CN109885973B - Deformation cycle damage calculation method - Google Patents

Deformation cycle damage calculation method Download PDF

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CN109885973B
CN109885973B CN201910221689.3A CN201910221689A CN109885973B CN 109885973 B CN109885973 B CN 109885973B CN 201910221689 A CN201910221689 A CN 201910221689A CN 109885973 B CN109885973 B CN 109885973B
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伍凯
翟江棚
郑惠铭
谭程炜
林诗琪
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Hohai University HHU
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Abstract

The invention discloses a deformation cycle damage calculation method, which comprises the following steps: establishing a first load displacement curveA bar skeleton curve and a second skeleton curve; determining the intact slope k of a skeleton curve 1 Peak load of skeleton curve P m The point of failure of the test piece; determining characteristic load P under each stage of displacement control Ei 、P Ri 、P Ci And P △i (ii) a Determining a damage value D according to a damage calculation formula di 、D Ci And D Ri . According to the invention, a load displacement curve obtained by test loading is utilized, the bearing capacity is taken as a basic factor for evaluating the damage condition, the initial loading point is taken as a damage starting point or a self-defined damage starting point, and the influence of cyclic loading on the damage of a test piece under the same displacement is considered, so that a new method and a new thought are provided for structural earthquake damage research.

Description

Deformation cycle damage calculation method
Technical Field
The invention belongs to the field of structural damage calculation, and particularly relates to a deformation cycle damage calculation method.
Background
Since the earthquake action will cause damage to the building structure, and the damage is gradually accumulated along with the increase of the cycle number, the bearing capacity and the residual life of the building structure in the subsequent service period are greatly influenced after the building structure is subjected to the earthquake damage for a plurality of times. And the damage calculation method of the structure under the earthquake action is the theoretical basis of the earthquake-resistant design of the structure, and the internal damage condition of the structure is the important basis for reinforcing the structure after earthquake. Therefore, the method has great significance for the earthquake-resistant design and earthquake damage assessment of the structure by correctly mastering the damage level of the structure under the earthquake action and finding a reasonable calculation method to quantitatively describe the damage degree of the structural member under the earthquake action.
At present, the damage calculation method has the following defects: 1) the existing calculation method is complex, and the definition of the damage starting point is not accordant with the reality; 2) few studies are directed at cyclic damage of the test piece, which is not sufficient to reflect structural damage and damage degree in actual earthquake.
Disclosure of Invention
The invention aims to: aiming at the defects of the prior art, the invention provides the deformation cycle damage calculation method by carrying out statistical analysis on the damage calculation method of the building structure and summarizing the advantages and the disadvantages of the existing damage calculation method.
The technical scheme is as follows: a deformation cycle damage calculation method comprises the following steps:
step 1) establishing a first skeleton curve and a second skeleton curve; the first skeleton curve and the second skeleton curve are determined by a load displacement curve; in the anti-seismic test research, a loading system of first load control and second displacement control can be adopted: loading once under the control of each level of load; under each stage of displacement control, cyclic loading is required for three times; loading the test piece according to the loading system to obtain a load displacement curve; in the displacement control stage, each stage of displacement control is circularly loaded for three times, so that three hysteresis loops are arranged under each stage of displacement control in a load displacement curve;
