A method for acquiring rock material explosion impact data

Abstract

The application relates to the technical field of engineering material explosion and impact data evaluation, in particular to a rock material explosion impact data acquisition method, which comprises the following steps: based on the modification of an initial HJC model, a modified HJC model suitable for rock materials is obtained; the parameters in the modified HJC model are determined; and based on rock explosion experiments and impact experiments and the modified HJC model, rock material explosion experiment data and rock material impact experiment data are acquired. The rock material impact experiment data can be accurately acquired through the modified HJC model.

Description

TECHNICAL FIELD

[0001] The application relates to the technical field of engineering material explosion and impact data evaluation, in particular to a rock material explosion impact data acquisition method. BACKGROUND

[0002] In the field of civil engineering, for the process participated by building materials such as tunnel construction, it is necessary to comprehensively consider the possible conditions in the whole construction process to ensure the safety of construction. However, due to the limitation of test quantity, the traditional research method is limited in factors considered and often only obtains part of the law, which is difficult to meet the needs of engineering practice. With the development of technology, in recent years, many dynamic damage constitutive models for describing the internal force change process and failure mechanism of building materials under external load in the construction process have been proposed. The essence of the damage constitutive model is to study the constitutive relationship, that is, the relationship between the stress tensor and the strain tensor of the building material in the specific application scene. Correspondingly, a set of relations connecting the parameters describing the deformation of continuous medium and the parameters describing the internal force is called constitutive equation. The constitutive equation is a comprehensive reflection of the macroscopic mechanical properties of structure or material and is one of the important contents of rational mechanics research.

[0003] At present, HJC is one of the most commonly used constitutive models in engineering. Compared with other models, HJC model has a simpler constitutive relationship and fewer initial parameter quantities, and considers hydrostatic pressure, damage factor and strain rate dependence effect of material. However, since HJC model is originally proposed for concrete material, when it is applied to concrete material, the recommended parameter value can be directly used to describe the relationship between DIF and strain rate, but the parameter value in rock material needs further research. In addition to HJC model, other several commonly used dynamic damage constitutive models such as JH-2 model, K&C model and RHT model also have these shortcomings in describing rate effect.

[0004] Rock is a commonly used material in civil engineering and military engineering industries. In the process of roadway excavation, coal mining and projectile impact, rock material often presents different failure modes under the action of strong dynamic load. Among them, the rock material near the load usually occurs compressive-shear crushing failure, while the rock far from the load will occur tensile failure under the action of tensile stress, accompanied by the initiation and propagation of tensile cracks. In order to reasonably predict the failure form of rock material under different external loads and provide theoretical guidance for engineering, it is necessary to clarify the action mechanism of load and the corresponding internal force change process of rock material. Therefore, it is very important to take appropriate methods to improve HJC model and accurately obtain rock material explosion impact data through the improved HJC model. SUMMARY

[0005] In order to make the current HJC model be able to accurately obtain the explosion impact data of the rock material, the application provides a rock material explosion impact data obtaining method.

[0006] Embodiments of the application are implemented as follows:

[0007] A rock material explosion impact data obtaining method comprises:

[0008] Based on the correction of the initial HJC model, a corrected HJC model suitable for the rock material is obtained;

[0009] The parameters in the corrected HJC model are determined;

[0010] Based on the rock explosion experiment, the impact experiment and the corrected HJC model, the rock material explosion experiment data and the rock material impact experiment data are obtained;

[0011] The step of correcting the initial HJC model comprises,

[0012] Three limit surfaces are used to correct the strength model in the initial HJC model, wherein the three limit surfaces comprise a maximum strength surface, a residual strength surface and a yield surface, and the corrected strength model has continuity at the discontinuity point; wherein the maximum strength surface is represented by a piecewise function, the residual strength surface is in parallel relationship with the maximum strength surface, and the yield surface is determined based on an interpolation manner between the maximum strength surface and the residual strength surface;

[0013] The yield surface is corrected based on a dynamic enhancement factor, wherein the dynamic enhancement factor comprises a compression strain rate enhancement factor and a tensile strain rate enhancement factor; the compression strain rate enhancement factor is a ratio of a dynamic compressive strength to a static compressive strength, and the tensile strain rate enhancement factor is a ratio of a dynamic tensile strength to a static tensile strength.

[0014] The damage model in the initial HJC model is corrected into a total damage model coupling tensile damage and compression damage, and the tensile damage model is represented by an exponential tensile softening function.

[0015] In a possible implementation manner, the maximum strength surface σ m The piecewise function represented by formula (1) is used to represent,

[0016]

[0017] In the formula, a1 and a2 are limit surface parameters, The tensile-compression meridian ratio is used to describe the shape change of the failure surface with the change of hydrostatic pressure, and the tensile-compression meridian ratio Formula (2) is used to represent:

[0018]

[0019] In a possible implementation, the residual strength surface σ r is represented by formula (3):

[0020]

[0021] In a possible implementation, the yield surface is represented by formula (4):

[0022] σ y = r [D(σ r - σ m ) + σ m ] (4)

[0023] In the formula, r is the ratio of the current meridian to the compression meridian, which is related to the Lode angle, and is specifically shown in formula (5):

[0024]

[0025] In the formula, |S ij | is the determinant of the deviatoric stress tensor, that is, the third invariant.

[0026] In a possible implementation, the dynamic enhancement factor is shown in formula (6):

[0027]

[0028] In the formula: is the strain rate, is the reference strain rate, W x , W y , S and F m are related parameters, values of the related parameters are determined through rock dynamic tension and compression experiment data; at this time, the yield surface is represented by formula (7):

[0029]

[0030] In the formula: and are the yield surface, the maximum strength surface and the residual strength surface respectively after correction of the strain rate.

[0031] In a possible implementation, in formula (7), 1.0 / s.

[0032] In a possible implementation, the tension damage model can be represented by formula (8):

[0033] ​

[0034] where n1 and n2 are constants, ε frac is the tensile strain at break, ε p is the equivalent plastic strain; at this time, the total damage is shown as formula (9),

[0035] D total = 1 - (1 - D c )(1 - D t ) (9)

[0036] where D c is the compressive damage.

