CN102222126B - Method for simulating numerical value of graded crushed stone tri-axial test - Google Patents

Abstract

The invention discloses a method for simulating a numerical value of a graded crushed stone tri-axial test. The graded crushed stone tri-axial test is simulated by establishing a physical model and a mechanical model, and the method comprises the following steps of: testing basic parameters, stimulating die trial, and generating a graded crushed stone stimulating test-piece; endowing the physical model with micro mechanical parameters, constructing a mechanical model; and performing loading simulation on the graded crushed stone stimulating test-piece to obtain a stress-strain curve of graded crushed stone. By the method, the stress-strain curve of the graded crushed stone in the tri-axial test can be accurately and conveniently reproduced, a change rule of mechanical properties is revealed, and the deep study of a graded crushed stone deterioration mechanism is facilitated.

Description

A kind of method for numerical simulation of graded broken stone triaxial test

Technical field

The invention belongs to the Transportation and Civil Engineering field, relate to a kind of method for numerical simulation of graded broken stone triaxial test.The present invention is based on PFC ^2DSoftware platform can be predicted graded broken stone mechanical behavior under the load action accurately, easily.

Background technology

Graded broken stone belongs to typical road basement material, and physico mechanical characteristic is very complicated.At present, often adopt the strength and deformation rule of indoor Study on Triaxial Tests graded broken stone, its ultimate principle and step are as follows: (1) prepares test specimen by maximum dry density and optimum moisture content; (2) stress～strain monitoring system is installed; (3) test specimen is applied axle pressure; (4) the repairing experiment result obtains the graded broken stone stress-strain diagram.At present, there are no the report of graded broken stone triaxial test method for numerical simulation.

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

Summary of the invention

For the problem that above-mentioned prior art exists, the purpose of this invention is to provide a kind of method for numerical simulation of graded broken stone triaxial test.The method can be predicted the Changing Pattern of graded broken stone Mechanical Characters of Composite Ground under the load action accurately, easily.

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

A kind of method for numerical simulation of graded broken stone triaxial test is characterized in that, carries out according to following steps:

1) structure of physical model

(1) simulation of test specimen

1. the test of basic parameter:

Measure rubble density, determine 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 a leaf length be D and forms the semiclosed rectangle of opening upwards 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 _i, see formula (1).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;

$S_i=\frac{4\mathrm{dhK}{P}_i}{{\mathrm{\ρ}}_i}{\mathrm{\ρ}}_{\max }---\left(1\right)$

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

D: test specimen diameter, cm;

H: height of specimen, 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.

Generate successively as stated above each specification aggregate particle;

4. the generation of imitation specimen:

Utilize PFC ^2DIt is the simulation pressing plate of D that built-in command " wall " generates length.Pressing plate promotes to simulate aggregate particle in the die trial straight down with speed V, until the computing step number reaches till the n.N calculates by formula (2);

$n=\frac{L}{V{d}_t}=\frac{H-h}{{\mathrm{Vd}}_t}---\left(2\right)$

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

L: simulation pressing plate displacement, cm;

V: simulation pressing plate translational speed, cm/s;

d _t: time step, s/step;

H: die trial height, cm;

H: height of specimen, cm.

2) structure of mechanical model

1. choosing of contact model:

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

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 ν, shear modulus G, coefficientoffrictionμ.

The micro mechanics parameter can be obtained by the indoor 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 by control body of wall speed with the constant method of maintenance wall stress.Body of wall speed is calculated and is seen formula (3);

ν＝δ(σ _m-σ _n) （3）

In the formula: σ _n: target stress, KPa;

σ _m: the wall stress in the current Time step, KPa;

δ: servo coefficient, calculate by formula (4):

$\mathrm{\δ}=\frac{h}{\stackrel{\‾}{K_n}\mathrm{N\Δt}}\×{10}^{-2}---\left(4\right)$

In the formula:

The average contact strength of particle of the vertical body of wall of simulation die trial in the current Time step, KPa;

Δ t: accumulate computing time, s;

N: the particle number that contacts with the vertical body of wall of simulation die trial in the current Time step;

H: height of specimen, cm.

2. the simulation of loading procedure:

The control confined pressure promotes to simulate pressing plate straight down with constant speed, and records displacement and the contact force of simulation pressing plate in each Time step;

3. result's arrangement:

Draw the relation curve of axial stress～axial strain.

The present invention has the following advantages:

(1) can reproduce accurately, easily in the triaxial test graded broken stone stress～strain curve and disclose the Mechanical Characters of Composite Ground Changing Pattern, be conducive to further investigate the graded broken stone failure mechanism, improve the graded broken stone performance;

(2) avoid the high and unhandy problem of indoor triaxial test Instrumental cost, improved test efficiency, saved research cost.

