The rock damage mechanism of combined rock breaking with saw blade and conical pick

The combined rock breaking method with the saw blade and conical pick is proposed to improve the rock breaking efficiency. The numerical simulation of combined rock breaking with the saw blade and conical pick is established to investigate the rock damage mechanism. And verified and modified the numerical simulation model with the rock breaking comprehensive test bench, the quantitative analysis error is less than 0.05, indicated quantitative analysis system is accuracy. The result indicated that the cutting parameters of the saw blade and conical pick affect the rock damage. And the cutting parameters of conical pick and structural parameters of rock plate have been studied to influence rock breaking volume. The research result could help optimize the cutting parameters of the saw blade and conical pick to improve the rock breaking efficiency.


Rock damage theory
According to the rock's heterogeneity and porosity, the rock's damage mechanism is studied.The mechanism of rock damage evolution is studied based on the theory of rock damage caused by crack propagation of heterogeneous material homogenization mechanical properties and thermodynamic theory.To study the mechanical behavior of rock materials, the homogenization theory is adopted.The homogenization method generally adopts research path shown in Fig. 1.
Assume that there is a macroscopic uniform stress field at the outer boundary ∂A of a specific element A as σ , that is, equivalent to an additional uniform surface load t 1 (x)=σ • n(x), x ∈ ∂A .The internal stress field of the characteristic element satisfies the boundary conditions as σ x • n(x)=σ • n(x), x ∈ ∂A .When the physical force is ignored, the average local stress on the characteristic element body and the boundary stress satisfies Eq. ( 1). (1) among that, V-volume of feature element, σ A -average value on a characteristic element.Leave out the char- acteristic element body by A and the static equilibrium condition at any point in the characteristic element divσ (x) = 0 .Combined relation equation ∂x i /∂x j = δ ij , and the stress equation is shown in Eq. (2).
The relationship equation is established based on the Gaussian theorem, as shown if Eq. ( 3).The average value of the macroscopic uniform stress acting on the external boundary of the element is equal to that of the local stress in the characteristic element.
Local strain under small deformation condition ε(x) of the average volume strain on the characteristic element is equal to ε , shown as Eq.(4).
At the same time, under the condition of small deformation can be obtained by combining the Gaussian theorem, shown as Eq.(5).
Assume that all material phases in the characteristic elements are linear elastic mechanical behavior and conform to the generalized Hook's law that is σ (x) = C(x) : E(x), x ∈ A .C(x)-local elastic tensor.The elastic tensor of rock mass (Phase 1#) is C 0 , and that of impurity phase (r + 1), and that of impurity phase (r + 1) is C c,r , r = 0, 1, 2,……., N. The macroscopic mechanical properties of solid matrix impurity systems are linear elastic.
Among that, I is the fourth order symmetric element tensor, based on the second order symmetric element tensor δ .The tensor I is shown as Eq.(6).
Under the external load, the random distribution of cracks in the characteristic element body causes the rock to show significant anisotropy.Considering the discreteness of the normal vector of rock cracks, that is, the damage variable describing the state of cracks.The damage variable composition set of cracks C = {c 1 , c 2 , c 3 , c 4 , . . . . . ., c N } , c i indicates the i-th crack damage value.
Assuming the normal vector n of crack, and d = d(n) is used to represent the distribution density of rock fractures, and the free energy expression of the fracture matrix system is determined, according to the thermodynamic principle, to establish the damage mechanics, shown as Eq. ( 7).
Among that, C hom (d)-effective elastic tensor of damaged materials.The state variable is the thermodynamic force associated with the internal variable, and there is free energy to derive the internal variable energy to obtain the energy dissipation of the system.Established the macro stress-strain relationship as shown in Eq. ( 8). (2)

