A method for calculating tunnel surrounding rock loose circle associated with USC and H-B criterion

Abstract

The application discloses a tunnel surrounding rock loose circle calculation method associated with USC and H-B criteria, and comprises the following steps: S1. associating the strength criteria of USC and H-B; S2. selecting the parameters of the associated criteria; and S3. establishing a tunnel surrounding rock loose circle calculation model. The application aims at the deficiencies of the three commonly used rock mass strength criteria, namely, M-C criterion, H-B criterion and USC, in the current theoretical calculation model of the tunnel surrounding rock loose circle, and proposes a tunnel surrounding rock loose circle calculation model associated with USC and H-B criteria, which can fully utilize the advantages of the three models. The model fully considers the actual geological characteristics of the rock mass and well considers the influence of the intermediate principal stress.

Description

Technical Field

[0001] This invention belongs to the field of tunnel engineering technology, specifically relating to a method for calculating the loosened zone of tunnel surrounding rock based on the USC and HB criteria. Background Technology

[0002] Tunnel excavation (often referred to as roadway in the mining industry) disrupts the original stress equilibrium of the surrounding rock, generating secondary or tertiary stress fields. When the adjusted surrounding rock stress exceeds the tensile or shear strength of the rock, the surrounding rock will fail, leading to the formation of a circumferential fracture zone around the tunnel, also known as the loosened zone. The proper determination of the loosened zone's extent is of significant theoretical and practical engineering importance for evaluating tunnel surrounding rock stability and designing support structures, thus attracting widespread attention from scholars. Research methods for the loosened zone mainly include three types: field or experimental testing, numerical simulation, and theoretical calculation. Theoretical calculation methods are widely used due to their relative convenience and universality. Liu Gang et al. further categorized theoretical methods into the strength criterion method and the mathematical model method. The former, primarily based on Kastner's elastoplastic theory of circular tunnel surrounding rock, provides a calculation model for the loosened zone and has become the theoretical foundation for research on the loosened zone of tunnel surrounding rock. However, this theory follows the following assumptions: the self-weight of the rock mass is not considered; the rock is an isotropic homogeneous body that obeys the Mohr-Coulomb (MC) strength criterion and an ideal elastoplastic model; and the support force is constant. However, as research has progressed, many scholars have argued that these assumptions do not quite match reality and have made numerous improvements to them.

[0003] The calculation results of the loosened zone of the surrounding rock are closely related to the strength criterion used. Due to the wide variety of rock types and complex mechanical properties, many strength criteria have been proposed for different rock types and various complex stress states. Bahrami et al. compared the advantages and disadvantages of 15 common strength criteria and classified them into three categories: biaxial strength criteria, triaxial strength criteria, and unified strength criteria. Biaxial strength criteria mainly include the commonly used MC and Hoek-Brown (HB) criteria. Their biggest drawback is that they do not consider the influence of intermediate principal stresses, while triaxial strength criteria such as the Drucker-Prager (DP) criterion effectively compensate for this deficiency. Unified strength criteria are usually a combination of multiple strength criteria. The most representative is the Unified Strength Criterion (USC) proposed by Yu Maohong et al., which not only considers the influence of intermediate principal stresses well but also allows for the adjustment of certain key parameters to cover other strength criteria.

[0004] Numerous scholars have conducted in-depth studies on the loosened zone of tunnel surrounding rock using various rock strength criteria. Their research generally concludes that different rock strength criteria lead to different calculation results, making the selection of an appropriate criterion crucial. However, the conclusions of different scholars are not entirely consistent. For example, Jing Laiwang et al., Chen Qiunan et al., and Su Shilong et al. respectively believe that calculation results based on the Mogi-Coulomb criterion, HB criterion, and USC are better. This may be related to the rock type and its geological and mechanical environment, as well as the reasonable selection of calculation parameters. For instance, the MC criterion, DP criterion, and USC typically treat the actual rock mass as a homogeneous continuum, while actual engineering rock masses are fractured. Therefore, it is necessary to convert the physical and mechanical parameters obtained from rock block tests into actual rock mass mechanical parameters before calculations can be performed based on the aforementioned rock strength criteria, inevitably leading to significant errors. In contrast, the HB criterion can fully consider the geological characteristics of the rock mass, such as rock mass quality and geological structure, as well as the damage caused to the surrounding rock by tunnel construction factors (such as drilling and blasting), thus potentially yielding calculation results that are more consistent with reality. However, on the other hand, while more model parameters can more comprehensively consider the actual characteristics of the rock mass, they also increase the difficulty of selecting appropriate parameters. Summary of the Invention