[0037] In one possible implementation, the state equation in the modified HJC model is expressed by the following piecewise function:

[0038]

[0039] where μ is the volumetric strain, f t is the tensile strength of the material, D is the damage factor, μ crush and μ plock are the volumetric strains corresponding to P crush and P lock respectively, where μ plock includes the plastic volumetric strain μ lock and the elastic volumetric strain.

[0040] In one possible implementation, the volumetric strain K, the elastic limit hydrostatic pressure P crush and the elastic limit volumetric strain μ crush are calculated by the following three formulas respectively:

[0041]

[0042] P crush = f c / 3

[0043] μ crush = P crush / K

[0044] The plastic compaction volumetric strain μ lock is calculated by the following two formulas:

[0045] μ lock = ρ g / ρ0

[0046] ρ g = ρ0 / (1-q)

[0047] where q is the porosity of the granite. K1, K2 and K3 are calculated by the state equation P > Plock The curve of the stage is fitted with Hugoniot experimental data points, and the value of the pressure parameter is obtained, and the value of μ is obtained by back calculation after the value of the pressure parameter is obtained. plock

[0048] Optionally, the Hugoniot experimental data is selected from literature reference values or data points are obtained by the Hugoniot empirical formula as follows,

[0049] In the formula, C1 and S1 are empirical coefficients related to the properties of the rock.

[0050] In a possible implementation, the rock material explosion experiment data and impact experiment data include at least one of the shape and size of a crater and a plug, a residual velocity of a projectile, reflected and transmitted waveforms, brittle tensile failure of the rock, crack-related data, unit peak pressure at different positions of a blast hole, and a final failure mode of a sample.

[0051] The technical solution provided in the application can achieve at least the following beneficial effects:

[0052] In view of the deficiencies of the existing constitutive model, the strength model and the damage model in the initial HJC constitutive model are improved, and the optimization of the strain rate relationship and the determination of each parameter are also involved. A modified HJC model that can accurately describe the failure mode of geotechnical brittle materials under external dynamic load is obtained, which helps to accurately obtain rock material impact experiment data through the modified HJC model, and provides certain theoretical guidance for the field of rock material explosion impact data evaluation in the future. DETAILED DESCRIPTION

[0053] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed to be used in the embodiments or the prior art description will be briefly introduced. Obviously, the drawings in the following description are some embodiments of the present application, and other drawings can also be obtained by those skilled in the art without creative labor.

[0054] Figure 1 It is a constitutive relationship diagram of the initial HJC model, wherein Fig. (a) represents a state equation; Fig. (b) represents a strength model; and Fig. (c) represents a damage model.

[0055] Figure 2 It is a flowchart of a rock material explosion impact data acquisition method in an embodiment;

[0056] Figure 3 It is a specific step flowchart of step 100 in the embodiment; Figure 2

[0057] ​​Figure 4 The intensity model diagram after correction, wherein, diagram (a) represents the relationship diagram among three limit surfaces; diagram (b) represents the deviation plane diagram;

[0058] Figure 5 The rock material DIF data fitting curve diagram, wherein, diagram (a) represents the DIF fitting curve; diagram (b) represents the DIF fitting curve; T C

[0059] Figure 6 The three tensile strain softening curve schematic diagram;

[0060] Figure 7 The rock material Hugoniot data fitting result, wherein, diagram (a) represents the fitting result of different types of rocks; diagram (b) represents the granite fitting result based on the Hugoniot empirical formula;

[0061] Figure 8 The granite limit surface parameter fitting result diagram;

[0062] Figure 9 The projectile penetrating granite target plate schematic diagram, wherein, diagram (a) is the experimental scene schematic diagram; diagram (b) is the experimental model diagram;

[0063] Figure 10 The damage form comparison diagram of the experimental group, the corrected HJC constitutive model group and the initial HJC constitutive model group after the granite target plate is impacted;

[0064] Figure 11 The comparison diagram of the theoretical and the residual velocity of the projectile predicted by the corrected HJC constitutive model and the initial HJC constitutive model;

[0065] Figure 12 The corrected HJC model parameter sensitivity analysis result;

[0066] Figure 13 The tuffaceous sandstone SHPB experimental scene diagram and experimental model diagram;

[0067] Figure 14 The three wave comparison diagram in the tuffaceous sandstone SHPB experiment;

[0068] Figure 15 The damage form comparison diagram of the tuffaceous sandstone sample after being impacted (the real length of the steel rod is not shown), wherein, diagram (a) is the improved HJC-100μs; diagram (b) is the improved HJC-160μs; diagram (c) is the improved HJC-500μs; diagram (d) is the corrected HJC-internal damage diagram; diagram (e) is the initial HJC-internal damage diagram; diagram (f) is the actual state diagram in the experiment;

[0069] ​​Figure 16 Figure 1 is a diagram of a granite air coupling single-hole blasting experiment scene and an experimental model diagram;

[0070] Figure 17 Figure 2 is a diagram of a granite single-hole blasting damage form comparison diagram, wherein Figure (a) represents an initial HJC-copper-containing tube; Figure (b) and Figure (c) represent an improved HJC-copper-containing tube; Figure (d) represents an experimental real state diagram; Figure (e) represents an original HJC-copper-free tube; Figure (f) and Figure (g) represent an improved HJC-copper-free tube;

[0071] Figure 18 Figure 3 is a diagram of a unit peak pressure attenuation law, wherein Figure (a) represents an improved HJC; Figure (b) represents an original HJC;

[0072] Figure 19 Figure 4 is a diagram of a water coupling blasting experiment device;

[0073] Figure 20 Figure 5 is a diagram of a water coupling blasting experiment model;

[0074] Figure 21 Figure 6 is a diagram of a water coupling blasting rock damage process, wherein Figure (a) is 5 μs; Figure (b) is 10 μs; Figure (c) is 20 μs; Figure (d) is 100 μs;

[0075] Figure 22 Figure 7 is a diagram of a water coupling blasting damage form comparison diagram. DETAILED DESCRIPTION

[0076] In order to make the purposes, implementations and advantages of the present application clearer, the following will clearly and completely describe the exemplary implementations of the present application with reference to the accompanying drawings of the exemplary implementations of the present application. Obviously, the described exemplary implementations are only a part of the implementations of the present application, but not all the implementations of the present application. It should be understood that the specific implementations described herein are only used to explain the present application, and are not intended to limit the present application.