Macroscopic stress
Homogenization Homogenization

Local stress
Stress localization Obtain the thermodynamic force and damage driving force associated with the damage variable, shown as The effective mechanical properties of materials are determined through micromechanics, and the mechanical mechanism and mechanism of material damage and failure need be fully considered.The constitutive equation and internal variable evolution criterion are established.According to the second law of thermodynamics, the energy dissipation caused by a crack expansion is nonnegative, which is meeting D e = F d ḋ ≥ 0.
On the basis of thermodynamics, the damage criterion based on strain energy release rate is adopted g(F d , d) = F d − R(d) ≤ 0 .Among that, R(d)-resistance function of damage evolution (crack propagation).For the damage criterion, conditions are as shown in Eq. ( 9) The need for analytical mathematics expression and the convenience of numerical program research are considered in micro damage mechanics research.It is assumed that the crack propagation process is self similar and only expands in its own plane, so the normal vector of the crack surface does not change.The rock is assumed to be a normal orthogonal material, and the damage evolution follows the orthogonalization criterion.
In which, d -damage multiplier.The damage evolution equation considering loading and unloading conditions is shown in Eq. (11).
The damage multiplier d The damage consistency condition is determined as Eq.(12).
Based on the damage evolution criterion, the stress-strain relationship in the form of rate is established.The macro stress-strain relationship is expressed in a differential form σ = Ċhom : ε + C hom : ε , and the relationship equation is shown as (13).

Constitutive model of rock material
The paper selects the RHT material as the rock material model, with the constitutive model tests of different rock materials.The constitutive model of RHT material, coupling shear force and pressure.The relation describes the pressure by polynomial Hugoniot curve and p-α form of compaction.For the compression model, define a variable whose initial value is greater than 0 representing porosity, which represents the material's density fraction and decreases with the increase of pressure.The reference density can be expressed as αρ.The porosity is shown in Eq. ( 14).
Among that, α(t)-the pressure of time t, p el -initial pore crushing pressure, p comp -compaction pressure, and N-porosity index.To define the cap pressure, the current pore crushing pressure equation is as follows Eq. ( 15) The residual pressure model is determined by the porous density ρ and the specific internal energy e.According to the input value, it is determined by B 0 ( B 0 > 0).
, and η (ρ) = ∂ρ/(∂ 0 ρ 0 ) − 1 , shear strength p * =p/f c .s-deviatoric stress tensor, εp -plastic strain rate.ε * p -effective plastic strain.For a given stress the two functions and the compression strength parameter f c .The first describes the principal stress condition pressure relationship σ 1 < σ 2 = σ 3 .The failure surface and normalized plastic strain , the relationship equation is shown as Eq. ( 17) Among that, is the failure crushing pressure, F r -dynamic increment factor, and Use the relative tensile strength f * t , shear strength f * s and compressive strength of concrete f c and Q values explain the correlation between tensile and shear meridians.Further details describe the factor that reduces the shear and tensile meridian strength, shown as Eq. ( 18).
The relation equation between Load angle θ and deviator stress tensor s is shown in Eq. (19).
Relative pressure function reduced the maximum strength as Q=Q(p * )=Q 0 + Bp * .And the relative strain rate coefficient is shown as Eqs.( 20) and (21) The parameters involved in the expression is shown in Eq. (22).
According to the continuity requirements, input the rate parameters through.The plastic strength factor is shown in Eq. ( 23).
Among that, p * c = p c /f c , and The hardening behavior is linear with the plastic strain.
Among that, G-shear modulus of the original material, ξ-hardening attenuation coefficient in the model.When the hardening state reaches the ultimate strength of the failure surface, the damage further accumulates in the plastic strain and inelastic loading process.The failure elastic strain equation is shown as ( 27) The damage parameters are accumulated by plastic strain, shown as (28).
The damage surface equation is shown as Eq. ( 28).
Among that, σ * r p * = A f p * n f , plastic flow along the direction of deviatoric stress εp ∼ s .However, for ten- sion, the parameter PFC can be selected to correspond to the influence value of plastic volumetric strain, ≤ 1 is used to indicate the variable, the special value = 1 , εp ∼ s − pI.

