Setting method of approximate equation of equivalent elastic modulus of spray concrete and design method of timbering of mountain tunnel

Abstract

To provide a setting method of an approximate equation of an equivalent elastic modulus of spray concrete, capable of identifying an equivalent elastic modulus of the spray concrete with accuracy in which actual phenomenon can be reflected, and a design method of timbering of a mountain tunnel.SOLUTION: A setting method of an approximate equation of an equivalent elastic modulus of spray concrete, comprises: an A step for performing multi-stage stress relaxing test, to a sample of the spray concrete; a B step for executing reproduction analysis for reproducing a stress-time relationship; a C step for executing successive digging analysis of the tunnel; and a D step for setting an equivalent elastic modulus, from a stress-strain relationship of a spray concrete model which is determined by the digging analysis of the tunnel. In the C and D steps, to at least one of parameters formed of a tunnel diameter, an elastic coefficient of natural ground, a cycle time, and intensity of the spray concrete, the successive digging analysis of the tunnel is executed by parametric study, and on the basis of the analysis result, an approximate equation of the equivalent elastic modulus being at least one function in parameters, is created.SELECTED DRAWING: Figure 1

Description

[Technical field]

[0001] The present invention relates to a method for setting an approximation formula for the equivalent elastic modulus of shotcrete and a method for designing supports for mountain tunnels. [Background technology]

[0002] Mountain tunnels are structures in which the ground being excavated itself forms an arch structure to support the space, and immediately after excavation, shoring is installed to ensure the stability and safety of the ground. This shoring mainly consists of sprayed concrete, steel shoring, and rock bolts. Among these, sprayed concrete is a thin, flexible support material that supports the ground. Its features include the ability to spray onto the tunnel wall without the need for formwork and to adhere to the ground surface, the ability to quickly develop strength using an accelerator, and a material age of 5 to 10 N / mm 2 The strength of the material can be expected to be approximately the same. The functions of sprayed concrete include axial compression resistance, shear resistance, and bending resistance, as well as a support function that distributes the loads received by these various resistance functions to the natural ground. Here, axial compression resistance is the function of resisting axial force caused by external forces and deformations acting on the arch of the natural ground in the inward direction, shear resistance is the function of resisting shear force and shear displacement caused by localized collapse of the natural ground, and bending resistance is the function of resisting bending moment caused by localized collapse of the natural ground. The effects of sprayed concrete include preventing surface collapse, retaining small rock masses, applying internal pressure to the ground (especially in ground that is subject to large deformations or soil and sand), reinforcing weak layers and retaining shape, smoothing out stress distribution, and providing coverage and preventing deterioration of the ground (for example, preventing deterioration due to air or spring water).

[0003] When designing sprayed concrete, workability is taken into consideration and the appropriate construction timing, thickness, strength, mix ratio, etc. are determined based on the natural ground conditions. There are three design methods for sprayed concrete: empirical methods based on natural ground classification, methods based on similar conditions, and analytical methods. Of these, when designing shotcrete using analytical methods, design specifications are determined mainly through numerical analysis such as FEM (Finite Element Method) and FDM (Finite Difference Method), and the appropriateness of the support is evaluated by determining the stress and displacement of the surrounding ground and the load acting on the support members. Shotcrete is a support used under special conditions where it is subjected to most of the deformation of the ground caused by excavation at an early age when the strength and elastic modulus change greatly, and since the deformation of shotcrete is the sum of elastic deformation, creep deformation, and drying shrinkage deformation, it is necessary to take viscoelasticity into consideration. For this reason, even in numerical analysis, an equivalent elastic modulus (apparent elastic modulus) that takes viscoelasticity into account is used. However, since this equivalent elastic modulus has a significant effect on the analysis results, its setting is extremely important. In cases where the elastic modulus of the ground is small (and therefore the elastic modulus of the shotcrete is relatively large compared to the elastic modulus of the ground), setting the elastic modulus of the shotcrete (equivalent elastic modulus) becomes even more important.

[0004] Here, as a method for setting the elastic modulus of conventional shotcrete, the design elastic modulus: E is indicated by each client organization as follows. For example, for railway tunnels, E = 3.4 kN / mm 2 (Japan Railway Construction, Transport and Technology Agency: Mountain Tunnel Design and Construction Standards and Commentary) indicates that E=4.0kN / mm 2 (Japan Highway Public Corporation Testing Research Institute Tunnel Laboratory: Tunnel Numerical Analysis Manual) is shown, and all of these elastic coefficients are set based on the results of experiments conducted by Tsuchiya of the former Japanese National Railways. The experiment conducted by Tsuchiya was aimed at determining the elastic modulus for numerical analysis of sprayed concrete. The experimental method involved applying sprayed concrete to the side walls of the tunnel, then extracting a core (a cylindrical core with a circular cross section of φ100mm and a height of 200mm) when the concrete was 12 hours old, and conducting a creep test in which a load was applied to the core equal to 1 / 3 of the compressive strength. Three test cases were performed in which loading began when the concrete was 2, 3, and 7 days old, and the equivalent elastic modulus (elastic modulus taking into account elastic deformation, creep, and drying shrinkage deformation) was determined 28 days after loading began. The test results showed that the earlier the loading started, the greater the creep deformation and drying shrinkage deformation, and the equivalent elastic modulus 28 days after loading was 3 to 4 kN / mm 2 It has been specified that the extent of