determining a connecting line of the highest point of the loading hysteresis loop in the load control stage and the highest point of the first hysteresis loop in each stage of displacement control loading as a first skeleton curve, and assuming that the function expression is P ═ f 1 (△ i ) (ii) a Determining a connecting line of the highest point of the loading hysteresis loop in the load control stage and the highest point of the third hysteresis loop in each stage of displacement control loading as a second skeleton curve, and assuming that the function expression is P ═ f 2 (△ i )；
Step 2) determining a damage starting point of the test piece, and determining a no-damage slope k according to the damage starting point 1 The non-destructive linear function expression is P ═ k 1 △ i (ii) a Determining a test piece damage point to obtain a load when the test piece is damaged;
step 3) determining the total residual load P under each stage of displacement control Ei Third cycle residual load P Ri Cyclic consumption load P Ci Displacement effective loss load P △i ；P Ei The difference between the bearing capacity of the test piece without damage and the load of the test piece without damage in the same displacement state; p Ri Loading the test piece to the difference between the bearing capacity of the test piece in the third cycle under the ith-level displacement control and the load of the test piece in the damage process; p is Ci For loss of load capacity due to circulationAccumulation is the accumulation of the difference between the first skeleton curve and the second skeleton curve under the control of displacement at each level, i.e. accumulation
Figure GDA0003739836840000021
P △i The loss of load bearing capacity for increased displacement is given by: p △i ＝P Ei －P Ri －P Ci (ii) a The values of the negative loading and the positive loading are the same;
step 4) determining a damage value D according to a damage calculation formula di 、D Ci And D Ri ；
The method adopts the concept of damage transmission, quantitatively describes the damage caused by displacement increase and the damage caused by load circulation, and has the following calculation formula:
Figure GDA0003739836840000022
Figure GDA0003739836840000023
Figure GDA0003739836840000024
in the formula: d di Controlling damage caused by 'displacement increase' for the ith-level displacement, and is called displacement damage for short; d Ci Damage caused by load circulation in the ith displacement control stage and the previous displacement control stage is referred to as circulation damage for short; d Ri The residual rate of the bearing capacity under the i-th level displacement control is called residual rate for short; the sum of the three is equal to 1.
Further, if the loading initial point is taken as the damage starting point, in the above steps:
the failure point of the test piece in the step 2) is E (delta) u ，0.85P m )；P m The peak load is obtained; the breaking point is the load from the peak value P m Down to 0.85P m A point in time; damage by O pointStarting point, if the test piece is not damaged, the load displacement curve will develop along the tangent of the point O of the initial loading point, and the straight line is called as a non-damaged straight line; assuming that the slope of the tangent line at the initial point of the forward loading, i.e. the initial slope of the skeleton curve, is k 1 So the function expression of the intact line is P ═ k 1 △ i (ii) a If the completely damaged test piece is loaded, the load displacement curve of the test piece develops along a straight line OE, and the straight line is called a damage straight line; suppose the slope of the damage line is k 2 ，k 2 ＝0.85P m /△ u So the functional expression of the damage line is P ═ k 2 △ i (ii) a The initial slope, peak load, failure point and slope of the damage line of the negative skeleton curve are the same as those of the positive calculation method.
P in step 3) Ei ＝k 1 △ i －k 2 △ i ；P Ri ＝f 2 (△ i )－k 2 △ i 。
Step 4), the damage value calculation of the ith level displacement control is specifically as follows:
Figure GDA0003739836840000031
Figure GDA0003739836840000032
Figure GDA0003739836840000033
the calculation method of the negative load is the same.