Description of drawings

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

Fig. 2 is the synoptic diagram of graded broken stone three axis values testphysical prototypes;

Fig. 3 is the synoptic diagram of graded broken stone three axis values test loading procedure;

Fig. 4 is the axial stress～axial strain curve (A grating) of graded broken stone triaxial test;

Fig. 5 is the axial stress～axial strain curve (B grating) of graded broken stone triaxial test;

Fig. 6 is the axial stress～axial strain curve (C grating) of graded broken stone triaxial test;

Fig. 7 is the contrast (A grating) of graded broken stone triaxial test numerical simulation result and indoor measured result;

The present invention is described in further detail below in conjunction with drawings and Examples.

Embodiment

According to technical scheme of the present invention, present embodiment provides a kind of method for numerical simulation of graded broken stone triaxial test, and take lake, safe and comfortable sea limestone gravel as example, the rubble density measurement the results are shown in Table 1, and the micro mechanics parameter sees Table 2, and the grating that adopts sees Table 3.

Table 1 rubble density

Aggregate size (mm)	20～40	10～20	5～10	2～5
					Apparent density (g/cm 3）	2.712	2.709	2.692	2.681

Table 2 micro mechanics parameter

Poisson ratio	Shear mode (GPa)	Friction factor
			0.2	400	0.7

Table 3 aggregate grading

Lower in the table 3 grating A as the implementation step of example explanation graded broken stone triaxial test method for numerical simulation be:

1) structure of physical model

1. utilize PFC ^2DIt is the vertical body of wall of 75cm and the horizontal body of wall that a leaf length is 30cm that built-in command " wall " generates two leaf length, and the semiclosed rectangle of the opening upwards that it forms is the simulation die trial, sees Fig. 1;

2. by 98% compactness prepare test specimen (Φ 30cm * h60cm), then graded broken stone mineral aggregate particle generative process is as follows:

Calculate the two-dimensional map area that 19～31.5mm gathers materials: $S_1=\frac{4\mathrm{dhK}{P}_1}{{\mathrm{\ρ}}_1}{\mathrm{\ρ}}_{\max }=$ $\frac{4\×60\×30\×0.98\×0.24}{2.712}\×2.402=1499.9\left({\mathrm{cm}}^2\right),$ Utilize PFC ^2DBuilt-in command " ball " generates the particle of diameter between 19～31.5mm constantly, when its total area reaches 1499.9cm ²The time, stop particle and generate; Calculate the two-dimensional map area that 9.5～19mm gathers materials: $S_2=\frac{4\mathrm{dhK}{P}_2}{{\mathrm{\ρ}}_2}{\mathrm{\ρ}}_{\max }=\frac{4\×60\×30\×0.98\×0.20}{2.709}\×2.402=1251.3\left({\mathrm{cm}}^2\right),$ Utilize PFC ^2DBuilt-in command " ball " generates the particle of diameter between 9.5～19mm constantly, when its total area reaches 1251.3cm ²The time, stop particle and generate; Calculate the two-dimensional map area that 4.75～9.5mm gathers materials: $S_3=\frac{4\mathrm{dhK}{P}_3}{{\mathrm{\ρ}}_3}{\mathrm{\ρ}}_{\mathrm{nax}}=\frac{4\×60\×30\×0.98\×0.2}{2.692}\×2.402=1259.2\left({\mathrm{cm}}^2\right),$ Utilize PFC ^2DBuilt-in command " ball " generates the particle of diameter between 4.75～9.5mm constantly, when its total area reaches 1259.2cm ²The time, stop particle and generate; Calculate the two-dimensional map area that 2.36～4.75mm gathers materials: $S_4=\frac{4\mathrm{dhK}{P}_4}{{\mathrm{\ρ}}_4}{\mathrm{\ρ}}_{\max }=\frac{4\×60\×30\×0.98\×0.20}{2.681}\×2.402=1264.3\left({\mathrm{cm}}^2\right),$ Utilize PFC ^2DBuilt-in command " ball " generates the particle of diameter between 2.36～4.75mm constantly, when its total area reaches 1264.3cm ²The time, stop particle and generate; Calculate the two-dimensional map area that 0.6～2.36mm gathers materials: $S_5=\frac{4\mathrm{dhK}{P}_5}{{\mathrm{\ρ}}_5}{\mathrm{\ρ}}_{\max }=\frac{4\×60\×30\×0.98\×0.16}{2.681}\×2.402=1011.5\left({\mathrm{cm}}^2\right),$ Utilize PFC ^2DBuilt-in command " ball " generates the particle of diameter between 0.6～2.36mm constantly, when its total area reaches 1011.5cm ²The time, stop the particle generation, thereby finish the generation of graded broken stone;

3. determine that body of wall speed is 0.1cm/s, Time step is 0.001, and then computing step number is: $n=\frac{L}{V{d}_t}=\frac{H-h}{{\mathrm{Vd}}_t}=\frac{75-60}{0.1\×0.001}=150000\left(\mathrm{step}\right).$ So utilize PFC ^2DBuilt-in command " wall " generate length be the horizontal body of wall of 30cm with the simulation pressing plate, and make its speed with 0.1cm/s vertically promote to simulate aggregate particle in the die trial, until the step reach till 150000 during computing, see Fig. 3.