[0005] To address the aforementioned issues, embodiments of the present invention propose a method for calculating the loosened zone of tunnel surrounding rock by associating the USC and HB criteria.

[0006] The method for calculating the loosened zone of tunnel surrounding rock based on the associated USC and HB criteria of the present invention includes the following steps:

[0007] S1. Strength criterion for linking USC and HB;

[0008] S2. Selection of correlation criterion parameters;

[0009] S3. Establish a calculation model for the loosened zone of the surrounding rock in the tunnel.

[0010] The strength criterion for the association between USC and HB refers to establishing the association between the two through parameter transformation.

[0011] The parameter transformation refers to first establishing the parameter transformation relationship between the HB criterion and the MC criterion, as well as the parameter transformation relationship between the USC criterion and the MC criterion, and finally establishing the relationship between the USC criterion and the HB criterion using the MC criterion as a medium.

[0012] The parameter conversion relationship between the USC and MC criteria is as follows:

[0013]

[0014] In the formula: , These are the maximum and minimum principal stresses, respectively, c t φ t These are the equivalent cohesion and the equivalent internal friction angle, respectively. , c and φ are the rock cohesion and internal friction angle, respectively, and b (=0~1) is the intermediate principal stress coefficient. When b=0 and 1, this criterion corresponds to the MC criterion and the double shear strength criterion, respectively.

[0015] The parameter conversion relationship between the HB criterion and the MC criterion is as follows:

[0016]

[0017] In the formula: a is an empirical parameter reflecting the characteristics of the rock mass, m b As an empirical parameter reflecting the characteristics of the rock mass, s reflects the degree of rock mass fragmentation, with a value range of 0.0 (fragmented rock mass) to 1.0 (intact rock mass). The uniaxial compressive strength of intact rock. For deeply buried chambers,

[0018] Where γ is the rock mass and H is the tunnel depth.

[0019] The parameters for the association criterion include m. b The four parameters are m, s, a, and D. i The GSI and D basic parameters are calculated.

[0020] The damage to the rock mass caused by construction disturbances such as blasting and excavation is quantified by the change in longitudinal wave velocity in the rock mass before and after blasting.

[0021]

[0022] In the formula: V pd V pi These represent the longitudinal wave velocities before and after rock mass disturbance.

[0023] The calculation model for the loosened zone of the surrounding rock in a tunnel substitutes the parameters sinφ and c, which are related to the USC and HB criteria, into the radius r of the loosened zone of the surrounding rock in a circular tunnel under a non-uniform stress field. b It is obtained from the calculation formula.

[0024] The parameter sinφ that relates the USC and HB criteria is:

[0025]

[0026] The parameter c value for relating the USC and HB criteria is:

[0027]

[0028] In the formula, c and φ are the rock cohesion and internal friction angle, respectively, and b (=0~1) is the intermediate principal stress coefficient.

[0029] The radius r of the loosened zone of the surrounding rock of the circular tunnel under a non-uniform stress field. b The calculation formula is:

[0030]

[0031] In the formula: r0 is the tunnel radius, p s The supporting force acting on the tunnel wall is p0, which is the vertical ground stress (generally including the rock mass self-weight stress and tectonic stress), λ is the lateral pressure coefficient, θ is the polar angle, and c is the vertical ground stress (generally including the rock mass self-weight stress and tectonic stress). t φ t Let be the equivalent cohesion and the angle of internal friction, respectively, and their expressions are as follows: , c and φ are the rock cohesion and internal friction angle, respectively.

