CN102564855A - Numerical method for graded crushed stone dynamic triaxial test - Google Patents

Abstract

The invention discloses a numerical method for a graded crushed stone dynamic triaxial test. The numerical method comprises the following steps of: simulating the graded crushed stone dynamic triaxial test through establishing a physical model and a mechanical model by using a PFC2D software platform, wherein the simulation operation comprises test of basic parameters, simulation of a test model and generation of a graded crushed stone simulation specimen; secondly, giving micro mechanical parameters to the physical model, and constructing the mechanical model; and then, carrying out repeated dynamic load simulation on the graded crushed stone simulation specimen so as to obtain a graded crushed stone stress-strain curve and a graded crushed stone permanent deformation-loading frequency curve. According to the numerical method disclosed by the invention, the graded crushed stone permanent deformation-loading frequency curve in a triaxial test can be reproduced accurately, conveniently and quickly, and a graded crushed stone deformation rule is disclosed, so that the graded crushed stone fracture mechanism is favorable to research intensively; and the problems of high instrument price and inconvenience for operation in an indoor dynamic triaxial test are avoided, so that the test efficiency is improved, and the research cost is saved.

Description

The numerical method of the moving triaxial test of a kind of graded broken stone

Technical field

The invention belongs to the Traffic Civil field, relate to the numerical method of the moving triaxial test of a kind of graded broken stone.This method adopts PFC ^2DSoftware can accurately be simulated load and act on down graded broken stone plastic yield accumulation repeatedly as basic platform, and prediction graded broken stone permanent strain rule.

Background technology

Graded broken stone belongs to typical road basement material, and physico mechanical characteristic is very complicated.At present, often adopt indoor moving Study on Triaxial Tests graded broken stone deformational behavior, its ultimate principle and step are following: (1) prepares test specimen by maximum dry density and optimum moisture content; (2) erection stress～strain monitoring system; (3) test specimen is applied axial hydrodynamic power; (4) the arrangement test findings is obtained graded broken stone permanent strain～axle and is carried the number of times relation curve.At present, do not see the report that the moving triaxial test numerical experimentation method of graded broken stone is arranged.

The applicant analyzes the indoor moving triaxial test method of above-mentioned graded broken stone, has following defective: (1) experimentation cost is high, efficient is low, is unfavorable for disclosing the graded broken stone deformational behavior; (2) inner material that is difficult to monitor graded broken stone under the load action is migrated and the mesomechanics characteristic.

Summary of the invention

Problem to above-mentioned prior art exists the objective of the invention is to, and the numerical method of the moving triaxial test of a kind of graded broken stone is provided, and this method is utilized PFC ^2DSoftware platform can accurately be simulated load and acted on down graded broken stone plastic yield accumulation repeatedly, and prediction graded broken stone permanent strain rule.

In order to realize above-mentioned task, the present invention takes following technical solution to be achieved:

The numerical method of the moving triaxial test of a kind of graded broken stone is characterized in that, carries out according to following steps:

1) CONSTRUCTINT PHYSICAL MODELS

(1) simulation of test specimen

1. the test of basic parameter:

Measure rubble density, confirm graded broken stone maximum dry density and optimum moisture content;

2. the simulation of die trial:

Utilize PFC ^2DBuilt-in command " wall " generates the horizontal body of wall that vertical body of wall that two leaf length are H and two leaf length are D and forms the sealing rectangle with the simulation die trial;

3. the generation of graded broken stone:

Calculate the two-dimensional map area S that i kind specification is gathered materials according to mineral aggregate gradation, rubble density, compactness, sample dimensions and maximum dry density by formula (1) _i

$S_i=\frac{\mathrm{dhK}{P}_i}{{\mathrm{\ρ}}_i}{\mathrm{\ρ}}_{\max }---\left(1\right)$

In the formula: ρ _Max: maximum dry density, g/cm ³

D: test specimen diameter, cm;

H: test specimen height, cm;

K: compactness, %;

P _i: the grader retained percentage that i kind specification is gathered materials, %, i are the natural number greater than 0;

ρ _i: the density that i kind specification is gathered materials, g/cm ³, i is the natural number greater than 0.

Utilize PFC ^2DBuilt-in command " ball " generates particle in the simulation die trial, and makes it to meet the particle diameter requirement that i kind specification is gathered materials, when the total area that generates particle reaches S _iThe time, stop particle and generate;

Generate each specification aggregate particle as stated above successively.