[0077] It should be noted that the brief description of the terms in the present application is only for the convenience of understanding the implementations described next, and is not intended to limit the implementations of the present application. Unless otherwise specified, these terms should be understood according to their ordinary and general meanings.

[0078] The terms "first", "second", "third", etc. in the specification and claims and the above-mentioned drawings are used to distinguish similar or similar objects or entities, and do not necessarily mean to limit the specific order or sequence, unless otherwise specified. It should be understood that the terms used in this way can be interchanged under appropriate circumstances.

[0079] The terms "comprising" and "having" and any variations thereof are intended to cover a non-exclusive inclusion, for example, a product or apparatus that comprises a list of components does not necessarily comprise only those components in the list and can include other components not expressly listed or inherent to such product or apparatus.

[0080] For the convenience of clearly describing the technical solutions of the embodiments of the present application, the following briefly introduces some terms and technologies involved in the embodiments of the present application:

[0081] As shown in Figure 1 , the initial HJC constitutive model is composed of a state equation, a strength model and a damage model, and the strain rate effect of the material is considered. Under the action of strong dynamic load from outside, the material will be in a high pressure state and a large volume strain will be generated, and the state equation can be used to describe the quantitative correspondence between the hydrostatic pressure and the volume strain. The state equation relationship in the HJC constitutive model can be represented by the following piecewise function, and the state equation can be represented by the graph (a) in Figure 1 .

[0082]

[0083] In the formula: μ is the volume strain, f t is the tensile strength of the material, D is the damage factor, μ crush and μ plock are the volume strains corresponding to P crush and P lock respectively, wherein μ plock includes the plastic volume strain μ lock and the elastic volume strain, K1, K2 and K3 are all undetermined parameters.

[0084] As can be seen from the graph (a) in Figure 1 , when the hydrostatic pressure P is greater than 0, the material will first experience an elastic stage; after P is greater than the pore collapse pressure P crush , the internal micro-pores begin to be gradually compacted, entering a plastic compaction stage; after P reaches the pore compaction pressure P lock , the internal air is discharged and the internal micro-pores have been completely extruded and compacted, thus entering a plastic complete compaction stage; when P is less than 0, after experiencing an elastic stretching stage, there will be a cut-off pressure of-f t (1-D), which can be regarded as an ideal elastic-plastic stretching stage.

[0085] With the increase of the hydrostatic pressure, the material strength will gradually increase. In the initial HJC constitutive model, the material strength is represented by the equivalent stress, and the normalized equivalent stress is represented by the following strength equation, and the strength model graph can be referred to the graph (b) in Figure 1 .

[0086]

[0087] wherein: σ * is the normalized equivalent stress, P * is the normalized hydrostatic pressure, A, B, N are strength related parameters (limit surface parameters), C is a strain rate related parameter, is the characteristic strain rate, is the reference strain rate, S max is the maximum normalized equivalent stress.

[0088] In addition, the damage model is calculated by the equivalent plastic strain and plastic volume strain accumulation, specifically, the damage model D can be represented by the following formula:

[0089]

[0090] wherein: Δε p and Δμ p are the equivalent plastic strain increment and plastic volume strain increment respectively, and are the fracture plastic strain and fracture volume strain respectively. The damage model diagram can be referred to Fig. (c) in Figure 1 With the increase of the strain rate and the damage degree, the strength of the material will increase and decrease respectively to a certain extent. However, with the increase of the hydrostatic pressure, the influence of A(1-D) part on the strength gradually decreases, which also leads to the small difference in the strength of the undamaged and completely damaged units under high hydrostatic pressure.

[0091] Since the above initial HJC constitutive model is initially proposed for concrete materials, the recommended parameter values can be directly used for description when it is applied to concrete materials, but the parameter values in rock materials need further research.

[0092] It should be noted that the stress-strain relationship of the material under static action and dynamic action is different, the most important reason is that the strain rate causes the change of the material strength, in addition, the initial HJC constitutive model also ignores the influence of the third invariant of the deviatoric stress tensor on the yield surface. Based on this, the application provides a rock material explosion impact data acquisition method, as shown in Figure 2 , specifically including the following schemes:

[0093] Step 100, based on the modification of the initial HJC model, a modified HJC model suitable for rock materials is obtained. As shown in Figure 3 , this step specifically includes steps 110-130:

[0094] Step 110, the strength model in the initial HJC model is corrected by using three limit surfaces, including the maximum strength surface σ m , the residual strength surface σ r and the yield surface σ y , and the corrected strength model has continuity at the discontinuous point.

[0095] Firstly, referring to Fig. (a) in Figure 4 , the maximum strength surface σ m is expressed by a piecewise function shown in formula (1), which ensures continuity at the discontinuous point.

[0096]

[0097] In the formula, a1 and a2 are limit surface parameters, f c represents static compressive strength, is the tensile-compressive meridian ratio, is used to describe the shape change of the failure surface with the change of hydrostatic pressure P; referring to Fig. (b) in Figure 2 , it can be expressed by formula (2), which uses linear interpolation at the discontinuous point.

[0098]

[0099] Secondly, the residual strength surface σ r is approximately parallel to the maximum strength surface σ m , so σ r can be expressed by formula (3).

[0100]

[0101] Then, the yield surface σ y is determined by interpolating between the maximum strength surface and the residual strength surface, and the yield surface σ y is expressed by formula (4).

[0102] σ y = r [D (σ r - σ m ) + σ m ] (4)

[0103] In the formula, r is the ratio of the current meridian to the compression meridian, which is related to the Lode angle , and is specifically shown in formula (5).

[0104]

[0105] In the formula, |S ij | is the determinant of the deviatoric stress tensor, i.e. the third invariant.

[0106] It can be understood that, by introducing the relationship between the third invariant of the deviatoric stress tensor, the Lode angle and the meridian, the yield surface is reasonably corrected, the problem that the initial HJC model cannot describe the shape change of the yield surface when it is from low pressure to high pressure is improved, and the HJC model finally obtained by the scheme can be applied to rock materials, so that the blasting impact data of the rock materials can be accurately obtained by the HJC model finally obtained.