[0032] The beneficial effects of this invention are:

[0033] (1) In view of the shortcomings of the three rock mass strength criteria commonly used in the current theoretical calculation model of the loosening zone of tunnel surrounding rock, namely MC criterion, HB criterion and USC, a calculation model of the loosening zone of tunnel surrounding rock with the correlation of USC and HB criteria is proposed. This model fully considers the actual geological characteristics of the rock mass and also takes into account the influence of the intermediate principal stress.

[0034] (2) By utilizing the relationship between the HB criterion and the MC criterion, as well as the relationship between the USC and the MC criterion, the connection between the criterion and the USC was established, namely the strength criterion that links the USC and the HB, and the reasonable selection of its calculation parameters was studied in depth.

[0035] (3) The strength criteria relating USC and HB were substituted into the calculation model of the loosened zone of tunnel surrounding rock based on the ideal elastoplastic theory, and an improved calculation model of the loosened zone of tunnel surrounding rock was established. The model was then compared with the field measurement results of a tunnel project, and it was found that the two were in good agreement. Subsequently, parameter sensitivity analysis was used to study the main relevant parameters such as m. i The influence of GSI, D, and b on the calculation results of the loosened zone of surrounding rock was investigated. It was found that as m... i As GSI and b increase, the relative radius of the loosened zone of the surrounding rock decreases, while as D increases, the relative radius of the loosened zone of the surrounding rock increases. Attached Figure Description

[0036] Figure 1 It is the σ1-σ3 plane area equivalence method.

[0037] Figure 2 It is the relationship between the three intensity criteria.

[0038] Figure 3 It is the plastic zone and stress distribution of the surrounding rock of a circular tunnel.

[0039] Figure 4 It is a comparison between the calculated results of the loosened zone of the surrounding rock in the tunnel and the measured values.

[0040] Figure 5 It is m i Impact on the range of tunnel loosening zone.

[0041] Figure 6 This refers to the impact of GSI on the range of the tunnel loosening zone.

[0042] Figure 7 This refers to the influence of D on the range of the tunnel loosening zone.

[0043] Figure 8 This refers to the impact of b on the range of the tunnel loosening zone. Detailed Implementation

[0044] Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0045] The method for calculating the loosened zone of tunnel surrounding rock based on the associated USC and HB criteria of the present invention includes the following steps:

[0046] S1. Strength criteria for linking USC and HB;

[0047] For plane strain problems, Yu Maohong et al. gave the USC formula expressed in the form of the MC criterion, namely:

[0048] (1)

[0049] , (2)

[0050] In the formula: c and φ are the rock cohesion and internal friction angle, respectively, and b (=0~1) is the intermediate principal stress coefficient. When b=0 and 1, the criterion corresponds to the MC criterion and the double shear strength criterion, respectively.

[0051] Hoek et al. proposed that within a certain minimum principal stress range, based on, as... Figure 1The two criteria shown have equal coverage areas, thus revealing the parameter transformation relationship between the HB and MC criteria:

[0052] (3)

[0053] In the formula: σ c The uniaxial compressive strength of intact rock; ,

[0054] For deeply buried chambers,

[0055]

[0056] In the formula, γ is the rock mass weight and H is the tunnel burial depth.

[0057] The interrelationships of the three strength criteria, MC, HB, and USC, are as follows: Figure 2 As shown, it can be seen that both the HB criterion and the USC criterion have established a parameter transformation relationship with the MC criterion. Therefore, the relationship between the USC criterion and the HB criterion can be established by using the MC criterion as a medium. That is, by substituting equation (3) into equation (2) and then into equation (1), the strength criterion associated with the USC criterion and the HB criterion can be obtained. This criterion can take into account the influence of the intermediate principal stress and can also take into account the geological characteristics of the actual rock mass. Therefore, it is more suitable for actual rock mass engineering.

[0058] S2. Selection of correlation criterion parameters;

[0059] The applicability of the USC-HB correlation criterion is closely related to the rationality of its parameter selection. Its main parameters remain the three key parameters of the HB criterion. Taking the latest 2018 version of the HB criterion as an example, these mainly include: m b The four parameters, s, a, and D, can be derived from m. i The three basic parameters, GSI and D, are calculated.

