Graded broken stone anisotropic parameter determination method based on virtual triaxial test
阅读说明：本技术 基于虚拟三轴试验的级配碎石各向异性参数确定方法 (Graded broken stone anisotropic parameter determination method based on virtual triaxial test ) 是由 张军辉 李崛 于 2021-07-20 设计创作，主要内容包括：本发明公开了一种基于虚拟三轴试验的级配碎石各向异性参数确定方法,具体为：根据实际碎石试件的级配筛选合适粒径的真实集料,获取对应数字集料的几何轮廓信息,将试件的材料参数输入离散元颗粒流软件中；数字集料的形态参数与真实集料的形态参数实测结果保持一致,数字集料的随机投放；当数字集料的形状参数的Weibull分布参数满足投放目标要求时,建立指定形态的虚拟试件；构建级配碎石的虚拟三轴试验模型,计算级配碎石的各向异性参数,建立各向异性参数的预估方程,输出级配碎石的各向异性参数。本发明将集料图像和虚拟试验的结合,确定级配碎石力学各向异性参数,提高了效率、准确性的同时降低了成本,拓展了适用范围。(The invention discloses a method for determining anisotropic parameters of graded crushed stones based on a virtual triaxial test, which specifically comprises the following steps: screening real aggregates with proper particle sizes according to the grading of an actual gravel test piece, acquiring the geometric outline information of the corresponding digital aggregates, and inputting the material parameters of the test piece into discrete element particle flow software; the morphological parameters of the digital aggregate are consistent with the actual measurement result of the morphological parameters of the real aggregate, and the digital aggregate is randomly put in; when Weibull distribution parameters of the shape parameters of the digital aggregates meet the requirement of a throwing target, establishing a virtual test piece in a specified form; and constructing a virtual triaxial test model of the graded broken stone, calculating the anisotropic parameters of the graded broken stone, establishing a pre-estimation equation of the anisotropic parameters, and outputting the anisotropic parameters of the graded broken stone. The invention combines the aggregate image and the virtual test to determine the mechanical anisotropy parameters of the graded macadam, thereby improving the efficiency and the accuracy, reducing the cost and expanding the application range.)
1. A method for determining anisotropic parameters of graded crushed stones based on a virtual triaxial test is characterized by comprising the following steps:
s1: screening real aggregates with proper particle sizes according to the grading of an actual gravel test piece, acquiring the geometric outline information of the corresponding digital aggregates, and simultaneously inputting the material parameters of the test piece into discrete element particle flow software; the measuring system actually measures morphological parameters of the real aggregate, namely a sphericity index SP, a two-dimensional shape index Form2D and a gradient corner value GA, and the morphological parameters of the digital aggregate are consistent with the actual measurement result of the morphological parameters of the real aggregate; realizing random feeding of digital aggregates in the cylindrical space;
s2: acquiring Weibull distribution parameters of the shape parameters of the digital aggregates, compacting and molding the test piece when the Weibull distribution parameters of the shape parameters of the digital aggregates meet the requirement of a throwing target, and establishing a virtual test piece with a specified shape; if the Weibull distribution parameters do not meet the requirement of the throwing target, the digital aggregate throwing is carried out again;
s3: constructing a virtual triaxial test model of graded crushed stones; after the virtual test piece formed by compaction reaches initial balance, loading to a specified three-dimensional static stress, and then carrying out multistage staged dynamic loading to obtain the stress and strain of the wall body;
s4: if the stress peak value does not meet the requirements of the test loading sequence, adjusting the friction coefficient and the servo factor of the virtual test piece, and performing initial balance again and triaxial loading; when the stress peak value meets the requirement of the test loading sequence, calculating the normal anisotropy parameter g of the graded crushed stone according to the formula (8) and the formula (9)nTangential anisotropy parameter gm，
The method comprises the steps of obtaining test piece strain results under different stress states through graded broken stone virtual triaxial test determination, and calculating according to an ICAR (independent component analysis) reported standard method and an elastic mechanics theory and a system identification method to obtain a corresponding vertical resilience modulus E1Horizontal modulus of restitution E3Shear modulus G;
s5: establishing a pre-estimation equation of the anisotropic parameters of the graded crushed stone considering the grading and the shape parameters, and obtaining an equation (10):
g＝a0+a1ln(G/S)+a2ln(λF)+a3ln(λG)+a4ln(λS) (10)
wherein g represents gnOr gm；a0、a1、a2、a3And a4Representing the fitting parameters; G/S represents the thickness ratio of gradation; lambda [ alpha ]FWeibull distribution parameter, λ, representing a two-dimensional shape indexGWeibull distribution parameter, λ, representing gradient edge indexSWeibull distribution parameters representing sphericity index;
s6: the normal anisotropy parameter g of the graded crushed stone obtained in the step S4nTangential anisotropy parameter gmWeibull distribution parameter lambda corresponding to digital aggregate shape parameter respectivelyF、λG、λSAnd G/S linear regression fitting to obtain Gn、gmCorresponding fitting parameter a0、a1、a2、a3And a4Then rapidly estimating the normal anisotropy parameter g of the graded crushed stone according to the formula (10)nTangential anisotropy parameter gm。
2. The method for determining anisotropic parameters of graded crushed stone based on virtual triaxial test as claimed in claim 1, wherein in step S1, the geometric profile information of the digital aggregate is obtained, specifically: and acquiring point cloud data of the real aggregate surface, reconstructing a digital aggregate external contour curved surface by adopting a Marching Cubes equivalent surface algorithm, and simplifying the contour curved surface into a triangular mesh by adopting an Edge-Collapsing algorithm.