[0107] In step 120, the yield surface is corrected based on a dynamic enhancement factor, wherein the dynamic enhancement factor includes a compression strain rate enhancement factor and a tensile strain rate enhancement factor; the compression strain rate enhancement factor is a ratio of a dynamic compressive strength to a static compressive strength, and the tensile strain rate enhancement factor is a ratio of a dynamic tensile strength to a static tensile strength.

[0108] Specifically, since the compression strain rate enhancement factor is a ratio of a dynamic compressive strength to a static compressive strength, and the tensile strain rate enhancement factor is a ratio of a dynamic tensile strength to a static tensile strength, the dynamic enhancement factor can be expressed by the following formula:

[0109]

[0110] In the formula, DIF C and DIF T are the compression strain rate enhancement factor and the tensile strain rate enhancement factor respectively. c f c , f t and f t represent the dynamic compressive strength, the static compressive strength, the dynamic tensile strength and the static tensile strength of the material respectively.

[0111] Since the initial HJC constitutive model is initially proposed for concrete materials, the relationship between the dynamic enhancement factor DIF and the strain rate is basically the recommended value of CEB-FIB, which also has two unavoidable problems: one is that the recommended value is reasonable for concrete materials, but it is often difficult to determine for rock materials. In addition, previous studies have found that both concrete and rock materials have an upper limit value of DIF, which is ignored by existing models, so it is easy to overestimate DIF under high strain rate conditions, but this problem has not been effectively solved, so step 120 is performed.

[0112] In this step, the dynamic enhancement factor DIF can be expressed by formula (6):

[0113]

[0114] In the formula, is the strain rate, For the reference strain rate, W x S, F m and W y These are the relevant parameters.

[0115] Currently, for W x W y S and F m The reference values ​​are all limited to concrete materials. Therefore, this application determines the DIF of rock materials as shown in Equation (6) by fitting a large amount of dynamic tensile and compression test data of rocks. T and DIF C Relationship with strain rate.

[0116] The process of determining the relationship between DIFT and DIFC as a function of strain rate in equation (6) above can be found in [reference needed]. Figure 5 As shown, through analysis Figure 5 It can be seen that the strain rate of rock materials is around 10. 0 When the value is around / s, DIF begins to increase rapidly, so the rock's Taking 1.0 / s, when the strain rate reaches 10 4 / time, DIF T It approaches the limiting value of 8.56. DIF at different strain rates. C The experimental data are generally within the predicted range of tensile-compressive strength ratio between 0.1 and 0.3, and the data are particularly relevant when the strain rate reaches 10. 4 When the value is / , the corresponding limit value can be predicted. Therefore, it can be seen that the experimental data for tensile DIF and compressive DIF are consistent with the DIF determined in this application. T and DIF C The goodness of fit of the relationship with strain rate variation is high.

[0117] Based on equation (6), the yield surface is modified, and the modified yield surface can be expressed by equation (7):

[0118]

[0119] In equation (7): and These are the yield surface, maximum strength surface, and residual strength surface after strain rate correction, respectively. It can be understood that the selection of tension and compression of DIF is positively or negatively correlated with hydrostatic pressure.

[0120] Since step 120 uses DIF to modify the yield surface, that is, it takes into account the strain rate dependence effect of the material, the HJC model finally obtained in this application can be accurately applied to rock materials.

[0121] The initial HJC model does not reasonably consider the brittle tensile damage of the rock-soil material under the action of external dynamic load in the process of describing the material compression damage, and therefore the step 130 is further performed.

[0122] In the step 130, the damage model in the initial HJC model is modified into a total damage model in which the tensile damage and the compression damage are coupled, and the tensile damage model is expressed by an exponential tensile softening function.

[0123] It should be noted that the tensile strain softening of the material mainly has three forms of linear softening, bilinear softening and exponential softening, and the three different tensile strain softening forms can be referred to in Figure 6 .

[0124] Since the rock material is more consistent with the exponential softening form, the exponential tensile softening function shown in the following formula (8) is used to describe the tensile damage of the rock material.

[0125]

[0126] In the formula (8), n1 and n2 are constants, n1 can be 3.0, and n2 can be 6.93; ε frac is the tensile fracture strain. ε p is the equivalent plastic strain.

[0127] By coupling the tensile damage and the compression damage, a total damage model can be obtained, which can be expressed by the formula (9):

[0128] D total = 1-(1-D c )(1-D t ) (9)

[0129] In the formula (9), D c is the compression damage, which is consistent with the damage calculation method in the initial HJC model, that is, In the formula, Δε p and Δμ p are the equivalent plastic strain increment and the plastic volume strain increment, and are the fracture plastic strain and the fracture volume strain.

[0130] After the above steps 110-130 are modified, the new HJC model suitable for the rock-soil material obtained by the present application can be expressed by the following three parts:

[0131] The first part is a state equation, which can be expressed by the following segmented function:

[0132]

[0133] Wherein: μ is the volumetric strain, f t is the tensile strength of the material, D is the damage factor, μ crush and μ plock are the volumetric strain corresponding to P crush and P lock respectively, wherein μ plock contains the plastic volumetric strain μ lock and the elastic volumetric strain.

[0134] Second part: strength model, the strength model is represented by the maximum strength surface σ m , the residual strength surface σ r and the yield surface σ y , in particular:

[0135]

[0136] In the above formula: a1 and a2 are the limit surface parameters, is the meridian ratio of tension and compression, for describing the shape change of the failure surface with the change of hydrostatic pressure; The relationship between the third invariant of deviatoric stress tensor, Lode angle and meridian can be seen from the above formula (5), and the dynamic enhancement factor DIF can be represented by the above formula (6), which will not be repeated here. and are the yield surface, the maximum strength surface and the residual strength surface respectively after strain rate correction.

[0137] Third part, damage model, the damage model can be represented by the following formula: D total =1-(1-D c )(1-D t ), wherein, D c is Δε p and Δμ p are the equivalent plastic strain increment and the plastic volumetric strain increment, and are the fracture plastic strain and the fracture volumetric strain.