[0005] In conventional methods for determining the equivalent elastic modulus of sprayed concrete, the elastic modulus based on the above-mentioned Tsuchiya experiment has generally been used, but such conventional methods for determining the equivalent elastic modulus have various inherent problems. The first issue is that the elastic modulus is obtained by a load-controlled creep test. Since the actual shotcrete receives a load in the form of a displacement load as a reaction force when attempting to restrain the deformation of the ground caused by excavation, it is difficult to say that the load-controlled creep test reflects the actual phenomenon. The second issue is that creep and drying shrinkage deformation at very early ages (e.g., less than 24 hours) are not taken into consideration. The age at which the effects are greatest is thought to be less than 24 hours (less than one day), but this behavior is not reflected in the evaluation. The third problem is that the behavior of the ground during excavation is not taken into consideration. In reality, the shotcrete is subjected to gradual displacement during tunnel excavation, but this behavior of the ground is not simulated in creep tests under a constant load.

[0006] For these reasons, when designing shotcrete using analytical methods, it is desirable to have a method for determining the equivalent elastic modulus of shotcrete that reflects the actual phenomenon in which shotcrete is subjected to a displacement load and further to gradual displacement due to tunnel excavation, and that takes into account creep and drying shrinkage deformation at very early ages.

[0007] Here, Patent Document 1 proposes a method for estimating the static elastic modulus of early-age shotcrete from which a core cannot be extracted for a uniaxial compression test. This estimation method includes: (a) a preliminary test step in which a pullout test or a needle penetration test is performed as a preliminary test on a sample made of early-age shotcrete from which a core cannot be extracted, to determine the relationship between the age and the converted compressive strength; (b) a main test step in which a core is extracted from the shotcrete from which a core can be extracted, to perform a uniaxial compression test as a main test, to determine the relationship between the age and the uniaxial compressive strength and the relationship between the age and the static elastic modulus; (c) an approximation curve setting step in which an approximation curve is set that approximates the relationship between the converted compressive strength and the static elastic modulus of the sample; and (d) a static elastic modulus estimation step in which the static elastic modulus of the sample is estimated from the converted compressive strength of the sample based on the approximation curve. [Prior art documents] [Patent documents]

[0008] [Patent Document 1] JP 2013-72738 A Summary of the Invention [Problem to be solved by the invention]

[0009] Even the method of estimating the static elastic modulus of early-age shotcrete described in Patent Document 1 cannot resolve the various problems inherent in the above-mentioned conventional methods for setting the equivalent elastic modulus of shotcrete.

[0010] In addition, in the design of mountain tunnel supports, mountain tunnels at each site are modeled in a computer and three-dimensional sequential excavation analysis of the tunnel is performed, faithfully reproducing the material properties of the shotcrete, to improve the accuracy of the behavior of the ground and the stress of the supports, etc. However, the method of modeling mountain tunnels at each site and performing three-dimensional sequential excavation analysis requires a lot of time and effort in the process from creating the model to carrying out the analysis and interpreting the analysis results. For this reason, there is a need for a support design method that can reflect the conditions at each site and design efficient and suitable mountain tunnel supports, eliminating the need to model mountain tunnels for each site and perform three-dimensional sequential excavation analysis of the tunnel that faithfully reproduces the material properties of the sprayed concrete.

[0011] The present invention aims to provide a method for setting an approximate equation for the equivalent elastic modulus of sprayed concrete, which can specify the equivalent elastic modulus of sprayed concrete with high accuracy, reflecting the actual phenomenon in which sprayed concrete is subjected to a displacement loading load and further subjected to gradual displacement associated with tunnel excavation, and a design method for mountain tunnel supports, which can efficiently design suitable mountain tunnel supports that reflect on-site conditions. [Means for solving the problem]

[0012] In order to achieve the above object, one aspect of the method for setting an approximation equation for the equivalent elastic modulus of sprayed concrete according to the present invention is as follows: A method for setting an approximation formula for the equivalent elastic modulus of sprayed concrete, taking into account the rigidity of the sprayed concrete applied to the wall surface of a tunnel over time, comprising: A step A includes carrying out a multi-stage stress relaxation test on a specimen of the sprayed concrete, in which a displacement that changes stepwise with each elapsed time according to the age of the specimen is loaded, and identifying the stress-time relationship of the specimen; A process B of performing a reproduction analysis to reproduce the stress-time relationship and identifying mechanical properties according to the age of the specimen; A step C of carrying out a sequential excavation analysis of a tunnel using an analytical model including a shotcrete model having mechanical properties according to the age of the material and a surrounding ground model; and a step D of setting the equivalent elastic modulus from the stress-strain relationship of the shotcrete model obtained by the sequential excavation analysis of the tunnel; In the steps C and D, A stepwise excavation analysis of the tunnel is carried out by a parametric study for at least one of the parameters consisting of the tunnel diameter, the elastic modulus of the ground, the cycle time, and the strength of the shotcrete; The method is characterized in that an approximation equation for an equivalent elastic coefficient, which is a function of at least one of the parameters, is created based on the results of the sequential excavation analysis of the tunnel by the parametric study.