Established and modified model
Established the numerical simulation model According to combined rock breaking method with saw blade and conical pick in the actual work progress, establish the saw blade cutting rock simulation model and conical pick cutting rock plate simulation model.The structural model of SolidWorks was imported into ANSYS/LS-DYNA to establish the simulation model.The structural model is meshed with the ANSYS/MeshTool with SOLID_164.The saw blade and conical pick material are defined as MAT_RIGID, and the rock material is defined as RHT, and rock key parameters is shown in Table 1.The contact type between the cutting tool and rock is defined as ERODING_SURFACE_TO_SURFACE.The constraints were added to the rock, the full constraints is added to the bottom surface of rock, the x-axial and y-axial displacement constraints is added to the right and left surface of rock, and the y-axial and z-axial displacement constraints is added to the front and behind the surface of the rock.The loads are added to the cutting tool, the rotary load around the x-axial, displacement along y-axial and z-axial added to the saw blade.The displacement load along x-axial added to the conical pick.The numerical simulation model of saw blade cutting rock and conical pick cutting rock are shown in Fig. 2. The calculation step is set to 0.01 s and the cutting speed and cutting distance define the calculation.After the setting are completed, the K file generated and imported into ANSYS/SLOVER for a solution.The high-performance WorkStation with 40 computing cores and 128 GB memory is used.

Quantitative analysis system of rock damage
The quantitative analysis model of rock damage based on image recognition is established, and the quantitative analysis software of rock damage based on Python is compiled to quantify the rock damage and realize the quantitative analysis of rock damage.Based on ANSYS/LS-DYNA, the combined rock breaking of saw blade and pick was numerically simulated.Use LS-PrePost to post process the numerical simulation results and slice the (27) The key parameters of rock material.rock damage model at a specific interval to form a rock damage picture.The rock damage pictures are imported into the rock damage calculation system.The system analyzes each damage picture separately and then quantifies the rock damage volume with the cumulative method.The block diagram of the rock damage analysis software is shown in Fig. 3a.Quantitative analysis software for rock damage is established and packaged based on Python to simplify the steps of analyzing rock damage, as shown in Fig. 3b.Import the storage path of the rock damage slice image into the software, set the output position, rock size and damage scale value, and click the calculation to realize the quantitative processing of rock damage.

Verification and modification
Built a rock breaking experiment system of combined rock breaking with saw blade and conical pick and a tradition rock breaking experiment system, as shown in Fig. 4. Conduct rock breaking experiments and verify the numerical simulation model.The combined rock breaking with saw blade and conical pick multi-function test bench can complete the saw blade cutting experiment and the conical pick cutting rock with saw blade pre-cutting experiment.The saw blade rock cutting test bench mainly includes the main control cabinet, servo motor, electric cylinder, servo control system, rock fixed base and signal acquisition system.The rock pre-cutting test bench for pick cutting saw blade mainly includes: rock fixed base, cutting components, static torque sensor, pump station, pump station control system, signal acquisition system, etc. Saw blade cuts into rock with the rotation speed of 1000 r/min, a feed speed of 0.20 m/min, and the experiment and numerical simulation result is shown as Fig. 5a.The result of a saw blade cutting rock with constant experiment and numerical simulation with a rotation speed of 1000 r/min, feed speed of 0.20 m/min, and cutting depth of 5 mm is shown as Fig. 5b.The result of experiment and numerical simulation with a cutting speed of 1 m/s, and cutting angle of 50°, cutting depth of 15 mm, cutting rock plate with a width of 300 mm, the height of 150 mm and a thickness of 20 mm is shown as Fig. 5c.A comparison of the experiment and numerical simulation results can be indicated that the saw blade cuts into the rock to form a saw joint, which is basically the same.The rock walls on both sides of the middle position of the saw joint are broken to a certain extent.The saw blade cuts  the rock with a constant cutting depth to form a saw joint, forming a certain crushing range on the rock walls on both sides of the saw joint, as shown in Fig. 5b.According to the numerical simulation results of the rock cut by the conical pick with pre-cutting, it can be clearly seen that the rock plate fracture of the rock with pre-cutting by the conical pick is similar, and broken volume is basically the same, as shown in Fig. 5c.
In order to verified the quantitative analysis system of rock damage, the test pictures are imported into the system.The test pictures are shown in Fig. 6, there are five different color area with same size in each picture.
The test result of rock damage calculation system analysis the test pictures is shown in the Table 2.There are five colors of the same proportion and size in the test picture.Therefore, it is obvious that the analysis result of test pictures is accuracy.The test picture result error is 0.003 and 0.002, respectively, which is less than 0.005, shown as Table 2.The rock damage calculation system is accurate.