[0138] Through the above complete new HJC model suitable for rock and soil materials, it can be known that the new HJC model suitable for rock and soil materials in the application contains pressure parameters K, K1, K2, K3, P crush , P lock , μ crush , μ lock and μ plock , limit surface parameters a1 and a2, rate effect parameters W x , S, F mand W y , damage parameters D1, D2 and ε frac and basic mechanical parameters f c , f t , G, p0 and Poisson's ratio γ. Among them, the rate effect parameter can be directly taken as 1.0 / s. The remaining parameters to be determined can be determined by the following steps 200:

[0139] Step 200, determine each parameter in the modified HJC model (i.e. a new HJC model suitable for rock-soil materials).

[0140] Specifically, (1) the determination of each parameter in the state equation, the method is as follows:

[0141] The volumetric strain K, the elastic limit hydrostatic pressure P crush and the elastic limit volumetric strain μ crush can be calculated by the following three formulas respectively:

[0142]

[0143] P crush = f c / 3

[0144] μ crush = P crush / K

[0145] The plastic compaction volumetric strain μ lock can be calculated by the following two formulas:

[0146] μ lock = p g / p0

[0147] p g = p0 / (1-q)

[0148] Wherein, q is the porosity of granite.

[0149] K1, K2 and K3 are obtained by fitting the Hugoniot experimental data points to the curve in the state equation P>P lock stage, and the Hugoniot experimental data of some rocks can be found in the previous scholars' research. For rock materials lacking Hugoniot experimental data, the data points can be obtained through the Hugoniot empirical formula shown in formula (10).

[0150]

[0151] wherein C1 and S1 are empirical coefficients related to rock properties. It is noted that formula (10) is used to fit Hugoniot experimental data of most rock materials, and the fitting results can be seen in Fig. (a) of Figure 7 , it can be seen that the fitting curve and experimental data points are very consistent, proving that it is reasonable to calculate Hugoniot data points by the above formula. Therefore, Hugoniot data points can be calculated by the above formula, and C1 and S1 of granite are taken as 2100 m / s and 1.65 respectively. The state equation P > P lock , and the fitting results of Hugoniot data points in the phase can be seen in Fig. (b) of Figure 7 , from which the value of the pressure parameter can be obtained, and based on this, the value of μ plock is obtained by back calculation.

[0152] (2) Determination of parameters in the strength model, the method is as follows:

[0153] Since the effective stress values of the last two segments of the maximum strength surface are all less than the compressive strength of the material, the triaxial test data cannot be used to determine the strength-related parameters a1 and a2. For rock materials, the expression of the first segment of the maximum strength surface is used to fit the triaxial test data of the rock. Taking granite as an example, the fitting results based on the triaxial test data can be seen in Figure 8 , in the strength model of granite, a1 is 0.454, and a2 is 0.055. W x , S, F m and W y are determined by fitting.

[0154] (3) Determination of parameters in the damage model, the method is as follows:

[0155] The value of ε frac is related to the element size of the numerical model, so it can be calculated by the following formula:

[0156]

[0157] wherein G f is the fracture energy (taken as 80 Nm / m 2 ). h e is the equivalent element size, which can be approximately calculated by taking the cube root of the element volume in three-dimensional analysis. f t is the tensile strength of the material.

[0158] D1 and D2 mainly control the compression damage range and size, which can be taken as 0.04 and 1.0 respectively according to empirical values, and then adjusted according to specific application situations.

[0159] Step 300, obtaining rock explosion experiment data and impact experiment data based on rock explosion experiment and impact experiment and the modified HJC model. As an example, the projectile penetration granite target experiment, the SHPB experiment of tuff sandstone, the granite air coupling explosion experiment and the water coupling explosion experiment can be simulated.

[0160] It should be noted that when obtaining the rock material explosion experiment data and impact experiment data by the modified HJC constitutive model, the modified HJC constitutive model needs to be introduced into the LS-DYNA material library, and the strain increment is obtained through the experimental parameters in the rock explosion experiment and impact experiment. The strain increment can be used to represent the current strain, volume strain, deviatoric strain and equivalent strain and other physical quantities. Based on these physical quantities and combined with the yield criterion, it is judged whether the material is yielded, and the stress value is updated cyclically. Among them, the judgment of tensile and compressive damage is based on hydrostatic pressure, and then the required rock material explosion experiment data and impact experiment data are obtained through the state equation, damage model and strength model in the modified HJC constitutive model. And the rock material explosion experiment data and impact experiment data include but are not limited to the shape and size of the crater and the plug, the residual velocity of the projectile, the reflection and transmission waveform, the brittle tensile failure of the rock, the crack related data, the peak pressure of the unit at different positions of the blast hole, and the final failure form of the sample. The specific calculation process is as follows:

[0161] (1) Projectile penetration granite target experiment

[0162] As shown in Figure 9 , the following experimental conditions are set to simulate the projectile penetration granite target experiment: the compressive strength of the granite used in the experiment is 163 MPa, the tensile strength is 7.1 MPa, and the Young's modulus is 54 GPa. The size of the target plate is 60 cm x 60 cm x 10 cm, the bottom radius and length of the steel projectile are 1.0 cm and 9.49 cm respectively, and the CRH of the projectile is 3.0. The density of the projectile can be approximately calculated from the mass of the projectile (197 g) as 7.85 g / cm 3 . Since the model has symmetry, a 1 / 4 model is established, and a symmetric boundary is added at the symmetric position; At the same time, fixed constraints are added at the boundary of the model. The parameter values of the improved HJC model in this application for the above granite are shown in Table 1.

[0163] Table 1. Improved HJC model parameter values of the impacted granite target

[0164]

[0165] As shown in Figure 10As shown in the experiment, a certain range of front crater is formed on the impact surface after the projectile impacts the target plate; after the compression-shear crushing zone and the tunnel zone are formed in the middle of the target plate, the rock of the rear crater is stripped and a conical plug is formed. By comparison, it can be seen that, compared with the original HJC constitutive model (i.e. the initial HJC model), the improved HJC constitutive model (i.e. the modified HJC constitutive model) can better represent the actual fracture mode of the target plate after the projectile penetration, and the shape and size of the front and rear craters and the conical plug calculated by the improved HJC constitutive model are in good agreement with the experiment.