[0013] According to this embodiment, a multi-stage stress relaxation test is performed to load a stepwise-changing displacement according to the age of a test specimen of shotcrete, and the stress-time relationship is identified, and a reproduction analysis is performed to reproduce the identified stress-time relationship to identify the mechanical properties according to the age of the test specimen. A sequential tunnel excavation analysis is then performed using an analysis model including a shotcrete model having mechanical properties according to the age of the test specimen and a surrounding ground model to determine the stress-strain relationship of the shotcrete model during the tunnel excavation process, and an equivalent elastic modulus is set from this stress-strain relationship, so that an equivalent elastic modulus of the shotcrete can be set that reflects the actual phenomenon that the shotcrete is loaded in a displacement loading manner and is subjected to stepwise displacement due to tunnel excavation. Furthermore, with regard to the sequential tunnel excavation analysis, a parametric study is performed on at least one of the parameters consisting of the tunnel diameter, the elastic modulus of the ground, the cycle time, and the strength of the sprayed concrete. Based on the results of the parametric study of the sequential tunnel excavation analysis, an approximation equation for the equivalent elastic modulus, which is a function of at least one of the parameters, is created and used, making it possible to set with high precision the equivalent elastic modulus of the sprayed concrete according to the conditions of various mountain tunnel sites. In other words, the (three-dimensional) sequential excavation analysis of a tunnel only needs to be performed once, and by inputting parameters including the tunnel diameter, elastic modulus of the ground, cycle time, and strength of the sprayed concrete for each site into the approximation formula for the equivalent elastic modulus of the shotcrete set in this sequential excavation analysis, it is possible to easily determine the equivalent elastic modulus with high accuracy.

[0014] Here, the "multi-stage stress relaxation test" in process A is a test in which a fixed displacement is applied to a specimen of specified specifications and the change in stress over time is measured, and the test fully reflects creep and drying shrinkage deformation at very early ages according to the (time interval between) construction steps of the tunnel. In this multi-stage stress relaxation test, in order to reproduce the behavior of the ground associated with excavation, the same specimen is repeatedly subjected to a constant rate of displacement and a loading displacement that substantially corresponds to the time interval between the construction steps.

[0015] In addition, in the reproduction analysis in process B, numerical analysis methods such as FEM and FDM are used to perform an analysis to reproduce the stress-time relationship of the test specimen obtained in process A. For example, in order to achieve this reproduction (fitting), the mechanical properties, which are the viscoelastic parameters of the sprayed concrete, are identified.

[0016] In addition, when carrying out the sequential excavation analysis of the tunnel in Process C, for example, construction conditions and ground conditions at a selected specific construction site may be set, and the sequential excavation analysis of the tunnel may be carried out under the various set conditions. In addition, with regard to "performing sequential excavation analysis of the tunnel using a parametric study on at least one of the parameters consisting of the tunnel diameter, the elastic modulus of the ground, the cycle time, and the strength of the sprayed concrete," a parametric study may be performed on one of the parameters given as examples here, but it is preferable to perform a parametric study on all parameters from the viewpoint of improving the accuracy of the approximation formula.

[0017] After conducting a parametric study to organize the equivalent elastic modulus, an approximate equation for the equivalent elastic modulus is created as a function of each of the following conditions based on the relationship between the equivalent elastic modulus and the tunnel diameter, elastic modulus of the ground, cycle time, and strength of the sprayed concrete.

[0018] In addition, another aspect of the method for setting an approximation formula for the equivalent elastic modulus of sprayed concrete according to the present invention is as follows: The approximation formula is created by assuming a Gompertz curve as a function of the cycle time.

[0019] According to the present embodiment, by creating an approximation equation by assuming a Gompertz curve as a function of cycle time, since fluctuations in cycle time among the above parameters cause large fluctuations in the equivalent elastic modulus, it is possible to determine with high accuracy the equivalent elastic modulus of sprayed concrete for each cycle time appropriate to the site. Here, the Gompertz curve is a linear curve that passes through the origin, increases gradually, increases sharply, and then increases gradually again before converging to a constant value. A curve with such a linear trend well reflects the relationship between the age and strength of concrete, and is therefore suitable as an approximation formula for the equivalent elastic modulus of shotcrete.

[0020] In addition, another aspect of the method for setting an approximation formula for the equivalent elastic modulus of sprayed concrete according to the present invention is as follows: The present invention is characterized by creating the following approximate formula (A).

[0021]

number

[0022] According to the present embodiment, by creating a specific approximation formula (A) as a Gompertz curve as a function of cycle time, the equivalent elastic modulus of sprayed concrete for each cycle time according to the site can be determined with high accuracy.

[0023] In addition, another aspect of the method for setting an approximation formula for the equivalent elastic modulus of sprayed concrete according to the present invention is as follows: The mechanical property in the step B is a viscoelastic property.

[0024] According to the present embodiment, since the mechanical properties in step B are viscoelastic properties, it is possible to simulate with high reproducibility that the deformation of the sprayed concrete is the sum of elastic deformation, creep deformation, and drying shrinkage deformation.

[0025] In another aspect of the method for setting an approximation equation for the equivalent elastic modulus of sprayed concrete according to the present invention, In the reproduction analysis in the step B, a viscoelastic model expressing the stress-time relationship is used as a mechanical model, The viscoelastic model is composed of spring elements that represent elastic behavior and dashpot elements that represent viscous behavior, The step B is characterized in that the viscosity coefficient of the dashpot element is adjusted to fit the mechanical characteristics to the stress-time relationship of the specimen.