3. The method for determining anisotropic parameters of graded crushed stones based on virtual triaxial test according to claim 2, wherein in step S1, morphological parameters of digital aggregates are obtained, specifically: processing point cloud coordinates on the surface of the digital aggregate through MATLAB software, and constructing a directional bounding box of space point cloud so as to automatically calculate the sphericity index of the digital aggregate, wherein the formula (1) is shown in the specification; two-dimensional contour information is obtained through projection of point cloud data on the surface of the digital aggregate in the Z direction, so that a two-dimensional shape index Form2D and a gradient edge angle value GA of the digital aggregate are determined, and the formula (2) and the formula (3) are shown;
in the formula (d)LThe length of the bounding box is the direction of the coarse aggregate; dIThe width of the bounding box is the direction of the coarse aggregate; dSThe height of the bounding box is the direction of the coarse aggregate; theta is a measurement angle; rθIs the radius of the two-dimensional profile in the theta angle direction; delta theta is the measurement angle increment; n is the total number of aggregate projection edge points; i isThe ith point of the aggregate projection edge; thetaiMeasured angle, theta, of the ith point representing projected edge of aggregatei+3The measured angle of the (i + 3) th point representing the projected edge of the aggregate.
4. The method for determining anisotropism parameters of graded crushed stones based on virtual triaxial test according to claim 3, wherein in the step S2, Weibull distribution parameters of shape parameters of digital aggregates are obtained, specifically: after the digital aggregates are randomly thrown in the cylindrical space, the shape parameters of each crushed aggregate are obtained, wherein the shape parameters comprise a sphericity index SP, a two-dimensional shape index Form2D and a gradient edge angle value GA, and the shape parameter probability distribution condition of the digital aggregate set in the cylindrical space is fitted through a Weibull distribution function, which is shown in formula (4):
wherein F is the cumulative probability; x is a two-dimensional shape index, a gradient edge angle index or a sphericity index; λ is a proportional parameter; alpha is a shape parameter; if x represents a two-dimensional shape index, the proportion parameter lambda is a Weibull distribution parameter of the two-dimensional shape index and is recorded as lambdaFThe shape parameter alpha is the corresponding curve fullness parameter aF(ii) a If x represents the gradient edge angle index, the proportion parameter lambda is the Weibull distribution parameter of the gradient edge angle index and is recorded as lambdaG(ii) a The shape parameter alpha is a corresponding curve fullness degree parameter aG(ii) a If x represents the sphericity index, the proportion parameter lambda is the Weibull distribution parameter of the sphericity index and is marked as lambdaSThe shape parameter alpha is the corresponding curve fullness parameter aS。
5. The method for determining anisotropic parameters of graded crushed stone based on virtual triaxial test of claim 1, wherein in the step S3, the multistage staged dynamic loading is specifically a staged constant rate loading based on target stress, and specifically the method is performed according to the following steps:
s31: equally dividing the loading time into a plurality of loading stages, and determining the initial stress and the target stress of each stage through a loading sequence;
s32: at the beginning of each loading stage, monitoring the contact between the wall and the particles, and calculating to obtain the integral rigidity K of the contact surfacewSimultaneously monitoring to obtain the contact area A of the wall body and the test piece;
s33: because the whole test process is in small stress loading, the contact rigidity K of the wall body and particles in stage loading is assumedwIf the variation is ignored, the constant loading rate v of the wall body at the current stage is calculated according to the formula (6)w(ii) a The target stress is taken as a convergence condition, and the loading stage is finished when the target stress is reached;
delta sigma represents the difference value of the current stress and the target stress of the wall; t iswRepresenting the total duration of the current loading phase;
s34: in the testing process, axial and radial stress of the wall body is recorded once every other certain time step length, whether the recorded stress is larger than a target stress for 3 times before and after the stress is judged, and whether the loading time meets the requirement of a loading sequence;
s35: if the wall stress and the loading time both meet the requirements, recalculating the constant loading rate v according to the steps S32-S33wStarting the loading of the next stage, and if the wall stress requirement is not met, continuing the loading until the wall stress reaches the target stress; if the loading time requirement is not met, the current loading speed v is setwSet to 0, the test is continued until a given load time is reached, ensuring that the corresponding stress state is reached within the specified load time.
6. The method for determining anisotropic parameters of graded crushed stone based on virtual triaxial test (S4), wherein the vertical modulus of resilience E in step S41Obtained according to the following method:
vertical modulus of resilience E is pre-estimated through NCHRP 1-37A three-parameter model1According to the change situation of the stress, see formula (7),
in the formula, thetatRepresents the bulk stress; tau isoctRepresents the octahedral shear stress; paIs at standard atmospheric pressure; k is a radical of1、k2And k3Fitting coefficients for the model; obtaining the vertical resilience modulus of the test piece according to the virtual dynamic triaxial test, and fitting the formula (7) through excel to obtain a model parameter k1、k2And k3Then obtaining the vertical modulus of resilience E corresponding to the stress according to the formula (7)1。
7. The method for determining anisotropic parameters of graded crushed stones based on virtual triaxial test according to claim 5, wherein the thickness ratio G/S of the grading is calculated according to equation (5):
p4denotes the percent passage of a sieve having a pore size of 4.75mm, p200Represents the percent passage of a sieve having a pore size of 0.075 mm.