[0166] Referring to Figure 11 , a theoretical model for predicting the residual velocity of the projectile after penetrating the target plate is given in the article of the projectile penetration experiment, and the calculation result can be well fitted by the Recht-Ipson formula shown in the following formula.

[0167] V r = a (V s -Vb 12 ) 1 / 2

[0168] In the formula, V r , V s and V b1 are the residual velocity, the initial velocity and the limit perforation velocity respectively, and a is the correlation coefficient.

[0169] By comparing the residual velocities of the projectiles calculated by the improved HJC, RHT and the theoretical prediction before and after the improvement, it can be seen that the residual velocities of the projectiles calculated by the improved HJC and the original HJC are closer to the theoretical prediction results, while the calculation result of RHT is obviously smaller than the theoretical prediction result when the initial velocity of the projectile is high. The reason for the above result is that the RHT model does not consider the upper limit value of the DIF of the material, and the strength of the rock target plate is overestimated at high strain rate, so that the residual velocity of the projectile is too small. The improved HJC considers the upper limit value of the DIF at high strain rate, and the strain rate related parameters of the rock material are reasonably determined in the present application, so that the calculation result is more accurate. It is worth noting that, although the original HJC does not consider the upper limit value of the DIF of the material, the parameter S max in the strength model controls the upper limit value of the strength surface, so the calculation result is also in good agreement with the theoretical prediction result.

[0170] In order to provide reference for parameter adjustment in the subsequent application process of the constitutive model, the parameter sensitivity analysis is carried out by taking the residual velocity of the projectile as the objective function. The parameters of the model are adjusted up and down by 20%, and the change rule of the residual velocity of the projectile is observed. We consider that the parameters which make the change range of the residual velocity of the projectile exceed 20% are extremely sensitive parameters, the parameters which make the change range of the residual velocity of the projectile between 10% and 20% are relatively sensitive parameters, and the remaining parameters are not sensitive parameters. The parameter sensitivity analysis result is shown in Table 1.Figure 12 As can be seen from the figure, the extremely sensitive parameters are ρ0 and f. t a1 and ε frac Among them, a1 has the most significant impact on the results. Other sensitive parameters include f. c G, F m W x W y P lock μ crush and a2.

[0171] (2) SHPB test on tuffaceous sandstone

[0172] The tuffaceous sandstone sample was taken from a tunnel in Xinjiang. The rock's compressive and tensile strengths were 60 MPa and 4 MPa, respectively, and its shear modulus was 10.08 GPa. (See also...) Figure 13 The rock was processed into standard cylindrical specimens with a diameter of 75 mm and a height of 37.5 mm. The processing non-uniformity of the specimens was less than 0.05 mm, and the end faces of the specimens were kept perpendicular to the axis. Dynamic splitting experiments were conducted using the SHPB system, with incident and transmission rods of 5 m and 4 m in length, respectively, and an impact velocity of 4.95 m / s. To maintain consistency with the experiment as much as possible, the actual incident waveform was extracted and applied to the beginning of the incident rod. A non-reflective boundary was applied to the end of the transmission rod to simulate the absorption effect of the energy-absorbing rod on the transmitted wave. The parameter values ​​of the improved HJC model in this application for the above-mentioned tuffaceous sandstone are shown in Table 2.

[0173] Table 2. Parameter values ​​of the improved HJC model for tuffaceous sandstone samples

[0174]

[0175] See Figure 14 Waveforms were extracted for comparison. Since the actual incident waveform from the experiment was directly extracted and applied to the beginning of the incident rod, the incident waveform used in the numerical simulation is consistent with the incident waveform in the experiment. The peak transmission strain calculated by the original HJC is very close to the experimental results, but it cannot predict the gradual softening stage after the tensile peak very well. The reflection and transmission waveforms calculated by the improved HJC in this application are in better agreement with the experimental results, where Tr represents the projected strain and Re represents the reflected strain.

[0176] See Figure 15 When the incident wave reaches the sample, compression-shear pulverization zones are generated at both ends, accompanied by the initiation of a crack in the center. As the stress wave continues to propagate, two main cracks and several secondary cracks form in the center of the sample. With the completion of the main cracks, the rock in the center of the sample peels off. Ultimately, a macroscopic fracture surface forms in the center of the sample. Compared to the original HJC, the improved HJC can better predict the brittle tensile failure of rock.

[0177] (3) Granite air-coupled explosion experiment

[0178] See Figure 16 A simulation of a single-hole explosive detonation experiment was conducted on granite. The granite specimen had a diameter and height of 14.4 cm and 15.0 cm, respectively. A borehole with a diameter of 0.645 cm was drilled at the center of the specimen. To prevent gas from entering cracks after the explosion and causing more severe damage, a copper tube with a thickness of 0.06 cm was placed on the borehole wall. Since the axial length of the explosive was much larger than its diameter, the problem could be considered as a plane strain problem. Based on this, a quasi-three-dimensional numerical model was established, considering the rock and copper tube as Lagrangian elements and the air and explosive as ALE elements, and a fluid-structure interaction algorithm was used for calculation. The parameter values ​​of the improved HJC model in this application for the above-mentioned granite are shown in Table 3.

[0179] Table 3. Parameter values ​​of the improved HJC model for air-coupled explosive granite.

[0180]

[0181] The explosive used in the experiment was PETN explosive. In the process of obtaining the corresponding data through the modified HJC constitutive model, the JWL equation of state (EOS) as shown below is usually used. The specific parameter values ​​are shown in Table 4.

[0182]

[0183] In the formula: P J V is the detonation pressure; E is the relative volume of the detonation products; A, B, R1, R2, and ω are the initial specific internal energy. J These are the parameters of the JWL state equations.