Further, if the damage starting point is customized, the steps are as follows:
determining the peak load P of the skeleton curve in the step 2) m Point of failure E (. DELTA. u ，0.85P m ) The failure point E is the load from the peak value P m Down to 0.85P m A point in time; making a horizontal line from the damage point to cross the skeleton curve at the damage starting point A(Δ 0 ，0.85P m ) If the specimen is not damaged, the load displacement curve develops a line OA, the line OA is called a damage-free line, and the functional expression of the line is assumed to be P ═ k 1 △ i ，k 1 ＝0.85P m /△ 0 (ii) a The peak load, the damage starting point, the damage point and the slope of the linear elastic straight line of the negative skeleton curve are the same as those of the positive skeleton curve;
p in step 3) Ei ＝k 1 △ i －0.85P m ；P Ri ＝f 2 (△ i )－0.85P m ；
Step 4), damage values of ith-stage displacement control are as follows:
Figure GDA0003739836840000034
Figure GDA0003739836840000035
Figure GDA0003739836840000036
has the advantages that: the deformation cycle damage calculation method taking the loading initial point as the damage starting point has the following beneficial effects:
1. based on the two skeleton curves, the initial loading point is taken as a damage starting point, and the total damage value of the damage point is 1, so that the method accords with the actual condition and is suitable for the working condition with larger damage influence in the early stage of component loading;
2. the cyclic damage can be considered and is unified with the reality, and the newly proposed damage line solves the problem that the damage value is not converged at the damage point, makes up the defects of the existing research and provides a new method for the structural damage test research;
the method for calculating the deformation cycle damage of the custom damage starting point has the following beneficial effects:
1. based on the two skeleton curves, the damage starting point is defined by the user according to the damage point, and the total damage value of the damage point is 1, so that the method is more suitable for the working condition with less damage influence in the early stage of loading the component;
2. the cyclic damage can be considered, the defect of cyclic damage research is overcome, the displacement damage and the cyclic damage are unified, the calculation is simpler and more convenient, and a new method is provided for the structural damage experimental research.
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FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a loading regime of the present invention;
FIG. 3 is a schematic view of a load displacement curve according to the present invention;
FIG. 4 is a schematic view of a skeletal curve of the present invention;
FIG. 5 is a schematic diagram of feature points and feature slopes according to embodiment 1 of the present invention;
FIG. 6 is a schematic diagram of a method for calculating damage in embodiment 1 of the present invention;
FIG. 7 is a diagram illustrating feature points and feature slopes according to embodiment 2 of the present invention;
fig. 8 is a schematic diagram of a method for calculating damage in embodiment 2 of the present invention.
Detailed Description
Example 1
A deformation cycle damage calculation method taking a loading initial point as a damage starting point comprises the following steps:
step 1, establishing a first skeleton curve and a second skeleton curve; the first skeleton curve and the second skeleton curve are determined by a load displacement curve; in the anti-seismic test research, a loading system of first load control and second displacement control can be adopted, and the loading system is shown in figure 2. The load control loading system is shown in (a) in fig. 2, and the loading is only carried out once under the control of each level of load; the displacement control loading system is shown in fig. 2 (b), and cyclic loading is required to be performed three times under each stage of displacement control. The test piece was loaded according to this loading schedule, and a load-displacement curve as shown in fig. 3 was obtained. Because the cyclic loading is carried out for three times under each stage of displacement control in the displacement control stage, three hysteresis loops (curve loops) are arranged under each stage of displacement control in the load displacement curve. In the figure, P is the load and Δ is the positionMoving; delta i The displacement is the positive maximum displacement under the ith displacement control;
Figure GDA0003739836840000041
the displacement with the maximum negative absolute value under the control of the ith displacement is obtained. In the context of figure 3, it is shown,
Figure GDA0003739836840000042
the stage is a load control stage, and the load displacement hysteresis loop is small; after the load control phase, it is a displacement control phase.
As shown in fig. 4, a connection line between the highest point of the loading hysteresis loop in the load control stage and the highest point of the first hysteresis loop in each stage of displacement control loading is determined as a first skeleton curve, and a function expression of the first skeleton curve is assumed to be P ═ f 1 (△ i ) (ii) a Determining a connecting line of the highest point of the loading hysteresis loop in the load control stage and the highest point of the third hysteresis loop in each stage of displacement control loading as a second skeleton curve, and assuming that the function expression is P ═ f 2 (△ i )。
Step 2, determining the initial slope k of the skeleton curve 1 Peak load P m Failure point (Delta) of test piece u ， 0.85P m ) And the slope k of the damage line 2 . As shown in fig. 5, point B is the peak point of the positive loading, and the corresponding load is the peak load P of the positive loading m (ii) a Point E (. DELTA.) of u ，0.85P m ) Is a failure point of the positive loading; taking the point O as a damage starting point, if the test piece is not damaged, developing a load displacement curve along a tangent line of the point O at the initial loading point, and calling the straight line as a non-damaged straight line (or a linear elastic straight line); assuming that the slope of the tangent line at the initial point of the forward loading, i.e. the initial slope of the skeleton curve, is k 1 ，k 1 Can be calculated by METLAB software, so that the function expression of the straight line is P ═ k 1 △ i (ii) a If a test piece that is completely damaged (damage value of 1) is loaded, the load-displacement curve of the test piece will develop along a straight line OE, which is called the damage straight line. Assuming that the slope of the damage line is k 2 ， k 2 ＝0.85P m /△ u So the function expression of the damage line is P ═ k 2 △ i (ii) a The initial slope, peak load, failure point and slope of the damage straight line of the negative skeleton curve are the same as those of the positive calculation method.