8. The method for determining anisotropic parameters of graded crushed stones based on virtual triaxial test according to claim 1, wherein the target requirements for delivery in S2 are as follows: the Weibull distribution parameter increases from 0.65 to 0.75 with an error value within 0.01.
Technical Field
The invention belongs to the technical field of road engineering, and relates to a method for determining anisotropic parameters of graded crushed stones based on a virtual triaxial test.
Background
The graded broken stone is a heterogeneous discrete material, and the mechanical properties of the graded broken stone are characterized by discreteness, stress dependence and anisotropy. When the size of the roadbed and pavement structure model is large enough, the influence of the shape and the particle size of the crushed stone on the integral uniformity is neglected in the traditional statics calculation theory, so that the graded crushed stone structure is assumed to be a homogeneous body to be appropriate. However, the existing pavement design method generally adopts dynamic structure calculation, the orthotropic characteristic of the structure becomes more obvious along with the increase of the design thickness of the crushed stone layer, and the influence of the stress dependence of the crushed stone layer in a load action area on the response of the structure is also very obvious, so that the theory of isotropy and linear elasticity is obviously not suitable for the dynamic calculation. Therefore, in order to accurately know the mechanical response of the graded broken stone structure layer, an appropriate graded broken stone structure constitutive model and calculation parameters need to be determined.
With the continuous and deep research on road material mechanics, domestic and foreign researches show that the mechanical behavior of the graded macadam has the characteristics of non-linearity and anisotropy of stress. At present, for the experimental test of the cross anisotropy parameter of graded crushed stones, most of the experimental tests are based on the research results of the American International center for research on aggregates (ICAR), namely, a variable confining pressure dynamic triaxial test scheme is adopted to describe the change of the vertical modulus, the horizontal modulus and the shear modulus of the crushed stones along with the stress. The loading scheme cannot be carried out in conventional dynamic triaxial test equipment, but a special rapid triaxial test (RaTT) unit is needed to realize the variable loading of confining pressure along with bias stress. However, whether the conventional dynamic triaxial test or the RaTT test is adopted, the equipment is expensive to purchase and needs experienced testing personnel to operate, and the factors make the test of the dynamic rebound modulus and the orthotropic parameter of the graded macadam difficult to effectively apply to the common pavement design.
At present, patent publication No. CN111475876A provides a method for obtaining dynamic resilience mechanical characteristic parameters of granules, which improves a stress loading sequence according to a derived stress increment constitutive equation, and performs parameter regression through a dynamic triaxial test result to determine model parameters, so as to obtain a nonlinear dynamic resilience mechanical characteristic parameter prediction model including a dynamic resilience modulus, a poisson ratio, and an orthotropic parameter. However, the parameter acquisition of the patent still depends on a variable confining pressure test scheme and loading equipment, and the influence of indexes such as particle grading, aggregate shape and the like on model parameters is not considered, so that the technical problems of high acquisition difficulty and high cost of the indexes of the rebound modulus and the anisotropy of graded crushed stones cannot be solved.
Disclosure of Invention
In order to solve the problems, the invention provides a method for determining the anisotropic parameters of graded broken stones based on a virtual triaxial test, which combines an aggregate image with the virtual test to determine the mechanical anisotropic parameters of the graded broken stones, improves the efficiency and the accuracy, reduces the cost, expands the application range and solves the problems in the prior art.
The technical scheme adopted by the invention is that a method for determining anisotropic parameters of graded crushed stone based on a virtual triaxial test is specifically carried out according to the following steps:
s1: screening real aggregates with proper particle sizes according to the grading of an actual gravel test piece, acquiring the geometric outline information of the corresponding digital aggregates, and simultaneously inputting the material parameters of the test piece into discrete element particle flow software; the measuring system actually measures morphological parameters of the real aggregate, namely a sphericity index SP, a two-dimensional shape index Form2D and a gradient corner value GA, and the morphological parameters of the digital aggregate are consistent with the actual measurement result of the morphological parameters of the real aggregate; realizing random feeding of digital aggregates in the cylindrical space;
s2: acquiring Weibull distribution parameters of the shape parameters of the digital aggregates, compacting and molding the test piece when the Weibull distribution parameters of the shape parameters of the digital aggregates meet the requirement of a throwing target, and establishing a virtual test piece with a specified shape; if the Weibull distribution parameters do not meet the requirement of the throwing target, the digital aggregate throwing is carried out again;
s3: constructing a virtual triaxial test model of graded crushed stones; after the virtual test piece formed by compaction reaches initial balance, loading to a specified three-dimensional static stress, and then carrying out multistage staged dynamic loading to obtain the stress and strain of the wall body;
s4: if the stress peak value does not meet the requirement of the test loading sequence, adjustingThe friction coefficient and the servo factor of the virtual test piece are initially balanced again and subjected to triaxial loading; when the stress peak value meets the requirement of the test loading sequence, calculating the normal anisotropy parameter g of the graded crushed stone according to the formula (8) and the formula (9)nTangential anisotropy parameter gm，
The method comprises the steps of obtaining test piece strain results under different stress states through graded broken stone virtual triaxial test determination, and calculating according to an ICAR (independent component analysis) reported standard method and an elastic mechanics theory and a system identification method to obtain a corresponding vertical resilience modulus E1Horizontal modulus of restitution E3Shear modulus G;
s5: establishing a pre-estimation equation of the anisotropic parameters of the graded crushed stone considering the grading and the shape parameters, and obtaining an equation (10):
g＝a0+a1 ln(G/S)+a2 ln(λF)+a3 ln(λG)+a4 ln(λS) (10)
wherein g represents gnOr gm；a0、a1、a2、a3And a4Representing the fitting parameters; G/S represents the thickness ratio of gradation; lambda [ alpha ]FWeibull distribution parameter, λ, representing a two-dimensional shape indexGWeibull distribution parameter, λ, representing gradient edge indexSWeibull distribution parameters representing sphericity index;
s6: the normal anisotropy parameter g of the graded crushed stone obtained in the step S4nTangential anisotropy parameter gmWeibull distribution parameter lambda corresponding to digital aggregate shape parameter respectivelyF、λG、λSAnd G/S linear regression fitting to obtain Gn、gmCorresponding fitting parameter a0、a1、a2、a3And a4Then rapidly estimating the normal anisotropy parameter g of the graded crushed stone according to the formula (10)nTangential anisotropy parameter gm。
Further, in step S1, the acquiring geometric contour information of the digital aggregate specifically includes: and acquiring point cloud data of the real aggregate surface, reconstructing a digital aggregate external contour curved surface by adopting a Marching Cubes equivalent surface algorithm, and simplifying the contour curved surface into a triangular mesh by adopting an Edge-Collapsing algorithm.