Combined rock breaking progress
According to the combined rock breaking method of saw blade and conical pick in engineering application, the rock is first cut by the saw blade and then cut by conical pick.The saw blade cutting rock progress can be divided The process of saw blade cutting into rock is shown as Fig. 7a.The saw blade cuts into rock with stable rotation speed and feed speed.When the saw blade contacts the rock, the rock damage appears at the contact point between the saw blade and rock, shown as Fig. 7a (1).With saw blade continue cutting rock, the rock element appear deformation with the shear action, shown as Fig. 7a (2).With the cutting distance of saw blade increasing, some rock elements are failing and deleting, forming joint formation, shown as Fig. 7a (4).A certain width of damage area is formed on both sides of the saw seam, the position with the widest damage width has a certain distance offset along the direction of saw blade rotation, as shown in Fig. 7a (5).The saw blade continues to cut into the rock, and the damage scope on both sides of the saw joint gradually narrows, and the rock damage scope is mainly concentrated at the front and rear ends of the saw blade, as shown in Fig. 7a (6).
The process of rock cutting by saw blade at fixed depth is shown in Fig. 7b.The saw blade cuts the rock at a stable feed speed, rotation speed and cutting depth.When the saw blade touches the rock, the rock damage occurs at the contact point between the saw blade and the rock, as shown in Fig. 7b (1).As the saw blade continues to cut the rock, the range of rock damage gradually increases, and the saw blade cuts the stable width and depth of the saw seam formed by the rock.The rock pre-cutting process of the pick cutting saw blade is shown in Fig. 7c.The pick contacts the plate rock, and the contact point between the pick and the rock plate is damaged.The pick cuts the rock plate with stable cutting parameters, and the rock plate begins to crack.With the increase of cutting distance, the crack continues to expand, and the rock plate intersects with the crack breaks, as shown in Fig. 7c.

Impact of sawing on rock damage
The sawing into rock process In the saw blade cutting into rock, the cutting parameters (rotation speed and feed speed) greatly influence rock damage.The saw blade cuts rock with a rotation speed of 1000 r/min, 1600 r/min, 2200 r/min, and 2800 r/min, feed speeds of 0.10 m/min, 0.16 m/min, 0.22 m/min, and 0.28 m/min, to study the influence of cutting parameter on rock damage.
The rock damage with different rotation speeds is shown in Fig. 8.The saw blade cuts rock with a feed speed of 0.20 m/min, and a rotation speed of 1000 r/min, 1600 r/min, 2200 r/min and 2800 r/min.According to the rock damage cloud with the same cutting speed and various rotation speeds, the rock damage area declines with the rotation speed increasing at the same cutting depth.
The saw blade cuts rock with rotation speed of 2200 r/min, feed speed of 0.10 m/min, 0.16 m/min, 0.22 m/ min and 0.28 m/min, the rock damage cloud with different feed speed is shown as Fig. 9.According to the rock damage cloud with same rotation speed and different feed speed, it is obvious that the rock damage area increase with feed speed increasing at the cutting depth.
Based on the quantitative analysis of rock damage by the statistical program of rock damage, the influence of saw blade rotation speed on rock damage is studied by the method of quantitative analysis.The relationship between rock damage and saw blade cutting parameters is shown in Fig. 10.The rock damage value increases with feed speed increasing and rotation speed declining.