[0184] Table 4. Parameters of PETN explosives

[0185] Density (kg / m 3 )]]> Detonation velocity (m / s) A (GPa) B (GPa) [R1] [R2] J ]]> ​ P CJ (GPa) E (GPa) 1320 6690 586 21.6 5.81 1.77 0.282 16 7.38

[0186] For a comparison of the data obtained using the modified HJC constitutive model and the experimental results, please refer to [the relevant documentation / reference]. Figure 17 After the explosives detonated, the rock near the borehole developed a dense crack zone under the influence of the blast shock wave. As the stress wave propagated further, the rock underwent significant radial crack propagation under the equivalent circumferential tensile stress. Although... Figure 17(d) is not typical of the ring tensile cracks, but also can be seen around the distribution of the approximate ring micro-cracks. Even if the literature for the sample boundary conditions are not made clear, but also from the analysis of the above experimental results, roughly judge the sample boundary is fixed by the steel plate or other materials. But it may be due to the sample around the lower flatness and lead to the sample and steel plate is not completely attached, part of the stress wave in the boundary still occurred reflection phenomenon, the rock sample under the action of the weak radial tensile stress wave ring micro-cracks. In view of this, the application in the use of improved HJC calculation considered no reflection boundary and free boundary two cases, the calculation results are shown in Figure 17 (b) and (c) of figure in the figure. Improved HJC can not only characterize the blast hole around the crack dense zone and radial tensile cracks, but also can characterize the ring crack caused by radial tensile stress, the rock sample after blasting the fracture mode is basically consistent with the experimental results. Contrary to the original HJC can only characterize the blast hole near the compression shear damage zone, and can not simulate the radial and ring tensile cracks. From Figure 17 (e) to (g) in the figure, after removing the copper pipe, the improved HJC calculation of the blast hole near the rock damage degree increases significantly, the crack distribution range increases, while the original HJC calculation results are basically the same as containing copper pipe. Thus, it is preliminarily judged that the copper pipe has little effect on the hole wall pressure, mainly to prevent the blast gas into the rock crack. And after removing the copper pipe, the rock damage degree near the blast hole increases is not due to the increase of the hole wall pressure, but due to the further expansion of the existing tensile micro-cracks under the action of the gas wedge.

[0187] In order to further verify the above guess, the peak pressure of the unit at different positions from the blast hole is extracted, and the peak pressure attenuation formula is as follows.

[0188] P r = P0(r e / r b ) -a

[0189] In the formula: P r is the peak pressure of the unit, P0 is the peak pressure of the hole wall, r e is the distance from the blast hole, r b is the blast hole radius, a is the attenuation index.

[0190] Referring to Figure 18 , the unit peak pressure attenuation law calculated by the improved HJC before and after is in good agreement with the empirical formula, and the copper pipe has little effect on the peak pressure value and the attenuation law, which also verifies the guess about the reason why the rock damage degree of the hole wall increases after removing the copper pipe is correct.

[0191] (4) Granite water coupling explosion experiment

[0192] To calculate the explosion effect of the improved HJC under different coupling media, the granite water coupling explosion experiment was simulated. The compressive strength of the granite used in the experiment was 150 MPa, the tensile strength was 7.5 MPa, and the density was 2660 kg / m 3 The bottom surface diameter of the cylindrical rock sample was 14.5 cm, and the height was 14.6 cm. A blast hole with a diameter of 0.9 cm and a height of 13.6 cm was drilled at the center of the sample. For details, please refer to Figure 19 The parameter values of the improved HJC model in this application for the above granite are shown in Table 5. The parameters of the PETN explosive used in the experiment are shown in Table 6, and the linear charge density is 3.2 g / m. According to these basic data, the diameter of the explosive can be calculated to be 0.165 cm. The cylindrical explosive was wrapped with a water hose and filled into the blast hole, and the initiation of the explosive was achieved through the detonating cord.

[0193] Table 5. Parameter values of the improved HJC model for water coupling explosion of granite

[0194]

[0195] Table 6. PETN explosive parameters

[0196] Density (kg / m 3 )]]> Detonation velocity (m / s) A (GPa) B (GPa) [R1] [R2] J ]]> ​ P CJ (GPa) E (GPa) 1500 7450 625.3 23.29 5.25 1.6 0.28 22 8.56

[0197] Referring to Figure 20 , a three-dimensional numerical model consistent with the experiment was established. Since the sample in the experiment was placed directly on the ground, a normal constraint was added to the bottom of the model. Because no circumferential cracks appeared on the top of the sample after blasting, a non-reflecting boundary was added to the periphery of the model. In order to avoid the problem of calculation interruption caused by large deformation of the element, an air coupling domain consistent with the size of the rock sample was established. In this way, the water inside the blast hole mainly serves as a detonation medium, and the air coinciding with the rock mainly serves as a flow space in the fluid-structure coupling algorithm. In this model, the water is described by the *MAT_NULL and GRUNEISEN state equation.

[0198] Referring to Figure 21 After the initiation of the explosive, the rock near the blast hole wall first underwent comminuted damage under the action of the explosion shock wave. Subsequently, the explosion shock wave decayed into a stress wave, and as the stress wave continuously propagated in the form of a cylindrical surface to the far end, the radial tensile cracks in the sample were initiated under the action of the equivalent tensile stress. With the increase of the solution time, the cracks continuously expanded, and finally a through crack was formed in the sample. Since the damage basically stopped evolving after 100 μs of calculation time, the calculation results at 100 μs can represent the final damage pattern of the sample.

[0199] Referring toFigure 22 After the explosion experiment, the sample exhibited a pulverized zone near the borehole and several radial cracks. Comparing the experimental and improved HJC calculations of the sample top damage, it is clear that the experimental sample showed asymmetric fracture, while the improved HJC calculation showed a more uniform fracture pattern. The reasons for this phenomenon may be twofold: First, real-world rocks contain numerous microcracks, but the modified HJC constitutive model treated the rock as a homogeneous material, potentially leading to a discrepancy between the calculated and experimental results. Second, given the experimental results showing a significant difference in damage on one side compared to the other, it could also be due to some eccentricity during explosive loading, resulting in uneven energy distribution. However, the rock explosion fracture mode calculated by the improved HJC is largely consistent with the experimental results, suggesting the calculation is reasonable. Compared to the improved HJC, the original HJC only characterizes the pulverized zone near the borehole, and the overall damage differs significantly from the experimental findings. Furthermore, the comparison... Figure 15 As shown in Figures (d)-(f), the improved HJC is also better than the original HJC in simulating the explosion microcracks inside the sample, which further verifies the accuracy of the improved HJC in explosion calculation.