Further, in step S1, the obtaining of the morphological parameters of the digital aggregate specifically includes: processing point cloud coordinates on the surface of the digital aggregate through MATLAB software, and constructing a directional bounding box of space point cloud so as to automatically calculate the sphericity index of the digital aggregate, wherein the formula (1) is shown in the specification; two-dimensional contour information is obtained through projection of point cloud data on the surface of the digital aggregate in the Z direction, so that a two-dimensional shape index Form2D and a gradient edge angle value GA of the digital aggregate are determined, and the formula (2) and the formula (3) are shown;
in the formula (d)LThe length of the bounding box is the direction of the coarse aggregate; dIThe width of the bounding box is the direction of the coarse aggregate; dSThe height of the bounding box is the direction of the coarse aggregate; theta is a measurement angle; rθIs the radius of the two-dimensional profile in the theta angle direction; delta theta is the measurement angle increment; n is the total number of aggregate projection edge points; i is the ith point of the aggregate projection edge; thetaiMeasured angle, theta, of the ith point representing projected edge of aggregatei+3Presentation setAnd measuring the angle of the (i + 3) th point of the projected edge of the material.
Further, in step S2, the Weibull distribution parameter of the shape parameter of the digital aggregate is obtained, specifically: after the digital aggregates are randomly thrown in the cylindrical space, the shape parameters of each crushed aggregate are obtained, wherein the shape parameters comprise a sphericity index SP, a two-dimensional shape index Form2D and a gradient edge angle value GA, and the shape parameter probability distribution condition of the digital aggregate set in the cylindrical space is fitted through a Weibull distribution function, which is shown in formula (4):
wherein F is the cumulative probability; x is a two-dimensional shape index, a gradient edge angle index or a sphericity index; λ is a proportional parameter; alpha is a shape parameter; if x represents a two-dimensional shape index, the proportion parameter lambda is a Weibull distribution parameter of the two-dimensional shape index and is recorded as lambdaFThe shape parameter alpha is the corresponding curve fullness parameter aF(ii) a If x represents the gradient edge angle index, the proportion parameter lambda is the Weibull distribution parameter of the gradient edge angle index and is recorded as lambdaG(ii) a The shape parameter alpha is a corresponding curve fullness degree parameter aG(ii) a If x represents the sphericity index, the proportion parameter lambda is the Weibull distribution parameter of the sphericity index and is marked as lambdaSThe shape parameter alpha is the corresponding curve fullness parameter aS。
Further, in step S3, the multistage phased dynamic loading is specifically a phased constant rate loading based on the target stress, and specifically is performed according to the following steps:
s31: equally dividing the loading time into a plurality of loading stages, and determining the initial stress and the target stress of each stage through a loading sequence;
s32: at the beginning of each loading stage, monitoring the contact between the wall and the particles, and calculating to obtain the integral rigidity K of the contact surfacewSimultaneously monitoring to obtain the contact area A of the wall body and the test piece;
s33: because the whole test process is in small stress loading, the wall body and the wall body in stage loading are supposed to be connectedContact stiffness K of the particleswIf the variation is ignored, the constant loading rate v of the wall body at the current stage is calculated according to the formula (6)w(ii) a The target stress is taken as a convergence condition, and the loading stage is finished when the target stress is reached;
delta sigma represents the difference value of the current stress and the target stress of the wall; t iswRepresenting the total duration of the current loading phase;
s34: in the testing process, axial and radial stress of the wall body is recorded once every other certain time step length, whether the recorded stress is larger than a target stress for 3 times before and after the stress is judged, and whether the loading time meets the requirement of a loading sequence;
s35: if the wall stress and the loading time both meet the requirements, recalculating the constant loading rate v according to the steps S32-S33wStarting the loading of the next stage, and if the wall stress requirement is not met, continuing the loading until the wall stress reaches the target stress; if the loading time requirement is not met, the current loading speed v is setwSet to 0, the test is continued until a given load time is reached, ensuring that the corresponding stress state is reached within the specified load time.