[0026] According to this aspect, the viscoelastic model, which is the mechanical model used in the reproduction analysis, is composed of spring elements that represent elastic behavior and dashpot elements that represent viscous behavior. By adjusting the viscosity coefficient of the dashpot elements and fitting the mechanical characteristics of the mechanical model to the stress-time relationship of the test specimen, it is possible to efficiently create a mechanical model in which the mechanical characteristics of the test specimen are simulated with as high an accuracy as possible. Here, the viscoelastic model composed of a spring element and a dashpot element can take various forms, such as a model in which a spring element and a dashpot element are connected in series, and a model in which a first spring element and a dashpot element are arranged in parallel and these are then arranged in series with a second spring element.

[0027] In addition, another aspect of the method for setting an approximation formula for the equivalent elastic modulus of sprayed concrete according to the present invention is as follows: The method further includes a step E of performing a compressive strength test on the specimen, The elastic modulus for each material age of the specimen, determined by the compressive strength test, is applied to the spring element in step B.

[0028] According to this embodiment, by applying the elastic coefficient for each material age determined by the compressive strength test on the test specimen to the spring element of the viscoelastic model in the reproduction analysis of process B, a mechanical model can be created in which the mechanical properties of the test specimen are simulated as accurately as possible.

[0029] In another aspect of the method for setting an approximation equation for the equivalent elastic modulus of sprayed concrete according to the present invention, In the multi-stage stress relaxation test in the step A, a constant displacement is maintained for a certain elapsed time, and the constant displacement is changed according to the elapsed time, The change in displacement is carried out instantaneously.

[0030] According to this embodiment, in the multi-stage stress relaxation test of step A, a constant displacement is maintained for a certain elapsed time, and the constant displacement is changed according to the elapsed time, so that the loaded displacement changes stepwise for each tunnel excavation speed (excavation cycle), which is a test that reproduces the phenomenon in which a displacement is loaded on the shotcrete according to the construction of an actual tunnel. Furthermore, by changing the displacement instantaneously, it is possible to eliminate the viscoelastic effect during the loading process. Here, "instantly changing the displacement" means that the displacement changes without taking any time at a certain time, but may also include the displacement changing in a short period of time (a few seconds compared to the elapsed time of several hours for an excavation cycle).

[0031] In addition, one aspect of the design method for mountain tunnel supports according to the present invention is to A step F of setting an equivalent elastic modulus of the sprayed concrete by a method for setting an approximation formula of the equivalent elastic modulus of the sprayed concrete; The method is characterized by having a G step of applying the equivalent elastic modulus of the sprayed concrete to a mountain tunnel model to perform a numerical analysis and design a specified support structure for the mountain tunnel.

[0032] According to this aspect, the equivalent elastic modulus of sprayed concrete is set using the method of the present invention for setting an approximate equation for the equivalent elastic modulus of sprayed concrete, the set equivalent elastic modulus is applied to a mountain tunnel model to perform a numerical analysis, and a specified support for the mountain tunnel is designed, thereby making it possible to efficiently design a support suitable for the site. Here, the "numerical analysis" in Process G involves creating a two-dimensional mountain tunnel model on a computer, applying a shotcrete model (part of the support) with a set equivalent elastic modulus, and then designing other supports such as steel supports and rock bolts. At this time, because the equivalent elastic modulus of the shotcrete is set with high precision, it is possible to realize rational design of supports such as steel supports. Effect of the Invention

[0033] According to the present invention's method for setting an approximate formula for the equivalent elastic modulus of sprayed concrete and the design method for mountain tunnel supports, it is possible to specify a highly accurate equivalent elastic modulus of sprayed concrete that reflects the actual phenomenon in which sprayed concrete is subjected to a displacement loading load and further to gradual displacement associated with tunnel excavation, and to efficiently design suitable mountain tunnel supports that reflect on-site conditions. [Brief description of the drawings]

[0034] [Figure 1] 1 is a flowchart showing an example of a method for setting an approximation equation for the equivalent elastic modulus of sprayed concrete according to an embodiment, and an example of a method for designing supports for a mountain tunnel. [Diagram 2] 1 is a table showing an example of a mix ratio for shotcrete having a typical design standard strength. [Diagram 3] FIG. 1 shows the results of a multi-stage stress relaxation test. [Figure 4] 1 is a graph showing the change over time in the elastic modulus of shotcrete. [Diagram 5] FIG. 1 is a diagram showing an example of a mechanical model of a test specimen (shotcrete) in a reproduction analysis. [Figure 6] FIG. 1 is a diagram for explaining an example of an analytical model applied in a sequential excavation analysis (parametric study) of a tunnel. [Figure 7] This is a table summarizing the analysis cases in the parametric study. [Figure 8] 13 is a diagram illustrating a method for calculating an equivalent elastic modulus based on a maximum stress value and an accumulated strain at the center position of an analysis model. FIG. [Figure 9] 1 is a graph showing the relationship between the magnitude relationship of various parameters and the equivalent elastic modulus. [Figure 10] This is a graph showing the stress-strain relationship of shotcrete in three types of mountain tunnels with different tunnel diameters. [Figure 11] 10 is a flowchart showing an example of a specific method for setting an approximation equation. [Figure 12] FIG. 1 is a diagram illustrating the assumption of a Gompertz curve as a function of cycle time. [Figure 13] FIG. 13 is a diagram for explaining a method for assuming a constant Ecfin in an approximate formula. [Figure 14] FIG. 1 is a diagram for explaining a method of assuming α and β for deformation coefficients of natural ground. [Figure 15] FIG. 13 is a diagram for explaining a method of assuming α and β for a tunnel diameter. [Figure 16] 1 is a graph comparing calculated values ​​using an approximate formula with analytical values, and showing the cycle time-equivalent elastic modulus relationship. [Figure 17] This is a graph comparing calculated values ​​using an approximate formula with analytical values, and shows the relationship between the elastic modulus of the natural ground and the equivalent elastic modulus. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0035] Hereinafter, a method for setting an approximate formula for the equivalent elastic modulus of sprayed concrete according to an embodiment and a method for designing supports for mountain tunnels will be described with reference to the attached drawings. Note that in this specification and the drawings, substantially identical components may be designated by the same reference numerals to avoid redundant explanations.