[0200] As can be seen from the above step 300, as long as the parameter values ​​in the rock material explosion test and impact test are substituted into the modified HJC model of this application, the modified HJC model can be accurately applied to obtain rock material explosion test data and rock material impact test data.

[0201] In summary, this application improves the strength and damage models of the initial HJC model, and also involves optimizing the strain rate relationship and determining various parameters. This results in an HJC model that can accurately describe the failure mode of brittle rock and soil materials under external dynamic loads. This provides theoretical guidance for future evaluation of explosive impact data in rock materials, and also has broad application prospects in numerous practical case analyses in civil engineering and military engineering (such as tunnel excavation, mining, and projectile impact problems).

[0202] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0203] The above embodiments only express several implementation ways of the present application, and the description is specific and detailed, but it should not be understood as a limitation to the patent scope of the application. It should be pointed out that for ordinary skilled in the art, without departing from the concept of the present application, several modifications and improvements can be made, which are all within the protection scope of the present application. Therefore, the protection scope of the patent of the present application should be subject to the appended claims.

Claims

1. A method of obtaining data on the explosive impact of rock material, characterized in that The method comprises the following steps: Based on the modification of the initial HJC model, a modified HJC model suitable for rock materials is obtained; Determine the parameters in the modified HJC model; Based on the rock explosion experiment and impact experiment and the modified HJC model, the rock material explosion experiment data and rock material impact experiment data are obtained; Wherein, the step of modifying the initial HJC model comprises, Three limit surfaces are used to correct the strength model in the initial HJC model, wherein the three limit surfaces include a maximum strength surface, a residual strength surface and a yield surface, and the corrected strength model has continuity at the discontinuity point; wherein the maximum strength surface is represented by a piecewise function, the residual strength surface is in parallel relationship with the maximum strength surface, and the yield surface is determined based on the interpolation between the maximum strength surface and the residual strength surface; The yield surface is modified based on a dynamic enhancement factor, wherein the dynamic enhancement factor includes a compression strain rate enhancement factor and a tensile strain rate enhancement factor; the compression strain rate enhancement factor is the ratio of dynamic compressive strength to static compressive strength, and the tensile strain rate enhancement factor is the ratio of dynamic tensile strength to static tensile strength; The damage model in the initial HJC model is modified to a total damage model coupling tensile damage and compression damage, and the tensile damage model is represented by an exponential tensile softening function.

2. The method of claim 1, wherein, The maximum strength surface σm is represented by a piecewise function as shown in formula (1), wherein f c is the uniaxial compressive strength of the rock, f t is the tensile strength of the rock, P is the hydrostatic pressure, D is the total damage degree of the material, a1 and a2 are limit plane parameters, and φ is a ratio of tensile to compressive meridians, which is used to describe a change in shape of the failure plane with changes in the hydrostatic pressure, and is expressed by Equation (2):

3. The method of claim 2, wherein, The residual strength surface σr is represented by formula (3):

4. The method of claim 3, wherein, The yield surface is represented by formula (4): σ y = r [D(σ r -σ m )+σ m ] (4) Wherein: r is the ratio of the current meridian to the compression meridian, which is related to the Lode angle θ, and is specifically as shown in formula (5), In the formula: |S ij | is the determinant of the deviatoric stress tensor, i.e., the third invariant.

5. The method of claim 4, wherein, The dynamic enhancement factor is as shown in formula (6): wherein tanh(x) is the hyperbolic tangent function, DIF is the dynamic enhancement factor, DIF T is the tensile dynamic enhancement factor, DIF C is the compressive dynamic enhancement factor, is the strain rate, is the reference strain rate, W x , W y , S and F m are relevant parameters, the values of which are determined by rock dynamic tensile and compressive experimental data; at this time, the yield surface is expressed by equation (7), In the formulae: and are the strain rate corrected yield surface, maximum strength surface and residual strength surface, respectively.

6. The method of claim 5, wherein, in the formula (7), Take 1.0 / s.

7. The method of claim 1, wherein, The tensile damage model is represented by formula (8) where D is the total damage of the material, n1 and n2 are constants, ε frac is the tensile strain at break, ε p is the equivalent plastic strain; at this point, the total damage model is given by equation (9), D total = 1 - (1 - D c )(1 - D t ) (9) In the formula: D c is the compression damage.

8. The method of claim 1, wherein, The equation of state in the modified HJC model is represented by the following piecewise function: where K is the bulk modulus, P is the hydrostatic pressure, D is the total damage of the material, K1, K2 and K3 are pressure dependent parameters, μ is the bulk strain, f t is the tensile strength of the material, P crush is the hydrostatic pressure at the elastic limit, P lock is the hydrostatic pressure at the compaction limit, μ crush and μ plock are the bulk strains corresponding to P crush and P lock respectively, where μ plock comprises the plastic bulk strain μ lock and the elastic bulk strain.

9. The method of claim 8, wherein, said bulk modulus K, elastic limit hydrostatic pressure P crush and elastic limit bulk strain μ crush are calculated by the following three equations, respectively: P crush = f c / 3 μ crush = P crush / K where G is the rock shear modulus, γ is the Poisson's ratio, f c is the uniaxial compressive strength of the rock, μ lock is calculated from the following two equations: μ lock = p g / p0 p g = p0 / (1 - q) In the formula, q is the porosity of granite, K1, K2 and K3 are obtained from the state equation P>P lock The pressure parameter is obtained by fitting the curve of the phase to the Hugoniot experimental data points, and the value of μ plock is obtained by inverse calculation. Optionally, the Hugoniot experimental data is selected from the literature reference value or the data points are obtained by the following Hugoniot empirical formula, wherein C1and S1are empirical coefficients related to the properties of the rock.

10. The method of claim 1, wherein, The rock material explosion experiment data and impact experiment data include at least one of the following: the shape and size of the crater and the impact plug, the residual velocity of the projectile, the reflection and transmission waveform, the brittle tensile failure of the rock, the crack related data, the unit peak pressure at different positions of the blast hole, and the final failure form of the sample.

Images