Further, the vertical modulus of resilience E in the step S41Obtained according to the following method:
vertical modulus of resilience E is pre-estimated through NCHRP 1-37A three-parameter model1According to the change situation of the stress, see formula (7),
in the formula, thetatRepresents the bulk stress; tau isoctRepresents the octahedral shear stress; paIs at standard atmospheric pressure; k is a radical of1、k2And k3Fitting coefficients for the model; obtaining the vertical resilience modulus of the test piece according to the virtual dynamic triaxial test, and fitting the formula (7) through excel to obtain a modelParameter k1、k2And k3Then obtaining the vertical modulus of resilience E corresponding to the stress according to the formula (7)1。
Further, the gradation thickness ratio G/S is calculated according to equation (5):
p4denotes the percent passage of a sieve having a pore size of 4.75mm, p200Represents the percent passage of a sieve having a pore size of 0.075 mm.
Further, the delivery target requirement in S2 is: the Weibull distribution parameter increases from 0.65 to 0.75 with an error value within 0.01.
The invention has the beneficial effects that:
according to the embodiment of the invention, aggregate images and virtual tests are combined, nonlinear and anisotropic behaviors of graded broken stone strength changes in different stress states are disclosed, mechanical anisotropic parameters of the graded broken stone are determined, the efficiency and the accuracy are improved, the cost is reduced, the application range is expanded, the problems of high cost and poor reproducibility of indoor tests are solved, the graded broken stone test piece is controllable in grading and adjustable in shape, the anisotropic behaviors of graded broken stones in different grades and aggregate appearance characteristics can be conveniently and accurately researched, and the method is high in reliability and strong in convenience.
The embodiment of the invention establishes the pre-estimation equation, directly utilizes the pre-estimation equation and the conventional AIMS equipment to determine the anisotropic parameters of the on-site graded broken stone without performing a virtual triaxial test, predicts and evaluates the integral mechanical anisotropic behavior of the on-site graded broken stone, does not need to measure the two-dimensional section of a graded broken stone test piece, does not need to perform a complex variable confining pressure dynamic triaxial test, provides convenience for road design and construction, improves the efficiency and the accuracy, reduces the cost and expands the application range.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a schematic representation of aggregate morphology index.
FIG. 2 is a flow chart of a virtual triaxial test loading and discriminating algorithm.
FIG. 3 is a schematic view of a virtual triaxial test piece.
FIG. 4 is a graphical illustration of a phased loading curve based on target stress.
FIG. 5 shows the anisotropy parameter gnThe fitting results of (1) are shown schematically.
FIG. 6 shows the anisotropy parameter gmThe fitting results of (1) are shown schematically.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The graded broken stone is a non-binding particle material, is a pile of discrete bodies similar to sand under the condition of lacking constraint, so that the aggregate in the broken stone and the long axis direction of the broken stone are continuously changed under different stress states, and the dynamic change process of a graded broken stone test piece under different stresses is difficult to obtain through static digital image acquisition, so that the anisotropic parameters of the graded broken stone cannot be determined.
In this embodiment, the method for determining anisotropic parameters of graded crushed stone based on a virtual triaxial test is specifically performed according to the following steps as shown in fig. 2:
s1: taking 3 grading actual gravels with different particle diameters in the table 1 as objects, screening real aggregates with proper particle diameters according to the grading of an actual gravel test piece, acquiring the geometric outline information of corresponding digital aggregates (three-dimensional), and simultaneously inputting the material parameters of the test piece into discrete element particle flow software (PFC 3D); the measurement system actually measures morphological parameters of real aggregate, namely a sphericity index SP, a two-dimensional shape index Form2D and a gradient corner value GA; the morphological parameters of the digital aggregate are consistent with the actual measurement result of the morphological parameters of the real aggregate. And importing STL file data (a data file format for describing the surface geometry of the three-dimensional object) of the digital aggregate into PFC3D software, creating a column block template, and randomly putting the digital aggregate in the cylindrical space.
TABLE 1 percent passage of particles of three continuous grades (%)
S11: acquiring geometric contour information of the digital aggregate; in the embodiment, point cloud data of a real aggregate surface is acquired through an X-ray CT or a laser scanner, then a digital aggregate external contour curved surface is reconstructed by adopting a Marching Cubes (MC) isosurface algorithm, and the contour curved surface is simplified into a triangular mesh through an Edge-Collapsing (EC) algorithm, so that the triangular mesh has 1500 triangular patches, the digital aggregate importing efficiency can be improved, the creation time of a column block template is saved, the time required for importing a single aggregate column in PFC3D software is changed into the original 1/10 time or less, and the actual use precision of the digital aggregate in the model is not influenced. For example, 1300 aggregates exist in one graded macadam test piece, so that the time for introducing and generating the columns is about 2-3 hours, but the specific method provided by the embodiment of the invention only needs about 10 minutes, and the modeling efficiency is greatly improved.
S12: acquiring morphological parameters of the digital aggregate; the digital aggregate form parameters (such as sphericity index, two-dimensional shape index and gradient edge angle value) applied in the embodiment are consistent with the test indexes (referring to the actual measurement result of the real aggregate) of the AIMS test system, and the AIMS test system is an indoor measurement system for testing the geometric shape of the real aggregate; processing point cloud coordinates on the surface of the digital aggregate through MATLAB software, and constructing a directional bounding box of space point cloud so as to automatically calculate the sphericity index of the digital aggregate, wherein the formula (1) is shown in the specification; two-dimensional contour information is obtained through projection of point cloud data on the surface of the digital aggregate in the Z direction, so that a two-dimensional shape index Form2D and a gradient edge angle value GA of the digital aggregate are determined, and the formula (2) and the formula (3) are shown;
in the formula (d)LThe length of the bounding box is the direction of the coarse aggregate; dIThe width of the bounding box is the direction of the coarse aggregate; dSThe height of the bounding box is the direction of the coarse aggregate; theta is a measurement angle; rθIs the radius of the two-dimensional profile in the theta angle direction; delta theta is the measurement angle increment; n is the total number of aggregate projection edge points; i is the ith point of the aggregate projection edge; thetaiMeasured angle, theta, of the ith point representing projected edge of aggregatei+3The measured angle of the (i + 3) th point representing the projected edge of the aggregate.