[0036] [Method of setting an approximate formula for the equivalent elastic modulus of shotcrete according to the embodiment and method of designing supports for mountain tunnels] A method for setting an approximation formula for the equivalent elastic modulus of shotcrete according to the embodiment and an example of a method for designing supports for a mountain tunnel will be described with reference to Figs. Here, FIG. 1 is a flowchart showing an example of a method for setting an approximation formula for the equivalent elastic modulus of shotcrete according to the embodiment, and an example of a method for designing a support for a mountain tunnel. FIG. 2 is a table showing an example of a mix ratio of shotcrete with a typical design standard strength, and FIG. 3 is a diagram showing the results of a multi-stage stress relaxation test. FIG. 4 is a graph showing the time change in the elastic modulus of shotcrete, and FIG. 5 is a diagram showing an example of a mechanical model of a test specimen (shotcrete) in a reproduction analysis. FIG. 6 is a diagram explaining an example of an analysis model applied in a sequential excavation analysis (parametric study) of a tunnel, FIG. 7 is a table summarizing analysis cases in the parametric study, and FIG. 8 is a diagram explaining a method for calculating the equivalent elastic modulus based on the maximum stress value and the accumulated strain at the center position of the analysis model.

[0037] As shown in FIG. 1, the method for setting an approximate equation for the equivalent elastic modulus of shotcrete (S10) includes a multi-stage stress relaxation test (step S12, process A), a reproduction analysis (step S14, process B), a compressive strength test (step S16, process E), and a sequential excavation analysis of the tunnel (step S18, processes C and D).

[0038] Furthermore, the design method for mountain tunnel supports (S20) includes setting the equivalent elastic modulus of sprayed concrete using the approximate equation set in the method for setting the approximate equation (S10) (step S22, process F), and designing the mountain tunnel supports (step S24, process G).

[0039] In the multi-stage stress relaxation test (step S12), a test specimen is prepared of shotcrete with a predetermined specification (predetermined mix ratio) to be used in the construction of a planned mountain tunnel. This test specimen is, for example, a cylindrical test specimen with a circular cross section of φ100 mm and a height of about 200 mm.

[0040] Here, two examples of specifications (mixture examples) for commonly used shotcrete are shown in Figure 2. The design standard strength is 18N / mm 2 (normal strength) and 36N / mm 2 (High strength) is a typical example.

[0041] A constant displacement is applied to this specimen, and the change in stress over time is measured. In this test, in order to reproduce the behavior of the ground during excavation, the same specimen is used, and a constant rate of displacement and loading displacement are maintained for each construction step (excavation step), and this is repeated over multiple construction steps.

[0042] The multi-stage stress relaxation test identifies the stress-time relationship of the shotcrete for each construction step, as shown in Figure 3. As is clear from this stress-time relationship, when a constant rate of displacement loading is applied, the stress of the shotcrete shows a nearly linear increasing trend, and when the loaded displacement is maintained, the shotcrete shows viscoelastic behavior in which the stress is released in a curved manner, and this is shown across multiple construction steps.

[0043] Here, the elapsed time for starting the loading of the displacement in step A is set to a time equivalent to the tunnel excavation cycle time. In the illustrated example, the tunnel excavation speed is 4 hours / m as the construction cycle, and a specified displacement is loaded onto the test specimen after the first construction cycle of 4 hours has elapsed, and these 4 hours are the time interval (displacement holding period) for gradually changing the loaded displacement.

[0044] Furthermore, the displacement load when moving to the next construction cycle is applied instantaneously (loading time is short, from one second to a few seconds).

[0045] In this way, by setting the time corresponding to the construction cycle as the start time of the displacement loading on the test specimen, and setting the time corresponding to the tunnel excavation cycle time as the time interval for gradually changing the loaded displacement, it is possible to realize tests that fully reflect the creep and drying shrinkage deformation of very early materials according to the time interval of the tunnel construction steps.

[0046] In addition, by changing the displacement instantaneously, the viscoelastic effects during the loading process can be eliminated.