[0060] First, regarding m i Many scholars have studied the value of m from test results of uniaxial / triaxial compression and direct / indirect tension of rocks. i The simplest and easiest-to-use methods are:

[0061] (1) Uniaxial compression test and direct tensile test

[0062] From uniaxial compressive strength σ c and direct tensile strength σ t We can obtain:

[0063] (4)

[0064] Strength is positively expressed as pressure (the same applies below).

[0065] (2) Uniaxial compression test and indirect tensile test

[0066] From uniaxial compressive strength σ c and indirect tensile strength σ tb We can obtain:

[0067] (5)

[0068] Secondly, regarding the value of GSI, Su Yonghua et al. introduced the block size index and the absolute weathering index of rock to quantitatively describe the structure and weathering status of the rock mass, and thus established a quantitative evaluation method for GSI, which greatly reduced the influence of human factors and is worth learning from.

[0069] Finally, regarding the value of D, in the field of engineering blasting, the change in longitudinal wave velocity in the rock mass before and after blasting is commonly used to quantitatively evaluate the damage caused to the rock mass by blasting, that is:

[0070] (6)

[0071] In the formula: V pd V pi These represent the longitudinal wave velocities before and after rock mass disturbance.

[0072] S3. Establish a calculation model for the loosened zone of the surrounding rock in the tunnel.

[0073] Currently, the classic theoretical calculation models for the plastic zone of tunnel surrounding rock are all based on circular tunnels and are obtained by using the rock-based MC criterion and ideal elastic-plastic model. Therefore, the theoretical model will be introduced first below.

[0074] Since actual tunnels are generally linear engineering projects, they can be simplified into a plane strain problem. Furthermore, since the initial ground stress is generally non-hydrostatic pressure, a method such as... Figure 3 The calculation model shown assumes that the surrounding rock of a circular tunnel is an isotropic homogeneous material. After tunnel excavation, a plastic zone, an elastic zone, and a pre-existing rock stress zone will sequentially form in the surrounding rock mass. The plastic zone can be further subdivided into a loosened zone and a general plastic zone (the outer ring of the plastic zone). According to the definition of the loosened zone of tunnel surrounding rock, that is, the circumferential normal stress σ of the surrounding rock at the boundary of the loosened zone... θ The initial horizontal ground stress (1+λ)p0 is equal to this. Based on this, the radius r of the loosened zone of the surrounding rock of a circular tunnel under a non-uniform stress field was obtained through research. b for:

[0075] (7)

[0076] In the formula: r0 is the tunnel radius, p sp0 is the support force acting on the inner wall of the tunnel (generally including the rock mass self-weight stress and tectonic stress), λ is the lateral pressure coefficient, and θ is the polar angle.

[0077] As mentioned earlier, sinφ in equation (7) t and c t As shown in equation (2). When the strength criterion for the correlation between USC and HB proposed in this application is adopted, sinφ in equation (2) is:

[0078] (8)

[0079] Substituting equation (8) into equation (9) below, we can find the value of c in equation (7):

[0080] (9)

[0081] Therefore, by substituting equations (8) to (9) into equation (7), we can obtain the formula for calculating the radius of the loosened zone of the surrounding rock of a circular tunnel that is related to the USC and HB criteria, which is the calculation model of the loosened zone of the surrounding rock of a circular tunnel.

[0082] Example

[0083] 1. Project Overview and Calculation Analysis of the Loosening Zone of Surrounding Rock

[0084] Taking the Xiaoxiangling Tunnel of the EMZQ-9 section of the Chengdu-Kunming Railway Expansion Project as an example, this study examines the tunnel located in Liangshan Yi Autonomous Prefecture, Sichuan Province. The tunnel spans from DK345+400 to DK367+175, with a total length of 21.775 km and a maximum burial depth of approximately 1350 m. It is a single-bore, double-track tunnel, classified as a Class I high-risk tunnel, constructed using smooth blasting technology. The tunnel traverses primarily sandstone strata of the Upper Triassic Baiguowan Formation, characterized by a gently dipping, medium-thick, hard rock interbedded with thin layers of soft rock. Joints are predominantly micro-tensional, and the rock mass is weakly weathered. To investigate the causes of large deformations in the surrounding rock during tunnel construction and to provide a basis for optimizing the support structure, a section at DK346+506, 24 m from the tunnel face (e.g., ...), was analyzed. Figure 4 As shown, a loosening zone test of the surrounding rock was conducted. The tunnel is buried at a depth of 310m. The surrounding rock strata are relatively homogeneous, mainly sandstone, and the structural differences are relatively small.