S2: acquiring Weibull distribution parameters of shape parameters of the digital aggregates; the method for acquiring the Weibull distribution parameter of the shape parameter of the digital aggregate comprises the following steps: extracting enough column block templates, randomly putting aggregate column blocks in a cylindrical space by adopting a rain falling method, calculating column block shape parameters, reading shape parameters of each crushed stone aggregate by using a Fish function, wherein the shape parameters comprise a sphericity index SP, a two-dimensional shape index Form2D and a gradient edge angle value GA, and fitting the shape parameter probability distribution condition of a digital aggregate set in the cylindrical space by using a Weibull distribution function, wherein the formula (4) is shown in the specification:
wherein F is the cumulative probability; x is a two-dimensional shape index, a gradient edge angle index or a sphericity index; λ is a proportional parameter; alpha is a shape parameter; if x represents a two-dimensional shape index, the proportion parameter lambda is a Weibull distribution parameter of the two-dimensional shape index and is recorded as lambdaFThe shape parameter alpha is the corresponding curve fullness parameter aF(ii) a If x represents the gradient edge angle index, the proportion parameter lambda is the Weibull distribution parameter of the gradient edge angle index and is recorded as lambdaG(ii) a The shape parameter alpha is a corresponding curve fullness degree parameter aG(ii) a If x represents the sphericity index, the proportion parameter lambda is the Weibull distribution parameter of the sphericity index and is marked as lambdaSThe shape parameter alpha is the corresponding curve fullness parameter aS。
When Weibull distribution parameters of shape parameters of the digital aggregates meet the requirement of a throwing target, calculating the total volume of the thrown aggregates according to the sub-counting screen residue rate, applying certain confining pressure to a boundary, compressing to a target void ratio, compacting and molding a test piece, and establishing a virtual test piece in a specified shape; and if the Weibull distribution parameters do not meet the requirements of the throwing target, the digital aggregate throwing is carried out again.
And (3) compacting and forming the test piece, wherein as shown in fig. 3, planes at the upper end and the lower end of the cylindrical test piece model are Wall boundary units created in PFC3D software, and are used for simulating a loading plate in an actual testing device, so that a certain load and speed can be applied to compact the cylindrical test piece. In addition, a cylindrical outer Wall, namely a Wall boundary unit, is arranged on the outer side of the test piece model, and a certain lateral confining pressure can be exerted.
Setting 11 parallel test pieces with the serial numbers of A1-A11, B1-B11 and C1-C11 for the three graded crushed stones in the table 1 according to the aggregate form, and calculating the thickness ratio of the grading according to the formula (5);
p4denotes the percent passage of a sieve having a pore size of 4.75mm (sieve No. 4), p200Represents the percent passage of a sieve having a pore size of 0.075mm (sieve No. 200).
According to the actual measurement result of the existing real aggregate (see table 1), a judgment criterion for shape parameter putting is established, namely Weibull distribution parameter lambda of the required shape parameterSIncreasing from 0.65 to 0.75, and if the error value is within 0.01, the distribution condition of each shape parameter of the graded broken stone virtual test piece meeting the requirements is met, as shown in table 2, the aggregate shape distribution of the virtual graded broken stone test piece generated by the method meets the structural requirements of a real test piece, and the accurate control of the aggregate shape distribution in the graded broken stone is realized, and the graded broken stone test piece generated by the method is very close to the structure of the real test piece obtained by X-ray CT. And the other two parameter distributions are obtained by automatic calculation according to the thrown aggregates. Why λ is chosenSThe other two parameters are not chosen because of the clear limitation on the pin content of the particles in the current specifications, whereas the range of the SP parameter is directly related to the pin content.
TABLE 2 thickness ratio and aggregate form parameter table of virtual test piece
The existing test technology is mainly based on manual and phenomenological methods, although a series of shape statistical distribution rules of real aggregates can be obtained through an AIMS test system, the statistical distribution parameters are random, and the accurate selection of the corresponding Weibull distribution parameter lambda by a manual method is difficultSThe coarse aggregate accumulation body of (1); meanwhile, in a graded broken stone test piece, hundreds of coarse aggregate particles exist, the time required for scanning the geometric shape of one coarse aggregate at present is usually several minutes, and the large-scale coarse aggregate scanning is usually required for obtaining a proper graded broken stone test piece, so the test and time cost generated by the scanning are difficult to estimate, and the existing test technology is difficult to estimateAnd controlling the shape of coarse aggregate particles in the graded macadam test piece. The method realizes extraction and screening of geometric shape characteristics of the coarse aggregate through a software built-in programming language, can repeatedly use the calculated geometric parameters of the aggregate, does not need to scan a single coarse aggregate, and can realize Weibull distribution parameter lambda of SP (service provider) of the tested aggregateSThe method has the advantages that accurate control is achieved, the creation efficiency of the graded broken stone test piece is improved undoubtedly, meanwhile, the method almost does not need testing cost, and resources are saved.