[0047] In process B (step S14), a reproduction analysis is carried out to reproduce the stress-time relationship, and the mechanical properties according to the age of the specimen are identified. This reproduction analysis is an analysis to reproduce the stress-time relationship of the specimen obtained in process A using a numerical analysis method such as FEM or FDM (for example, the finite difference method code FLAC3D.ver7), and specifies the mechanical properties, which are the viscoelastic parameters of the sprayed concrete, in order to achieve a highly accurate reproduction (fitting).

[0048] For this reproduction analysis, a compressive strength test is performed on the specimen in process E (step S16), and the elastic modulus for each age of the specimen identified by the compressive strength test is obtained. This compressive strength test complies with JIS regulations (JIS A1108:2018 Concrete compressive strength test method).

[0049] Figure 4 shows an example of a graph showing the logarithmic relationship between Young's modulus (elastic modulus, secant elastic modulus) and material age (hours) for each mix, based on the test results for each mix. Figure 4 shows that a good approximation is obtained as a logarithmic relationship for each mix.

[0050] For this reproduction analysis, a mechanical model is created, as shown in Figure 5 as an example. The mechanical model shown in Figure 5 is a viscoelastic model, and is composed of a spring element that expresses elastic behavior, and a dashpot element that expresses viscous behavior. The viscoelastic model shown in the example is a model in which a first spring element (elastic coefficient: Ek) and a dashpot element (viscosity coefficient: η) are arranged in parallel, and these are arranged in series with a second spring element (elastic coefficient: Es). There are various types of viscoelastic models composed of spring elements and dashpot elements. Here, the stress of the spring element (elastic component): σ s can be expressed as Eε (ε: strain), and the stress of the dashpot element (viscous component): σ d can be expressed as ηdε / dt (dε / dt: time derivative of strain).

[0051] In the reproduction analysis, a viscoelastic model, which is an analytical model, is created in a computer, and the elastic coefficients for each material age determined in the compressive strength test are applied to the elastic coefficients of this viscoelastic model.Then, while changing the viscosity coefficient: η, which is a dashpot element, as a parameter, a mechanical model (viscoelastic model) is created that reproduces (fits) with high accuracy the stress-time relationship of the specimen obtained in Process A.

[0052] In the reproduction analysis, the boundary conditions of the mechanical model (viscoelastic model) are full constraint on the bottom surface and horizontal displacement constraint on the top surface. s =E k Then, the loading process and the displacement holding process similar to those of the multi-stage stress relaxation test are repeated at each analysis step (corresponding to the construction step), and the elastic modulus of each material age (here, every 4 hours, which is the time interval of the construction step) obtained in the E step is calculated from the E s (=E k ) to determine

[0053] In step C, a sequential tunnel excavation analysis is carried out to determine the wall strain and the sprayed concrete strain for each elapsed time after the excavation of the tunnel under the installation conditions of sprayed concrete (support work). In step D, a sequential tunnel excavation analysis is carried out on a sprayed concrete model having mechanical properties according to the age of the material, and an equivalent elastic coefficient is set from the stress-strain relationship of the sprayed concrete model obtained by the sequential tunnel excavation analysis (step S18 is composed of steps C and D).

[0054] In step S18, a parametric study is performed. In the parametric study, a sequential excavation analysis of the tunnel is performed taking into account the time dependency of the shotcrete, and a parametric study is performed on the tunnel diameter, the earth covering, the elastic modulus of the ground, the cycle time, and the strength of the shotcrete.

[0055] As shown in Fig. 6, the analytical model for the sequential tunnel excavation analysis was designed with the model scale changed for each tunnel diameter, the effect of soil cover set at the initial earth pressure (= γH), the model was a single soil layer, the excavation length was standardized to 1 m, and the stress-strain relationship of the sprayed concrete at the center of the model (5D) at the completion of excavation of 10D (D is the tunnel diameter) was obtained.

[0056] As shown in Fig. 7, three types of tunnel diameters were set for the analysis cases. A tunnel diameter of 5 m was set to simulate a small-section escape tunnel or waterway, a tunnel diameter of 10 m was set to simulate a standard road or railroad tunnel, and a tunnel diameter of 15 m was set to simulate a large-section tunnel such as a three-lane road.

[0057] Regarding soil cover, a low soil cover is set at 10m, a standard soil cover at 50m, and a soil cover for a long tunnel in the mountains at 200m.

[0058] The elastic modulus of the ground was set at 150 MPa assuming road DII pattern, 1000 MPa assuming road CII pattern, and 5000 MPa assuming road B pattern.

[0059] Regarding cycle time, it was set at 6 hours assuming 4 cycles / day (earliest), 12 hours assuming 2 cycles / day (standard), and 24 hours assuming 1 cycle / day (when auxiliary construction methods are used).

[0060] Regarding the strength of sprayed concrete, the standard strength is 18N / mm 2 and high strength (suitable for large cross-section tunnels and fragile ground) of 36N / mm 2 It was decided.

[0061] As shown in FIG. 8, the maximum stress value / accumulated strain at the center (5D) of the analysis model was calculated as equivalent elastic modulus, and all analysis results were fitted to an approximate equation.

[0062] The approximate formula (A) for the equivalent elastic modulus of shotcrete is shown below.

[0063]

number

[0064] FIG. 9 is a graph showing the relationship between the magnitudes of various parameters and the equivalent elastic modulus, and FIG. 10 is a graph showing the stress-strain relationship of shotcrete in three types of mountain tunnels with different tunnel diameters.