[0085] Since this test aims to determine the extent of the loosened zone in the undisturbed surrounding rock, it was conducted before tunnel support was installed. Therefore, the support force p... s It is 0. Press Figure 4 The diagram shows seven test holes (S1-S7), each with a diameter of 50 mm. A single-hole, single-transmitter, dual-receiver acoustic wave testing method was used, and the test results are as shown. Figure 4As shown, the loosened zone ranges of the surrounding rock at the seven boreholes are 1.68m, 1.70m, 1.50m, 1.45m, 1.60m, 1.62m, and 2.53m, respectively. The deformation moduli of the rock mass measured through horizontal boreholes along the sidewall were 7.05GPa in the vertical direction and 9.55GPa in the direction along the tunnel axis, with an average of 8.30GPa. The uniaxial compressive strength of the rock ranged from 16.5 to 60.96 MPa, with an average of 37.24 MPa. The cohesion c0 and internal friction angle φ0 were 2.0 MPa and 50°, respectively. In-situ stress tests were conducted on three boreholes using hydraulic fracturing. The major principal stresses of ZK1, ZK2, and ZK3 were 10.84–13.10 MPa, 10.80–13.31 MPa, and 16.0–17.0 MPa, respectively, while the minor principal stresses were 6.25–7.91 MPa, 5.71–8.08 MPa, and 8.70–9.50 MPa, respectively. Therefore, the pressure coefficients λ were 1.66–1.73, 1.64–1.89, and 1.79–1.84, respectively, and their average value of 1.76 can be taken.

[0086] The method proposed in this application is used to calculate the range of the loosened zone of the surrounding rock in the tunnel, and the results are compared and analyzed with those obtained from actual measurements. Since the selection of calculation parameters has a significant impact on the calculation results, the values ​​of the main calculation parameters are first studied based on the project overview and relevant research findings.

[0087] ①Tunnel radius r0

[0088] Tunnel cross-section as Figure 4 As shown, the tunnel has an approximate horseshoe-shaped cross-section. Based on the method of the radius of the arch in the equivalent circle method and the 1 / 4 method of the sum of the height and span of the tunnel, the equivalent circle radii of the tunnel cross-section can be calculated to be 6.85m and 6.45m, respectively. Therefore, we take the average value of 6.65m here.

[0089] ②m i

[0090] Zheng Xing et al. used an RMT-150C rock mechanics testing machine to measure the average uniaxial compressive strength of saturated specimens as 37.24 MPa, but did not provide its tensile strength. Therefore, the tensile strength can only be determined based on the rock mass conditions. i Selection of the value. Since the rock mass in this project is medium-thick layered sandstone with weak weathering, the selection is based on the judgment criteria proposed by Hoek et al., m... i The value should be 19.

[0091] ③GSI

[0092] Using the method proposed by Su Yonghua et al., the rock mass blockiness index (RBI) and the absolute weathering index (AWI) were used to quantify the gas density index (GSI). First, a relationship between RBI and the rock mass deformation modulus E0 was established: E0 = 4.028 + 0.45RBI. Substituting E0 = 8.30 GPa, we get RBI = 9.49, corresponding to rock mass characteristics of poor integrity and jointed structure, which are consistent with actual rock mass characteristics.

[0093] Based on the AWI description table of rock mass weathering given by Su Yonghua et al. and combined with the actual situation of the rock mass in this project, the rock mass is in a weak weathering state, i.e., AWI = 0.75~0.55. Therefore, it can be approximated as 0.70.

[0094] Based on RBI=9.49 and AWI=0.70, the quantitative description table of rock mass geological strength index GSI given by Su Yonghua et al. shows that GSI≈49.