Step 3, determining the total residual load P under each level of displacement control Ei Third cycle residual load P Ri Cyclic effective consumption load P Ci Displacement effective loss load P △i (ii) a A simplification of the framework curve from fig. 5 with positive loading is shown in fig. 6. P Ei The difference between the bearing capacity of the test piece without damage and the load of the test piece with the same displacement, namely P Ei ＝k 1 △ i －k 2 △ i ；P Ri The difference between the bearing capacity of the test piece loaded to the ith displacement control in the third cycle and the load in the damage process, namely P Ri ＝f 2 (△ i )－k 2 △ i ；P Ci For the accumulation of the loss of bearing capacity caused by circulation, the difference between the first skeleton curve and the second skeleton curve under the control of displacement at each stage is accumulated, i.e. the difference is accumulated
Figure GDA0003739836840000051
P △i For the loss of bearing capacity due to displacement increase, the following formula can be obtained: p △i ＝P Ei －P Ri －P Ci (ii) a The values of the negative loading and the positive loading are the same.
Step 4, determining a damage value D according to a damage calculation formula di 、D Ci And D Ri . Point O is the starting point of the damage, point E (. DELTA.) u ，0.85P m ) The point of failure of the test piece is defined as the damage endpoint. Line OA is a tangent line of the origin and is defined as a no-damage straight line; the line OE is a damage line; curve OBC is referred to as the first skeleton curve; the curve ODE is called a second skeleton curve;
the method adopts the concept of damage transmission, quantitatively describes the damage caused by displacement increase and the damage caused by load circulation, and has the following calculation formula:
Figure GDA0003739836840000052
Figure GDA0003739836840000053
Figure GDA0003739836840000054
in the formula: d di Controlling damage caused by 'displacement increase' for the ith-level displacement, and is called displacement damage for short; d Ci Damage caused by load circulation in the ith displacement control stage and the previous displacement control stage is referred to as circulation damage for short; d Ri The residual rate of the bearing capacity under the i-th level displacement control is called residual rate for short; the sum of the three is equal to 1.
The damage value of the ith stage displacement control is as follows:
Figure GDA0003739836840000061
Figure GDA0003739836840000062
Figure GDA0003739836840000063
example (a): in the 1 st stage displacement control, the displacement is Δ 1 The displacement damage is
Figure GDA0003739836840000064
The circulatory impairment is
Figure GDA0003739836840000065
A residual rate of
Figure GDA0003739836840000066
In the 2 nd stage displacement control, the displacement is△ 2 The displacement damage is
Figure GDA0003739836840000067
The circulatory impairment is
Figure GDA0003739836840000068
The residual rate is
Figure GDA0003739836840000069
And so on … …
The same applies to the calculation of negative loading.