S3: constructing a virtual triaxial test model of graded crushed stones; after the virtual test piece formed by compaction reaches the initial balance, loading to the specified three-dimensional static stress, and then carrying out multistage staged dynamic loading to obtain the stress and displacement variation of the wall body, namely the body stress theta in the formula (7)tOctahedral shear stress tauoctThe displacement variation is the strain in table 3, the axial strain is the axial displacement variation divided by the axial length of the test piece (i.e., the height of the test piece), and the radial displacement is the radial displacement variation divided by the radial length of the test piece (i.e., the diameter of the test piece).
TABLE 3 dynamic triaxial test results (A1)
The static stress and the dynamic loading respectively correspond to static stress and dynamic stress states in a static + dynamic loading sequence of an ICAR test scheme in the table 4, wherein the static stress refers to a stress part which is constant in a loading period, and the dynamic stress refers to a part of stress which changes in a half sine manner in the loading period; in order to realize the periodic variation of stress loading, a general virtual test loading method aims at peak stress, adopts a variable-speed loading mode, and determines the loading rate of each step through a servo mechanism, but the method has the following defects: (1) in a cyclic loading period, a required half-sine loading waveform cannot be obtained by a common method, and the stress state in the loading process is difficult to effectively control; (2) the convergence criterion of the general method is based on the ratio of the current stress to the target stress, when the stress reaches the vicinity of the target stress, the loading rate is very small, the stress needs to be continuously adjusted to be close to the target value, the loading stress curve tends to be smooth, and the convergence time is long.
TABLE 4 static + dynamic Loading sequence for ICAR test protocol
The cyclic loading curve of the triaxial test is in a half sine wave form, and the loading stress is gradually reduced at the moment of reaching the peak value; the loading rate is required to be high, and the stress of the horizontal loading plate and the stress of the vertical loading plate need to be accurately controlled at the same time, so that the common virtual test loading method cannot meet the requirement. In order to realize accurate loading of a dynamic triaxial test piece, the embodiment of the invention provides a staged constant rate loading method based on target stress, which is used for loading a virtual test piece and measuring the strain response of graded crushed stones in different stress states so as to calculate and obtain corresponding elastic modulus estimation parameters and various anisotropy parameters and realize rapid loading and convergence balance of the test piece; the method specifically comprises the following steps:
s31: equally dividing the loading time into 20 loading stages, and determining the initial stress and the target stress of each stage through a loading sequence; the triaxial loading includes loading along both axial and radial directions, the two ways are basically the same, and the embodiment takes axial stress loading as an example, as shown in fig. 4; the complete load-time curve was divided into 20 relatively independent loading phases, replacing the "straight" curve.
S32: at the beginning of each loading stage, monitoring the contact between the wall and the particles, and calculating to obtain the integral rigidity K of the contact surfacewSimultaneously monitoring to obtain the contact area A of the wall body and the test piece;
s33: since the whole test process is under small stress loading, the stage loading is assumedContact rigidity K of middle wall body and particleswIf the variation is ignored, the constant loading rate v of the wall body at the current stage is calculated according to the formula (6)w(ii) a The target stress is taken as a convergence condition, and the loading stage is ended when the target stress is reached, so that a large amount of calculation time consumed by contact retrieval in each time step is avoided.
Delta sigma represents the difference value of the current stress and the target stress of the wall; t iswRepresenting the total duration of the current loading phase;
s34: in the testing process, the axial stress and the radial stress of the wall body are recorded once every 100 time steps, whether the recorded stress is larger than the target stress for 3 times or not is judged, and whether the loading time meets the requirement of a loading sequence or not is judged;
s35: if the wall stress and the loading time both meet the requirements, recalculating the constant loading rate v according to the steps S32-S33wStarting the loading of the next stage, and if the wall stress requirement is not met, continuing the loading until the wall stress reaches the target stress; if the loading time requirement is not met, the current loading speed v is setwSet to 0, the test is continued until a given load time is reached, ensuring that the corresponding stress state is reached within the specified load time.
S4: if the stress peak value does not meet the requirements of the test loading sequence, adjusting the friction coefficient and the servo factor of the virtual test piece, carrying out initial balance again and carrying out triaxial loading, and repeatedly debugging parameters until the loading requirements are met; when the stress peak value meets the requirement of a test loading sequence, the strain results of the test piece under different stress states are obtained through the graded broken stone virtual triaxial test, see table 3, and according to the standard method reported by ICAR, the corresponding vertical resilience modulus E is obtained through calculation according to the stress-strain relation of table 3 and by combining the elastic mechanics theory (modulus ═ stress/strain) and the system identification method1Horizontal modulus of restitution E3Shear modulus G.
According to the formulas (8) and (9), respectivelyCalculating the normal anisotropy parameter g of graded crushed stonenTangential anisotropy parameter gm：
Normal anisotropy parameter g of ballastnTangential anisotropy parameter gmThe results are calculated and shown in Table 5.