[0065] As shown in Figure 9, the analysis results using the proposed method that takes into account time dependency show that the equivalent elastic modulus increases with the tunnel diameter, deformation coefficient of the ground, cycle time, and shotcrete strength, and there is no difference due to soil covering.

[0066] These results suggest that, as shown in Figure 8, there is a large tendency for stress relaxation in the early stages of hardening of sprayed concrete, and therefore the effect of stress relaxation becomes more dominant as the strain acting in the early stages of hardening becomes larger relative to the final strain, resulting in a smaller equivalent elastic modulus.

[0067] From the above, by making the approximate formula (A) for the equivalent elastic modulus a function of the tunnel diameter, deformation modulus of the ground, cycle time, and sprayed concrete strength, it is possible to set an appropriate equivalent elastic modulus according to the various conditions in tunnel excavation.

[0068] Next, a specific method for setting the approximation formula will be described with reference to Fig. 11 to Fig. 15. Fig. 11 is a flow chart showing an example of a specific method for setting the approximation formula, and Fig. 12 is a diagram explaining the assumption of a Gompertz curve with the cycle time as a function. Figs. 13, 14, and 15 are diagrams explaining the assumption method of the constant Ecfin in the approximation formula, the assumption method of α and β for the deformation coefficient of the natural ground, and the assumption method of α and β for the tunnel diameter, respectively.

[0069] As shown in Fig. 11, in creating the approximation formula, first, the conditions that do not change the equivalent elastic modulus even if the conditions are changed are excluded from the approximation formula. As shown in Fig. 9, it is known that the equivalent elastic modulus does not change depending on the amount of earth covering, so "earth covering" is excluded from the parameters as described above (step S31).

[0070] Next, we assume a Gompertz curve as a function of cycle time. Since it is easy to imagine that the equivalent elastic modulus changes due to the influence of cycle time, we first organized the equivalent elastic modulus by cycle time, as shown in Figure 12. In Figure 12, the curve created by connecting each plot shows that the equivalent elastic modulus is also 0 MPa when the cycle time is 0 h, and it can be seen that as the cycle time increases, the equivalent elastic modulus tends to converge to a constant value.

[0071] In this way, a Gompertz curve is assumed, which is a curve that passes through the origin, gradually increases, then suddenly increases again, and gradually increases again before converging to a certain value (Ecfin in approximation formula (A)).Since the Gompertz curve is an equation that is often used in relation to the age and strength of concrete, this setting method assumes that a similar trend can be obtained by interpreting the cycle time as being approximately equal to the age of the concrete.

[0072] Ecfin is assumed to be a constant determined by the strength of the shotcrete. Specifically, as shown in Figure 13, for each concrete specification, the convergence value when the cycle time is infinite is set to Ecfin, and in the illustrated example, it is 18 N / mm 2 Ecfin = 2900MPa, 36N / mm 2 So Ecfin = 3700 MPa (this is the end of step S33).

[0073] Next, the optimum constants α and β are obtained by the least squares method under the same conditions except for the cycle time. This least squares method is a method for obtaining the most probable relational expression so as to minimize the sum of the squares of the errors (step S34).

[0074] Regarding the constant α, an equation for the constant α in the approximation formula (A) is assumed based on the relationship between the constant α, the tunnel diameter, and the elastic modulus (deformation modulus) of the natural ground, and the constant α is calculated by the least squares method (step S35).

[0075] Similarly, for the constant β, an equation for the constant β in the approximation formula (A) is assumed based on the relationship between the constant β, the tunnel diameter, and the elastic modulus (deformation modulus) of the natural ground, and the constant β is calculated by the least squares method (step S36).

[0076] FIG. 14 shows the relationship between the elastic modulus (deformation coefficient) of the natural ground and the constants α and β, and FIG. 15 shows the relationship between the tunnel diameter and the constants α and β.

[0077] In FIG. 11, in step S35, an example of the constant α (α=−412 / (D 1.3 ×E 0.405 )) in step S36, an example of the constant β (β=1.07×10 -4 ×E+(0.056×D-1.4)).

[0078] Next, the accuracy of the approximate formula (A) will be described with reference to Fig. 16 and Fig. 17. Fig. 16 is a graph comparing the calculated values ​​using the approximate formula with the analytical values, and is a graph showing the cycle time-equivalent elastic modulus relationship. Fig. 17 is a graph comparing the calculated values ​​using the approximate formula with the analytical values, and is a graph showing the natural ground elastic modulus-equivalent elastic modulus relationship.

[0079] Figure 16 compares the analysis results and the results of the proposed formula (approximate formula (A)) when the soil cover is 50 m and the elastic modulus of the ground is 1000 MPa. Figure 16 shows that the correlation between the analysis results and approximate formula (A) is extremely high, with a correlation coefficient of 0.9127.

[0080] On the other hand, Fig. 17 compares the analysis results and the results of the proposed formula (approximation formula (A)) when the cycle time is 12 hours and the tunnel diameter is 10 m. Fig. 17 demonstrates that the correlation between the analysis results and approximation formula (A) is extremely high.

[0081] Returning to Figure 1, according to the method for setting the approximate equation for the equivalent elastic modulus of shotcrete (S10), it is possible to determine a highly accurate equivalent elastic modulus of shotcrete that reflects the actual phenomenon in which shotcrete is subjected to a displacement loading load and further to gradual displacement associated with tunnel excavation.