2) structure of mechanical model

1. choosing of contact model:

Adopt Hertz model and gliding model to describe the graininess architectural feature and the nonlinear mechanics characteristic of graded broken stone, wherein, the Hertz model is through Poisson ratio v, shear modulus G definition, and gliding model is through the coefficientoffriction definition;

2. giving of physical model micro mechanics parameter:

Utilize PFC ^2DBuilt-in command " prop " is given the graded broken stone physical model with the micro mechanics parameter, comprises Poisson ratio v, shear modulus G, coefficientoffriction.

The micro mechanics parameter can be obtained through the indoor moving threeaxis test results inverse of graded broken stone.

3) simulation of loading procedure and result arrangement

1. the control of confined pressure:

Realize confined pressure control through control body of wall speed to keep the constant method of body of wall stress, body of wall speed is calculated by formula (2):

v＝δ(σ _m-σ _n) (2)

In the formula: $\mathrm{\δ}=\frac{L}{\stackrel{\‾}{K_n}\mathrm{N\Δ\; t}}---\left(3\right)$

σ _n: target stress, KPa;

σ _m: the body of wall stress during current calculating in the step, KPa;

δ: servo coefficient;

is current when the calculating average contact strength of particle of the vertical body of wall of simulation die trial in the step, KPa;

Δ t: accumulate computing time, s;

N: during current calculating in the step with simulate the particle number that the vertical body of wall of die trial contacts;

H: the length of the vertical body of wall of simulation die trial, m.

2. the simulation of a loading procedure:

Utilize two sides, left and right sides body of wall to keep the imitation specimen confined pressure steady, keep the bottom body of wall static, promote pressing plate straight down with constant acceleration a; And when reaching computing step number n, make the pressing plate displacement equal L; Make zero with seasonal presser motion speed, so far, one time loading procedure finishes; Body of wall acceleration a calculates by formula (4);

$a=\frac{2\mathrm{nL}}{t^2(n+1)}---\left(4\right)$

In the formula: a: simulation pressing plate translational acceleration, m/s ²

N: computing step number, step;

L: simulation pressing plate amplitude, m;

T: load time, s.

3. the simulation of a uninstall process:

After loading procedure finishes; Utilize two sides, left and right sides body of wall to keep the imitation specimen confined pressure steady, order bottom body of wall is static, promotes pressing plate simulation uninstall process straight up with constant acceleration a (seeing formula (4)); And when reaching computing step number n, make presser motion to initial position; Make zero with seasonal presser motion speed, so far, one time uninstall process finishes.

The simulation of 4. voltage stabilizing process:

After uninstall process finishes, utilize four sides, upper and lower, left and right body of wall to keep the imitation specimen confined pressure steady, static with seasonal four sides wall body and test specimen particle till the computing step number reaches N, so far, the voltage stabilizing process finishes.Computing step number N calculates by formula (5).

$N=\frac{T}{d_t}---\left(5\right)$

In the formula: N: computing step number, step;

T: voltage stabilizing time, s;

d _t: go on foot s/step during calculating;

5. repeat loading simulation:

By 2. to 3. imitation specimen being repeated loading, unloading, voltage stabilizing to 4. order, and the displacement and the contact force of simulation pressing plate in the step when writing down each and calculating.

6. result's arrangement:

Draw the axial strain～axial stress relation curve in loading, unloading and the voltage stabilizing process, the relation curve of axial strain～number of loading.

The present invention has the following advantages:

(1) can reproduce graded broken stone axial strain～number of loading curve in the moving triaxial test accurately, easily, disclose the graded broken stone deformation rule, help furtheing investigate the graded broken stone failure mechanism;

(2) avoid the high and unhandy problem of instrument cost in the indoor moving triaxial test, improved test efficiency, practiced thrift research cost.

Description of drawings

Fig. 1 is the synoptic diagram of the moving three axis values test simulation die trials of graded broken stone;

Fig. 2 is the synoptic diagram of the moving three axis values test of graded broken stone physical model;

Fig. 3 is the contrast (A grating) of moving three axis values test simulation results of graded broken stone and indoor measured result;

Fig. 4 is a loading-unloading-voltage stabilizing axial stress～axial strain curve (A grating) of the moving three axis values test of graded broken stone

Fig. 5 be the moving three axis values test of graded broken stone repeat to load axial stress～axial strain curve (A grating)

Fig. 6 is the axial strain～number of loading curve of the moving three axis values test of graded broken stone;

Below in conjunction with accompanying drawing and instance the present invention is done further detailed description.