The sawing rock with constant depth process
The process of saw blade cutting rock with constant depth is the main part of rock cutting process by saw blade.The effects of cutting parameters such as saw blade rotation speed, feed speed and cutting depth on rock damage are studied.The saw blade cuts rock with constant depth, with rotation speed of 1000 r/min, 1500 r/min, 2000 r/ min, 2500 r/min and 3000 r/min, feed speed of 0.10 m/min, 0.15 m/min, 0.20 m/min, 0.25 m/min and 0.30 m/ min and cutting depth of 4 mm, 8 mm, 12 mm, 16 mm and 20 mm.To investigate the cutting parameters of saw blade effect on rock damage.
The saw blade cuts rock with constant depth at feed speed of 0.30 m/min, cutting depth of 20 mm rotation speed 1000 r/min, 1500 r/min, 2000 r/min, 2500 r/min and 3000 r/min.The result of saw blade cutting rock with different rotation speed is shown as Fig. 11.According to the saw blade cutting rock with different rotation speed results, it can be seen that the rock damage are decreasing with the rotation speed increasing.
The saw blade cuts rock with cutting depth of 20 mm, rotation speed of 2000 r/min and feed speed of 0.10 m/ min, 0.15 m/min, 0.20 m/min, 0.25 m/min and 0.30 m/min.The result of saw blade cutting rock with different feed speeds is shown in Fig. 12.Compared the rock damage cloud with different feed speeds, the rock damage area increasing with the feed speed increasing.The feed speed of saw blade have great effect on rock damage.www.nature.com/scientificreports/with feed speed and cutting depth increasing and rotation speed declining.And the changing trends of the rock damage area is similar with the research result of Wang et al. 40, 41 .

The impact factor of rock damage
The process of combined rock breaking with saw blade and conical pick, conical pick breaking rock with saw blade pre-cutting is the essential process of the combined rock breaking.The conical pick cutting rock plate is influenced by the cutting parameters and structural parameters.The conical pick cutting rock plate with cutting angle of 30°, 40°, 45° and 50°, to research the cutting angle effect on rock plate breaking, the numerical simulation results are shown as Fig. 16.The numerical simulation result of conical pick cutting rock plate with different cutting angle indicated that the rock cracks and rock fragments increases and then declines with cutting angle increasing.
The conical pick cuts rock plate with different cutting depth to investigate the effect of cutting depth on rock breaking.The conical pick cuts rock plate with the cutting depth of 10 mm, 15 mm, 25 mm and 30 mm, and result of conical pick cutting rock is shown in the Fig. 17.The result of rock breaking indicated that the number of crack and rock fragment increases with cutting depth increasing.The rock plate is basically stripped from the base rock.Therefore, the fragmentation of rock plate can adjusted by controlling the cutting depth.
The conical pick cutting rock plate with cutting position of 1/10, 1/5, 3/10, 2/5 and 1/2 to investigate the effect of cutting position on rock plate breaking, the numerical simulation results are shown in Fig. 18.Compared with conical pick cutting rock plate of different cutting position, with the cutting position close to the middle position of rock plate, the rock breaking volume increases.Therefore, the cutting position of conical pick cutting rock have great influence on rock breaking.
The rock plate structural parameters have great influence on rock breaking with the conical pick.The rock plate structural parameters include height, width and thickness.Therefore, the height of rock plate has been set as 50 mm, 75 mm, 100 mm, 150 mm, 200 mm, 300 mm and 400 m to study the rock plate height influence on rock breaking.The result of conical pick cutting rock plate with different is shown in Fig. 19.It is obvious that the rock plate breaking ideal with the height increasing.However, the rock plate with different height is crushing completely.
The conical pick cutting rock plate with width of 50 mm, 70 mm, 90 mm, 150 mm, 200 mm, 300 mm and 500 mm to investigate the width of rock plate influence on rock breaking.The width of rock plate has great influence on rock breaking, according to the rock plate.The rock plate breaking volume, rock cracks and fragments number increases with the width of rock plate increasing is show as Fig. 20.
The thickness of rock plate is an important parameter of the rock plate.Therefore, the thickness of rock plate has been researched, by the thickness of rock plate setting as 5 mm, 10 mm, 15 mm, 20 mm, 25 mm and 30 mm.The results of conical pick cutting rock plate with various thickness is shown as Fig. 21.According to the result of conical pick cutting rock plate, the thickness of rock plate has great effect on rock breaking.The rock plate breaking volume increases with the thickness of rock plate increasing.