[0095] ④ Damage parameter D

[0096] Currently, acoustic wave testing is commonly used to test surrounding rock damage. Through field testing, the average longitudinal wave velocities of loosened and intact rock masses were measured as follows: v s =2870m / s and v0=3896m / s, then from equation (6), we can get the damage D=0.457.

[0097] ⑤ Intermediate principal stress coefficient b

[0098] As mentioned earlier, different values ​​of b can clearly reflect the influence of the intermediate principal stress. Based on the stability analysis of the underground chamber group, Li Yuan suggested that the value of b be 0.33.

[0099] ⑥m b s and a

[0100] According to the parameter calculation method of the 2018 version of the HB criterion in Table 1, we can obtain: m b =1.79, s=0.00125 and a=0.506.

[0101] Based on the above analysis, the calculation parameters are given in Table 1. Substituting these parameters into equation (7) yields the calculation results of the loosened zone of the surrounding rock in the tunnel. Figure 4 As shown, it can be seen that: ① The ranges of the loosened rock zone at the seven measuring points S1 to S7, calculated by the method of this application, are 1.69m, 1.71m, 1.55m, 1.50m, 2.04m, 2.06m, and 3.46m, respectively, with an average thickness of 2m. However, the average thickness of the loosened rock zone measured at the seven measuring points is 1.73m, meaning the calculated value is 13.5% larger than the measured value. Figure 4It can be seen that the largest calculation error occurs at point S7. Analysis suggests this is mainly because the theoretical calculations in this paper did not consider the self-weight of the surrounding rock, leading to an overestimation of the loosened rock zone at the tunnel bottom. In actual engineering, due to the influence of the surrounding rock's self-weight, a large plastic zone is less likely to form at the tunnel bottom compared to the tunnel top. However, overall, the calculation results are relatively consistent, indicating that the proposed method for calculating the loosened rock zone is reasonable. ② Comparing the calculated and measured values ​​at different locations, the test results from boreholes S1-S4 show the best agreement, followed by boreholes S5-S6, while borehole S7 has the largest error. This is because the loosened rock zone in actual tunnels is influenced by many factors, such as the non-uniformity of the rock mass structure and the rock mass's self-weight. Theoretical calculation methods typically do not consider the spatial differences in the rock mass within the study area and often ignore the influence of the rock mass's self-weight, inevitably leading to some discrepancies between the calculated and measured results. Moreover, theoretical calculation methods usually treat tunnels as equivalent to a circle, while actual tunnels are approximately straight-walled arches. Therefore, they fail to consider the impact of stress concentration caused by changes in tunnel structure on the loosening zone of the surrounding rock.

[0102] Table 1 Calculation Parameter Table

[0103]

[0104] 2. Parameter sensitivity analysis

[0105] Since this application links the HB criterion with the USC criterion to fully utilize their advantages, the main calculation parameters in both criteria will have a significant impact on the calculation results. However, due to the large variability of rock masses in actual engineering, it is very difficult to accurately determine the calculation parameters that conform to the actual physical and mechanical properties of rock masses. Therefore, the physical and mechanical parameters of rock masses within the scope of actual engineering are often within a range. Therefore, parameter sensitivity analysis will be used below to study the main relevant parameters such as m. i GSI, D, and b, etc. (while other parameters such as m) b The influence of parameters such as s and a (which can be calculated from the above parameters) on the calculation results of the loosened zone of the surrounding rock.