Embodiment

According to technical scheme of the present invention, this instance provides the method for numerical simulation of the moving triaxial test of a kind of graded broken stone, is example with lake, safe and comfortable sea limestone gravel, and rubble density measurement result sees table 1, and the micro mechanics parameter is seen table 2.

Table 1 rubble density

Aggregate size (mm)	20～40	10～20	5～10	2～5
					Apparent density (g/cm3)	2.712	2.709	2.692	2.681

Table 2 micro mechanics parameter

Poisson ratio	Modulus of shearing (GPa)	Friction factor
			0.2	220	0.5

Table 3 aggregate grading

With grating A in the table 3 is that example explains that the implementation step of graded broken stone triaxial test method for numerical simulation is:

1) CONSTRUCTINT PHYSICAL MODELS

1. utilize PFC ^2DIt is the vertical body of wall of 21cm and the horizontal body of wall that a leaf length is 10cm that built-in command " wall " generates two leaf length, and the semiclosed rectangle that its opening of forming makes progress is the simulation die trial, sees Fig. 1;

2. by 98% compactness prepare test specimen (Ф 10cm * h21cm), then graded broken stone mineral aggregate particle generative process is following:

Calculating particle size range is the two-dimensional map area that 19～31.5mm gathers materials:

${\mathrm{<figure-callout\; id="1"\; label="S"\; filenames="HDA0000127897130000022.png"\; state="\{\{state\}\}">S</figure-callout>}}_1=\frac{\mathrm{DhK}{P}_2}{{\mathrm{\&rho;}}_2}\&times;{\mathrm{\&rho;}}_{\mathrm{Max}}=\frac{21\&times;10\&times;0.98\&times;0.42}{2.709}\&times;2.402=76.6\left({\mathrm{Cm}}^2\right),$ Utilize PFC ^2DBuilt-in command " ball " generates the particle of diameter between 19～31.5mm constantly, when its total area reaches 76.6cm ²The time, stop particle and generate; Calculating particle size range is the two-dimensional map area that 9.5～19mm gathers materials:

$S_2=\frac{\mathrm{DhK}{P}_2}{{\mathrm{\&rho;}}_2}\&times;{\mathrm{\&rho;}}_{\mathrm{Max}}=\frac{21\&times;10\&times;0.98\&times;0.15}{2.709}\&times;2.402=27.4\left({\mathrm{Cm}}^2\right),$ Utilize PFC ^2DBuilt-in command " ball " generates the particle of diameter between 9.5～19mm constantly, when its total area reaches 27.4cm ²The time, stop particle and generate; Calculating particle size range is the two-dimensional map area that 4.75～9.5mm gathers materials:

$S_3=\frac{\mathrm{DhK}{P}_3}{{\mathrm{\&rho;}}_3}\&times;{\mathrm{\&rho;}}_{\mathrm{Max}}=\frac{21\&times;10\&times;0.98\&times;0.07}{2.692}\&times;2.402=12.9\left({\mathrm{Cm}}^2\right),$ Utilize PFC ^2DBuilt-in command " ball " generates the particle of diameter between 4.75～9.5mm constantly, when its total area reaches 12.9cm ²The time, stop particle and generate; Calculating particle size range is the two-dimensional map area that 2.36～4.75mm gathers materials:

$S_4=\frac{\mathrm{DhK}{P}_4}{{\mathrm{\&rho;}}_4}\&times;{\mathrm{\&rho;}}_{\mathrm{Max}}=\frac{21\&times;10\&times;0.98\&times;0.12}{2.681}\&times;2.402=22.1\left({\mathrm{Cm}}^2\right),$ Utilize PFC ^2DBuilt-in command " ball " generates the particle of diameter between 2.36～4.75mm constantly, when its total area reaches 22.1cm ²The time, stop particle and generate; Calculating particle size range is the two-dimensional map area that 0.6～2.36mm gathers materials:

$S_5=\frac{\mathrm{DhK}{P}_5}{{\mathrm{\&rho;}}_5}\&times;{\mathrm{\&rho;}}_{\mathrm{Max}}=\frac{21\&times;10\&times;0.98\&times;0.24}{2.681}\&times;2.402=44.3\left({\mathrm{Cm}}^2\right),$ Utilize PFC ^2DBuilt-in command " ball " generates the particle of diameter between 0.6～2.36mm constantly, when its total area reaches 44.3cm ²The time, stop particle and generate, thus the generation of completion graded broken stone;

2) input of micro mechanics parameter

Utilize PFC ^2DBuilt-in command " prop " is given the graded broken stone physical model with micro mechanics parameter in the table 2.