TABLE 5 Anisotropic parameters of graded crushed stone test pieces
Test piece
gn
gm
Test piece
gn
gm
Test piece
gn
gm
A-1
0.531
0.320
B-1
0.511
0.312
C-1
0.497
0.312
A-2
0.545
0.325
B-2
0.506
0.301
C-2
0.499
0.291
A-3
0.523
0.316
B-3
0.519
0.298
C-3
0.490
0.310
A-4
0.549
0.309
B-4
0.513
0.319
C-4
0.481
0.300
A-5
0.538
0.314
B-5
0.520
0.322
C-5
0.478
0.286
A-6
0.528
0.310
B-6
0.507
0.300
C-6
0.467
0.302
A-7
0.521
0.310
B-7
0.485
0.299
C-7
0.463
0.286
A-8
0.511
0.300
B-8
0.491
0.296
C-8
0.474
0.290
A-9
0.521
0.294
B-9
0.491
0.280
C-9
0.468
0.301
A-10
0.487
0.286
B-10
0.479
0.278
C-10
0.458
0.278
A-11
0.511
0.290
B-11
0.476
0.276
C-11
0.465
0.292
In some embodiments, vertical reboundModulus E1Obtained according to the following method:
vertical modulus of resilience E is pre-estimated through NCHRP 1-37A three-parameter model1According to the change situation of the stress, see formula (7),
in the formula, thetatRepresents the bulk stress; tau isoctRepresents the octahedral shear stress; paIs at standard atmospheric pressure; k is a radical of1、k2And k3Fitting coefficients for the model; obtaining the vertical resilience modulus of the test piece according to the virtual dynamic triaxial test, and fitting the formula (7) through excel to obtain a model parameter k1、k2And k3See table 6; then obtaining the vertical modulus of resilience E corresponding to the stress according to the formula (7)1。
TABLE 6 prediction parameters of vertical modulus of resilience
Grading
k1
k2
k3
R2
A
1.148
0.451
-0.073
98.34％
B
1.125
0.468
-0.019
98.45％
C
1.368
0.429
-0.016
98.26％
As can be seen from the formula (7), the vertical modulus of elasticity E of the graded crushed stone1The values of (A) are related to the stress state and correspond to the horizontal modulus of restitution E in different stress states3And the shear modulus G may also exhibit different values, i.e. the strength of the graded macadam under different stress conditions is anisotropic and varies non-linearly with stress.
S5: according to the test results of the step S1 and the step S4 (see tables 2 and 5), the influence of each parameter on the anisotropic parameter is obtained by using stepwise multiple regression, and a pre-estimation equation of the anisotropic parameter of the graded crushed stone considering the grading and the shape parameters is established, wherein the pre-estimation equation is shown as the formula (10):
g＝a0+a1ln(G/S)+a2ln(λF)+a3ln(λG)+a4ln(λS) (10)
wherein g represents gnOr gm；a0、a1、a2、a3And a4Representing the fitting parameters; G/S represents the thickness ratio of gradation; lambda [ alpha ]FWeibull distribution parameter, λ, representing a two-dimensional shape indexGWeibull distribution parameter, λ, representing gradient edge indexSWeibull distribution parameter representing sphericity index.
S6: the normal anisotropy parameter g of the graded crushed stone obtained in the step S4nTangential anisotropy ofSexual parameter gmRespectively corresponding to Weibull distribution parameter lambda of digital aggregate shape parameter through excelF、λG、λSAnd G/S linear regression fitting to obtain Gn、gmCorresponding fitting parameter a0、a1、a2、a3And a4A value of (i), i.e. gnCorresponding to a set of fitting parameters, gmAlso corresponding to a set of fitting parameters which do not interfere with each other, and then rapidly predicting the normal anisotropy parameter g of the graded crushed stone according to the formula (10)nTangential anisotropy parameter gm。
The fitting results are shown in table 7, and the results of the consistency check are all greater than 95%. As shown in fig. 5 and fig. 6, the correlation between the predicted value and the test value is high, which indicates that the estimation equation of the embodiment of the present invention has strong rationality.
TABLE 7 fitting results of anisotropy parameters
Anisotropy parameter
a0
a1
a2
a3
a4
R2
gn
0.0020
-0.0930
-0.0602
0.1186
-0.4003
0.9723
gm
0.0010
-0.0275
0.0552
0.0517
-0.2997
0.9674
The physical significance of the prediction equation is as follows: (a) the influence of the grading of the test piece on the anisotropy can be represented by the thickness ratio G/S, when the content of coarse particles is high, the graded broken stone is easy to form an inner arch effect in the forming process, the movement of the fine particles is hindered, a cavity is formed in a local area, the uniformity of the formed test piece is not facilitated, the anisotropy of the graded broken stone test piece is more obvious, and the anisotropy parameter is smaller; (b) the SP value of the aggregate particles is closer to 1.0, the particles are closer to perfect spheres, and the graded macadam is easy to be influenced by compaction and loading directions to generate an anisotropic deposition phenomenon, so that the anisotropic parameter is also reduced along with the increase of the SP value; (c) considering the contact effect among aggregate frameworks, the two-dimensional shape index Form2D has a large influence on the horizontal modulus and has a certain lifting effect on the shear modulus.
The method can quickly predict the resilience modulus of the graded broken stone in each direction under different stress states, and can provide theoretical guidance for material design of the graded broken stone without performing indoor tests, field tests and test piece two-dimensional section measurement. The existing test technology can not control the shape of coarse aggregate particles in the graded broken stone test piece, the shape distribution rule and the fitting result are usually difficult to predict and specify, and meanwhile, the obtained test result has large discreteness, so that the influence of indexes such as particle grading, aggregate shape and the like on model parameters can not be accurately obtained.
The above description is only for the preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention shall fall within the protection scope of the present invention.