[0106] (1) m i The influence of the loosening zone range

[0107] Take m i The values ​​are 10, 15, 20, and 25 respectively, with other parameters remaining unchanged. The relative range r of the loosened zone of the surrounding rock in the tunnel is... b The variation pattern of / r0 is as follows: Figure 5 It can be seen that: ① Firstly, from the perspective of the overall change pattern, as m... iAs the lateral pressure increases, the relative range of the loosened zone gradually decreases; secondly, considering the shape of the loosened zone, since the lateral pressure coefficient is not equal to 1, the tunnel is in a non-isobaric state. Therefore, the loosened zone is no longer circular but elliptical, meaning its range is smaller in the horizontal direction and larger in the vertical direction; it is also important to note that... Figure 5 The shape of the loose ring is significantly different from that of the others. Figure 4 The main difference is in the vertical direction, which is primarily due to... Figure 4 The shape of the entire loosening ring is deduced based on seven existing points. Therefore, apart from these seven points which have actual measurement or calculation results, the remaining points are all speculations, and thus may contain significant errors. Figure 5 This is a theoretical calculation result, which is relatively accurate. ③ Finally, considering the magnitude of change, when m i As the value increases from 10 to 15, 20, and 25, the relative range r of the loosened zone of the surrounding rock increases. b The maximum value of / r0 gradually decreased from 2.72 to 2.13, 1.84, and 1.68, with decreases of 21.8%, 13.3%, and 9.1% respectively. (From m) i As can be seen from the meaning, the larger the value, the better the rock mass properties and the higher the strength, and correspondingly the smaller the range of loosened surrounding rock caused by tunnel excavation. Therefore, the above variation law is very consistent with the actual situation.

[0108] (2) The influence of GSI on the range of loosening zone

[0109] With GSI values ​​of 40, 50, 60, and 70, and other parameters remaining constant, the variation pattern of the loosened zone range of the tunnel surrounding rock is as follows: Figure 6 It can be seen that: ① Firstly, from the overall change pattern, as GSI increases, the range of the loosened rock zone gradually decreases; ② Secondly, from the shape of the loosened zone, its shape is no longer circular, but elliptical, for the same reason as before, which will not be repeated here. It is important to note that when GSI=70, there is some overlap between the loosened rock zone and the actual cross-section of the surrounding rock at the lower left and lower right corners. This is impossible in reality, mainly because the theoretical solution is based on the method of equivalent circles. If the boundary of the equivalent circle is considered as the actual tunnel boundary, then the loosened rock zone and the tunnel boundary do not intersect. This indicates that as GSI increases, the range of the loosened rock zone gradually decreases until no loosened zone appears at all. ③ Finally, from the perspective of the change range, when GSI increases from 40 to 50, 60, and 70 respectively, the relative range r of the loosened rock zone... bThe maximum value of / r0 gradually decreased from 2.38 to 1.85, 1.53, and 1.33, with decreases of 22.4%, 17.1%, and 12.9% respectively. According to the meaning of GSI, a larger value indicates larger rock mass blocks, lower weathering degree, and thus higher overall strength. Correspondingly, the radius of the loosened surrounding rock caused by tunnel excavation is also smaller, which is consistent with actual conditions.

[0110] (3) The influence of D on the radius of the loosening zone

[0111] With D set to 0, 0.2, 0.4, 0.6, and 0.8 respectively, and other parameters remaining constant, the variation pattern of the loosened zone range of the tunnel surrounding rock is as follows: Figure 7 It can be seen that: ① Firstly, from the overall trend of change, as D increases, the relative radius of the loosened zone of the surrounding rock gradually increases; at the same time, the shape of the loosened zone is no longer circular, for reasons similar to those mentioned above, which will not be repeated here. ② Secondly, from the perspective of the magnitude of change, when D increases successively from 0 to 0.2, 0.4, and 0.6, the relative range r of the loosened zone of the surrounding rock... b The maximum value of / r0 gradually increased from 1.52 to 1.63, 1.82, and 2.14, with increases of 7.5%, 11.1%, and 17.6% respectively. As can be seen from the definition of D, a larger value indicates more severe damage to the rock mass caused by blasting and other construction activities, resulting in poorer rock mass properties, lower strength, and correspondingly, a larger radius of the loosened rock mass caused by tunnel excavation. Therefore, the above variation pattern is very consistent with actual conditions.

