12; S is the distance between the cutting edges of two adjacent hobs.

3. A TBM thrust and FPI index calculation and correction method according to claim 1, characterized in that: The total thrust F of the TBM in steps S3 and S4 is the sum of the thrust F1 exerted by the TBM cutterhead during excavation and the friction F2 of the shield. The calculation formula is as follows: F=F1+F2=F1+μG As can be seen from the above formula, changes in the cutterhead speed do not affect the magnitude of the shield friction force F2. Instead, they affect the total TBM thrust by affecting the cutterhead thrust F1. Therefore, the shield friction force F2 is not considered when calculating the effect of the cutterhead speed on the cutterhead thrust.

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