3) simulation of loading procedure and result arrangement

1. the control of confined pressure:

The confined pressure that this instance adopted is 50KPa, and the speed of simulating the vertical body of wall of die trial when then each calculates in the step should satisfy: $v=\mathrm{\&delta;}({\mathrm{\&sigma;}}_m-{\mathrm{\&sigma;}}_n)=\frac{L}{\stackrel{\&OverBar;}{K_n}\mathrm{N\&Delta;\; t}}({\mathrm{\&sigma;}}_m-{\mathrm{\&sigma;}}_n)=\frac{0.21}{\stackrel{\&OverBar;}{K_n}\mathrm{N\&Delta;\; t}}({\mathrm{\&sigma;}}_m-50),$ Here, PFC ^2DCan be when calculating the step variation and obtain automatically

N, Δ t and σ _m

2. the simulation of loading-unloading-voltage stabilizing process:

If left and right confined pressure is 50KPa, confirm that pressing plate amplitude L is 2mm, step d during calculating _tBe 0.00001, load time t is 0.05s, and the computing step number is:

The pressing plate acceleration $a=\frac{2\&times;5000\&times;2}{{0.05}^2(5000+1)}=\frac{2\&times;5000\&times;0.002}{{0.05}^2(5000+1)}=1.6(m/s^2),$ Keep two sides, left and right sides body of wall confined pressure 50KPa, keep the bottom body of wall static, promote pressing plate straight down with constant acceleration a, and when reaching computing step number n, make the pressing plate displacement equal L, make zero with seasonal presser motion speed, so far, loading procedure finishes.

If left and right confined pressure is 50KPa, confirm that pressing plate amplitude L is 2mm, going on foot dt during calculating is 0.00001, and discharge time t is 0.05s, and the computing step number is: The pressing plate acceleration $a=\frac{2\&times;5000\&times;2}{{0.05}^2(5000+1)}=\frac{2\&times;5000\&times;0.002}{{0.05}^2(5000+1)}=1.6(m/s^2),$ Utilize two sides, left and right sides body of wall to keep the imitation specimen confined pressure steady, order bottom body of wall is static, promotes pressing plate simulation uninstall process straight up with constant acceleration a; And when reaching computing step number n, make presser motion to initial position; Make zero with seasonal presser motion speed, so far, uninstall process finishes.

If the voltage stabilizing time is 0.9s, step d during calculating _tBe 0.00001, the computing step number

Utilize four sides, upper and lower, left and right body of wall to keep the imitation specimen confined pressure steady, static with seasonal four sides wall body and test specimen particle till the computing step number reaches N, so far, the voltage stabilizing process finishes.

Order by loading, unloading, voltage stabilizing applies the repetition dynamic load to imitation specimen, and writes down displacement and the contact force that goes on foot interior simulation pressing plate when each calculates.

3. result's arrangement:

Draw numerical simulation result and indoor measured result correlation curve, see Fig. 3.

Draw the relation curve of a loading-unloading-voltage stabilizing process axial stress～axial strain, see Fig. 4.

Repeating loading procedure with 100 times is the cycle, draws the relation curve of axial stress～axial strain, sees Fig. 5.

Draw the relation curve of axial strain～number of loading, see Fig. 6.

Claims (1)

1. the numerical method of the moving triaxial test of graded broken stone is characterized in that, carries out according to following steps:

1) CONSTRUCTINT PHYSICAL MODELS

(1) simulation of test specimen

1. the test of basic parameter:

Measure rubble density, confirm graded broken stone maximum dry density and optimum moisture content;

2. the simulation of die trial:

Utilize PFC ^2DBuilt-in command " wall " generates the horizontal body of wall that vertical body of wall that two leaf length are H and two leaf length are D and forms the sealing rectangle with the simulation die trial;

3. the generation of graded broken stone:

Calculate the two-dimensional map area S that i kind specification is gathered materials according to mineral aggregate gradation, rubble density, compactness, sample dimensions and maximum dry density by formula (1) _i

$S_i=\frac{\mathrm{dhK}{P}_i}{{\mathrm{\&rho;}}_i}{\mathrm{\&rho;}}_{\max }---\left(1\right)$

In the formula: ρ _Max: maximum dry density, g/cm ³

D: test specimen diameter, cm;

H: test specimen height, cm;

K: compactness, %;

P _i: the grader retained percentage that i kind specification is gathered materials, %, i are the natural number greater than 0;

ρ _i: the density that i kind specification is gathered materials, g/cm ³, i is the natural number greater than 0;

Utilize PFC ^2DBuilt-in command " ball " generates particle in the simulation die trial, and makes it to meet the particle diameter requirement that i kind specification is gathered materials, when the total area that generates particle reaches S _iThe time, stop particle and generate;

Generate each specification aggregate particle as stated above successively;

2) structure of mechanical model

1. choosing of contact model:

Adopt Hertz model and gliding model to describe the graininess architectural feature and the nonlinear mechanics characteristic of graded broken stone, wherein, the Hertz model is through Poisson ratio v, shear modulus G definition, and gliding model is through the coefficientoffriction definition;

2. giving of physical model micro mechanics parameter:

Utilize PFC ^2DBuilt-in command " prop " is given the graded broken stone physical model with the micro mechanics parameter, comprises Poisson ratio v, shear modulus G, coefficientoffriction;

The micro mechanics parameter can be obtained through the indoor moving threeaxis test results inverse of graded broken stone;

3) simulation of loading procedure and result arrangement

1. the control of confined pressure:

Realize confined pressure control through control body of wall speed to keep the constant method of body of wall stress, body of wall speed is calculated by formula (2):

v＝δ(σ _m-σ _n) (2)

In the formula: $\mathrm{\&delta;}=\frac{L}{\stackrel{\&OverBar;}{K_n}\mathrm{N\&Delta;\; t}}---\left(3\right)$

σ _n: target stress, KPa;

σ _m: the body of wall stress during current calculating in the step, KPa;

δ: servo coefficient;

is current when the calculating average contact strength of particle of the vertical body of wall of simulation die trial in the step, KPa;

Δ t: accumulate computing time, s;

N: during current calculating in the step with simulate the particle number that the vertical body of wall of die trial contacts;

H: the length of the vertical body of wall of simulation die trial, m;

2. the simulation of a loading procedure:

Utilize two sides, left and right sides body of wall to keep the imitation specimen confined pressure steady, keep the bottom body of wall static, promote pressing plate straight down with constant acceleration a; And when reaching computing step number n, make the pressing plate displacement equal L; Make zero with seasonal presser motion speed, so far, one time loading procedure finishes; Body of wall acceleration a calculates by formula (4);

$a=\frac{2\mathrm{nL}}{t^2(n+1)}---\left(4\right)$

In the formula: a: simulation pressing plate translational acceleration, m/s ²

N: computing step number, step;

L: simulation pressing plate amplitude, m;

T: load time, s;

3. the simulation of a uninstall process:

After loading procedure finishes; Utilize two sides, left and right sides body of wall to keep the imitation specimen confined pressure steady, order bottom body of wall is static, promotes pressing plate simulation uninstall process with the acceleration a of formula (4) straight up as constant acceleration; And when reaching computing step number n, make presser motion to initial position; Make zero with seasonal presser motion speed, so far, one time uninstall process finishes;

The simulation of 4. voltage stabilizing process:

After uninstall process finishes, utilize four sides, upper and lower, left and right body of wall to keep the imitation specimen confined pressure steady, static with seasonal four sides wall body and test specimen particle till the computing step number reaches N, so far, the voltage stabilizing process finishes, and computing step number N calculates by formula (5);

$N=\frac{T}{d_t}---\left(5\right)$

In the formula: N: computing step number, step;

T: voltage stabilizing time, s;

d _t: go on foot s/step during calculating;

5. repeat loading simulation:

By 2. to 3. imitation specimen being repeated loading, unloading and voltage stabilizing to 4. order, and the displacement and the contact force of simulation pressing plate in the step when writing down each and calculating;

6. result's arrangement:

Draw the axial strain～axial stress relation curve in loading, unloading and the voltage stabilizing process, the relation curve of axial strain～number of loading.

Images