[0112] (4) The influence of b on the radius of the loosening zone

[0113] With b set to 0, 0.33, 0.67, and 1 respectively, and other parameters remaining unchanged, the variation pattern of the loosened zone range of the tunnel surrounding rock is as follows: Figure 8 It can be seen that: ① Firstly, from the overall change pattern, as b increases, the relative radius of the loosened rock zone gradually decreases; at the same time, the shape of the loosened zone is no longer circular, for reasons similar to those mentioned above, which will not be repeated here. ② Secondly, from the perspective of the change range, when b increases successively from 0 to 0.33, 0.67, and 1, the relative range r of the loosened rock zone... b The maximum value of / r0 gradually decreased from 2.41 to 1.89, 1.65, and 1.53, with decreases of 21.6%, 12.4%, and 7.5% respectively. From the meaning of b, it can be seen that when b=0, only the influence of the maximum and minimum principal stresses on the loosened zone of the surrounding rock is considered. As the value of b increases, the influence of the intermediate principal stress on the loosened zone of the tunnel surrounding rock also increases. When the influence of the intermediate principal stress is considered, the strength of the surrounding rock will increase accordingly, and the radius of the loosened zone will decrease accordingly. Therefore, the above variation law is very consistent with the actual situation.

[0114] Although the above embodiments have been shown and described, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Any changes, modifications, substitutions and variations made to the above embodiments by those skilled in the art are within the protection scope of the present invention.

Claims

1. A method for calculating the loosened zone of tunnel surrounding rock based on the USC and HB criteria, characterized in that, Includes the following steps: S1. Strength criteria for linking USC and HB; The strength criterion for the association between USC and HB refers to establishing the association between the two through parameter transformation. The parameter transformation refers to first establishing the parameter transformation relationship between the HB criterion and the MC criterion, as well as the parameter transformation relationship between the USC and the MC criterion, and finally establishing the relationship between the USC and the HB criterion using the MC criterion as a medium. The parameter conversion relationship between the USC and MC criteria is as follows: In the formula: , These are the maximum and minimum principal stresses, c and These represent rock cohesion and internal friction angle, respectively. t , These are the equivalent cohesion and the equivalent internal friction angle, respectively. , b is the intermediate principal stress coefficient, and b = 0~1. When b = 0 and 1, this criterion corresponds to the MC criterion and the double shear strength criterion, respectively. The parameter conversion relationship between the HB criterion and the MC criterion is as follows: In the formula: a is an empirical parameter reflecting the characteristics of the rock mass, m b As an empirical parameter reflecting the characteristics of the rock mass, s reflects the degree of rock mass fragmentation. The uniaxial compressive strength of intact rock. For deeply buried chambers, Where γ is the rock mass and H is the tunnel depth; S2. Selection of correlation criterion parameters; S3. Establish a calculation model for the loosened zone of the surrounding rock in the tunnel; The calculation model for the loosened zone of the surrounding rock in the tunnel is based on parameters that correlate the USC and HB criteria. Substituting c into the radius r of the loosened zone of the surrounding rock of a circular tunnel under a non-uniform stress field... b It is obtained from the calculation formula.

2. The method for calculating the loosened zone of tunnel surrounding rock based on the associated USC and HB criteria according to claim 1, characterized in that, The parameters for the association criterion include m. b The four parameters are s, a, and D.

3. The method for calculating the loosened zone of tunnel surrounding rock based on the USC and HB criteria according to claim 2, characterized in that, Parameter D, which represents the damage to the rock mass caused by blasting and excavation disturbances, is quantified by the change in longitudinal wave velocity in the rock mass before and after blasting. In the formula: V pd V pi These represent the longitudinal wave velocities before and after rock mass disturbance.

4. The method for calculating the loosened zone of tunnel surrounding rock based on the associated USC and HB criteria according to claim 1, characterized in that, The parameter sinφ that relates the USC and HB criteria is: The parameter c that correlates the USC and HB criteria is: In the formula, c and denoted as rock cohesion and internal friction angle, respectively, and b is the intermediate principal stress coefficient, with b = 0~1.

5. The method for calculating the loosened zone of tunnel surrounding rock based on the USC and HB criteria according to claim 1, characterized in that, The radius r of the loosened zone of the surrounding rock of the circular tunnel under a non-uniform stress field. b The calculation formula is: In the formula: r0 is the tunnel radius, p s The force acting on the tunnel wall is the support force, p0 is the vertical ground stress, λ is the lateral pressure coefficient, θ is the polar angle, and c is the vertical ground stress. t , These are the equivalent cohesive force and the equivalent internal friction angle, respectively.

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