Conclusions
The paper establishes the numerical simulation model of combined rock breaking with saw blade and conical pick based on ANSYS/LS-DYNA to research cutting parameters and rock structural parameters on rock damage.
(1) The numerical simulation model of combined rock breaking with saw blade and conical pick has been established, and numerical simulation model is verified and modified with the experiment of saw blade and conical pick cutting rock.(2) The rock damage in the process of saw blade cutting rock increases with the feed speed and cutting depth increasing, and the rotation speed increasing causes the rock damage declining.(3) The conical pick cuts rock plate with different structural parameters, the structural parameters have great influence on rock, the width, height and thickness of rock plate and feed speed, cutting angle and cutting position of conical pick affect the rock breaking capacity of the conical pick.
The investigation results can be applied to optimize cutting parameters of saw blade and cutting parameters of conical pick to improve the combined rock breaking efficiency.

Figure 1 .
Figure 1.The research way of homogenization.

Parameter Density (kg/m 3 )Figure 2 .
Figure 2. The numerical simulation of combined rock breaking with saw blade and conical pick.

Figure 3 .
Figure 3.The rock damage calculation system.

Figure 4 .
Figure 4.The experimental bench of combined rock breaking and traditional rock breaking.

Figure 5 .Figure 6 .
Figure 5.The results of combined rock breaking with saw blade and conical pick.

Figure 7 .
Figure 7.The process of combined rock breaking with saw blade and conical pick.

Figure 8 .
Figure 8.The rock damage cloud with different rotation speeds.

Figure 9 .
Figure 9.The rock damage cloud with different feed speeds.

Figure 10 .
Figure 10.The rock damage cloud with different cutting parameters.

Figure 11 .
Figure 11.The rock damage cloud with different rotation speeds.

Figure 12 .
Figure 12.The rock damage cloud with different feed speeds.
The conical pick with feed speed of 0.50 m/s, 1.0 m/s, 1.5 m/s, 2.0 m/s, 2.5 m/s and 3.0 m/s, the cutting depth of 5 mm, 10 mm, 15 mm, 20 mm, 25 mm and 30 mm, and the cutting angle of 30°, 40°, 45°, 50°, 60° and 70° and the cutting station ( l x ′/l x ) of 1/10, 1/5, 3/10, 2/5 and 1/2.And the rock plate with width of 50 mm, 70 mm, 90 mm, 150 mm, 200 mm, 300 mm and 500 mm, height of 50 mm, 75 mm, 100 mm, 150 mm, 200 mm, 300 mm and 400 mm, thickness of 5 mm, 10 mm, 15 mm, 20 mm, 25 mm and 30 mm, to study the cutting parameters and structural parameters on rock damage.The conical pick cuts rock with feed speed of 0.50 m/s, 1.0 m/s, 1.5 m/s and 2.0 m/s, cutting angle of 50°, cutting depth of 30 mm and the cutting position of 1/2, and rock plate structural parameters with width of 300 mm, height of 200 mm and thickness of 20 mm, to study the feed speed on rock damage.The result of conical pick cutting rock plate with different feed speeds is shown as Fig.15.The feed speed increasing causes the rock plate creaks and rock fragments number increasing.

Figure 13 .
Figure 13.The rock damage cloud with different cutting depths.

Figure 14 .
Figure 14.The rock damage cloud with different cutting parameters.

Figure 15 .
Figure 15.The rock damage cloud with different cutting speeds.

Figure 16 .
Figure 16.The rock damage cloud with different cutting angles.

Figure 17 .
Figure 17.The rock damage cloud with different cutting depths.

Figure 18 .
Figure 18.The rock damage cloud with different cutting positions.

Figure 19 .
Figure 19.The rock damage cloud of rock plate with different height.

Figure 20 .
Figure 20.The rock damage cloud of rock plate with different width.

Figure 21 .Figure 22 .
Figure 21.The rock damage cloud of rock plate with different thickness.

Figure 23 .
Figure 23.Rock damage value with different cutting parameters and rock plate structural parameters.

Table 2 .
The test result of rock damage calculation system analysis test pictures.