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 present embodiment adopts is 40KPa, and then the speed of the vertical body of wall of simulation die trial should satisfy in each Time step: $\mathrm{\ν}=\mathrm{\δ}({\mathrm{\σ}}_m-{\mathrm{\σ}}_n)=\frac{h\×{10}^{-2}}{\stackrel{\‾}{K_n}\mathrm{N\Δt}}({\mathrm{\σ}}_m-{\mathrm{\σ}}_n)=\frac{60\×{10}^{-2}}{\stackrel{\‾}{K_n}\mathrm{N\Δt}}({\mathrm{\σ}}_m-40),$ Here, PFC ^2DCan be according to the variation of Time step and automatic acquisition

N, Δ t and σ _m

2. the simulation of loading procedure:

The control confined pressure is 40KPa, promotes straight down to simulate the pressing plate (see figure 3) with the speed of 3mm/min, and records displacement and the contact force of simulation pressure head in each Time step;

3. result's arrangement:

Draw the relation curve of axial stress～axial strain, see Fig. 4.

According to above-mentioned steps, can obtain successively the graded broken stone triaxial test analog result of grating B and grating C in the table 3, see Fig. 5～Fig. 6.

Fig. 7 has provided the contrast of numerical simulation result and indoor measured result, can find out, both are substantially identical; Simultaneously, whole process is all carried out by computing machine, need not to rely on expensive testing equipment, has also avoided the complicated processes of test material preparation, instrumentation, has improved test efficiency, has saved research cost.Proof the present invention can predict graded broken stone mechanical behavior under the load action accurately, easily.

Claims (1)

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

1) structure of physical model

1. the test of basic parameter:

Measure rubble density, determine 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 a leaf length be D and forms the semiclosed rectangle of opening upwards with the simulation die trial;

3. the generation of graded broken stone:

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

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;

$S_i=\frac{{4\mathrm{dhKP}}_i}{{\mathrm{\ρ}}_i}{\mathrm{\ρ}}_{\max }---\left(1\right)$

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

D: test specimen diameter, unit: cm;

H: height of specimen, unit: cm;

K: compactness, unit: %;

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;

Generate successively as stated above each specification aggregate particle;

4. the generation of imitation specimen:

Utilize PFC ^2DIt is the simulation pressing plate of D that built-in command " wall " generates length, and pressing plate promotes to simulate aggregate particle in the die trial straight down with speed V, until the computing step number reaches till the n, n is by calculating with following formula (2);

$n=\frac{L}{{\mathrm{Vd}}_t}=\frac{H-h}{{\mathrm{Vd}}_t}---\left(2\right)$

In the formula: n: computing step number, unit: step;

L: simulation pressing plate displacement, unit: cm;

V: simulation pressing plate translational speed, unit: cm/s;

d _t: time step, unit: s/step;

H: die trial height, unit: cm;

H: height of specimen, unit: cm;

2) structure of mechanical model

1. choosing of contact model:

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

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 ν, shear modulus G, coefficientoffrictionμ;

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

3) simulation of loading procedure and result arrangement

1. the control of confined pressure:

To keep the constant method of wall stress to realize confined pressure control, body of wall speed is calculated and is undertaken by formula (3) by control body of wall speed;

ν＝δ(σ _m-σ _n) （3）

In the formula: σ _n: target stress, unit: KPa;

σ _m: the wall stress in the current Time step, unit: KPa;

δ: servo coefficient, calculate by formula (4):

$\mathrm{\δ}=\frac{h}{\stackrel{\‾}{K_n}\mathrm{N\Δt}}\×{10}^{-2}---\left(4\right)$

In the formula:

The average contact strength of particle of the vertical body of wall of simulation die trial in the current Time step, KPa;

Δ t: accumulate computing time, unit: s;

N: the particle number that contacts with the vertical body of wall of simulation die trial in the current Time step;

H: height of specimen, unit: cm;

2. the simulation of loading procedure:

The control confined pressure promotes to simulate pressing plate straight down with constant speed, and records displacement and the contact force of simulation pressing plate in each Time step;

3. result's arrangement:

Draw the relation curve of axial stress～axial strain.

Images