[0082] In addition, by applying values ​​corresponding to various sites to each parameter of the set approximation formula (A), it is possible to quickly identify the equivalent elastic modulus of the sprayed concrete appropriate for the site, without the need to perform time-consuming and laborious sequential excavation analysis of the tunnel each time.

[0083] Next, the equivalent elastic modulus of the shotcrete is set (step S22) using the approximation formula (A) set by the method for setting the approximation formula for the equivalent elastic modulus of the shotcrete (S10).

[0084] Next, the equivalent elastic modulus of the sprayed concrete set in step S22 is applied to a mountain tunnel model (a two-dimensional model in a computer) corresponding to the site, and a numerical analysis is performed to design the specified support structure for the mountain tunnel (step S24).

[0085] Here, "specified support" means not only sprayed concrete with a set equivalent elastic modulus, but also steel support of specified specifications (including the pitch of the steel support), rock bolts of specified specifications (including the number of rock bolts), etc.

[0086] In this way, according to the design method for mountain tunnel supports (S20), by applying the equivalent elastic modulus of sprayed concrete set by the approximate formula (A) set by the method for setting the approximate formula for the equivalent elastic modulus of sprayed concrete (S10) to the analysis model, it is possible to efficiently design suitable and rational mountain tunnel supports that reflect the on-site conditions.

[0087] In addition, the present invention is not limited to the configuration shown here, and may be implemented in other embodiments in which other components are combined with the configurations and the like of the above-mentioned embodiment. In this regard, the present invention may be modified within the scope of the gist of the present invention, and may be appropriately determined according to the application form. [Explanation of symbols]

[0088] S10: Method for determining the approximate formula for the equivalent elastic modulus of shotcrete (method for determining the approximate formula) S12:A process S14:B process S16:E process S18:C process, D process S20: Design method of support for mountain tunnels (Design method of support) S22:F process S24:G process

Claims

1. A method for setting an approximation formula for the equivalent elastic modulus of sprayed concrete, taking into account the rigidity of the sprayed concrete applied to the wall surface of a tunnel over time, comprising: A step A includes carrying out a multi-stage stress relaxation test on a specimen of the sprayed concrete, in which a displacement that changes stepwise with each elapsed time according to the age of the specimen is loaded, and identifying the stress-time relationship of the specimen; A process B of performing a reproduction analysis to reproduce the stress-time relationship and identifying mechanical properties according to the material age of the specimen; A step C of carrying out a sequential excavation analysis of a tunnel using an analytical model including a shotcrete model having mechanical properties according to the age of the material and a surrounding ground model; A step D of setting the equivalent elastic modulus from the stress-strain relationship of the sprayed concrete model obtained by the sequential excavation analysis of the tunnel; In the steps C and D, A stepwise excavation analysis of the tunnel is carried out by a parametric study for at least one of the parameters including a tunnel diameter, an elastic modulus of the ground, a cycle time, and a strength of the shotcrete; A method for setting an approximate equation for the equivalent elastic modulus of sprayed concrete, characterized in that an approximate equation for the equivalent elastic modulus, which is a function of at least one of the parameters, is created based on the results of the sequential excavation analysis of the tunnel by the parametric study.

2. 2. The method for setting an approximate equation for the equivalent elastic modulus of sprayed concrete according to claim 1, characterized in that the approximate equation is created by assuming a Gompertz curve as a function of the cycle time.

3. A method for setting an approximate equation for the equivalent elastic modulus of sprayed concrete according to claim 2, characterized by creating the following approximate equation (A). [0010]

4. The method for setting an approximation equation for the equivalent elastic modulus of sprayed concrete according to claim 1 or 2, characterized in that the mechanical property in the step B is a viscoelastic property.

5. In the reproduction analysis in the step B, a viscoelastic model expressing the stress-time relationship is used as a mechanical model, The viscoelastic model is composed of spring elements that represent elastic behavior and dashpot elements that represent viscous behavior, The method for setting an approximation equation for the equivalent elastic modulus of sprayed concrete described in claim 1 or 2, characterized in that in step B, the viscosity coefficient of the dashpot element is adjusted to fit the mechanical characteristics to the stress-time relationship of the specimen.

6. The method further includes a step E of performing a compressive strength test on the specimen, A method for setting an approximation equation for the equivalent elastic modulus of sprayed concrete as described in claim 5, characterized in that the elastic modulus for each age of the test specimen determined by the compressive strength test is applied to the spring element in step B.

7. In the multi-stage stress relaxation test in the step A, a constant displacement is maintained for a certain elapsed time, and the constant displacement is changed according to the elapsed time, 3. The method for setting an approximation equation for the equivalent elastic modulus of sprayed concrete according to claim 1 or 2, characterized in that the change in displacement is performed instantaneously.

8. A process F for setting an equivalent elastic modulus of the sprayed concrete by the method for setting an approximation formula for the equivalent elastic modulus of the sprayed concrete according to claim 1 or 2; A method for designing supports for a mountain tunnel, comprising a step G of applying the equivalent elastic modulus of the sprayed concrete to a mountain tunnel model to perform a numerical analysis and designing a specified support for the mountain tunnel.

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