Example 2
A deformation cycle damage calculation method of a custom damage starting point comprises the following steps:
step 1, establishing a first skeleton curve and a second skeleton curve; the skeleton curve is determined by a load displacement curve; in the study of the anti-seismic test, a loading system of first load control and second displacement control can be adopted, and the loading system is shown in figure 2. The load control loading system is shown in (a) in fig. 2, and the loading is only carried out once under the control of each level of load; the displacement control loading system is shown in fig. 2 (b), and cyclic loading is required to be performed three times under each stage of displacement control. The test piece was loaded according to this loading system, and a load-displacement curve as shown in fig. 3 was obtained. Because the cyclic loading is carried out for three times under each stage of displacement control in the displacement control stage, three hysteresis loops (curve loops) are arranged under each stage of displacement control in the load displacement curve. In the figure, P is load and Delta is displacement; delta i The positive maximum displacement is the displacement control of the ith stage;
Figure GDA00037398368400000610
the displacement with the maximum negative absolute value is controlled by the displacement of the ith stage. In the context of figure 3, it is shown,
Figure GDA0003739836840000071
the stage is a load control stage, and the load displacement hysteresis loop is smaller; after the load control phase, it is a displacement control phase.
As shown in fig. 4, the load control phase loading is hystereticDetermining a connecting line between the highest point of the ring and the highest point of the first hysteresis ring in each stage of displacement control loading as a first skeleton curve, and assuming that the function expression is P ═ f 1 (△ i ) (ii) a Determining a connecting line of the highest point of the loading hysteresis loop in the load control stage and the highest point of the third hysteresis loop in each stage of displacement control loading as a second skeleton curve, and assuming that the function expression is P ═ f 2 (△ i )。
Step 2, determining the peak load P of the skeleton curve m Starting point of damage (Δ) of test piece 0 ，0.85P m ) Failure point (delta) u ，0.85P m ) And determining the slope k of the line elastic straight line according to the damage starting point 1 (ii) a As shown in fig. 7, point D is the peak point of the positive loading, and the corresponding load is the peak load P of the positive loading m (ii) a Point C (. DELTA.) u ，0.85P m ) Is a failure point of the positive loading; drawing a horizontal line from point C to cross the skeleton curve with point A (delta) 0 ，0.85P m ) If the specimen is not damaged, the load displacement curve develops a straight line OA, which is called a damage-free straight line (or linear elastic straight line), and the functional expression of the straight line is assumed to be P ═ k 1 △ i ， k 1 ＝0.85P m /△ 0 (ii) a The peak load, the damage starting point, the damage point and the slope of the linear elastic straight line of the negative skeleton curve are the same as those of the positive calculation method.
Step 3, determining the total residual load P under each level of displacement control Ei Third cycle residual load P Ri Cyclic effective consumption load P Ci Displacement effective loss load P △i ；P Ei The difference between the bearing capacity of the test piece without damage and the load of the test piece with the same displacement, P Ei ＝k 1 △ i －0.85P m ；P Ri The difference between the bearing capacity of the test piece loaded to the ith displacement control in the third cycle and the load in damage, P Ri ＝f 2 (△ i )－0.85P m ；P Ci For the accumulation of the loss of bearing capacity caused by circulation, the difference between the first skeleton curve and the second skeleton curve under the control of displacement of each stage is accumulated, i.e. the accumulation is carried out
Figure GDA0003739836840000072
P △i For the loss of bearing capacity due to the displacement increase, the following formula can be used: p △i ＝P Ei －P Ri －P Ci (ii) a The values of the negative loading and the positive loading are the same;
step 4, determining a damage value D according to a damage calculation formula di 、D Ci And D Ri . Point A is the starting point of injury, and Point C (. DELTA.) u ，0.85P m ) Is the test piece failure point and is defined as the damage endpoint. The line OA is a non-damaged line (or a linear elastic line); curve OAB is referred to as the first skeleton curve; curve OAC is referred to as the second skeleton curve;
the method adopts the concept of damage transmission, quantitatively describes the damage caused by displacement increase and the damage caused by load circulation, and has the following calculation formula:
Figure GDA0003739836840000073
Figure GDA0003739836840000074
Figure GDA0003739836840000075
in the formula: d di Controlling damage caused by 'displacement increase' for the ith displacement, and for short, displacement damage; d Ci Controlling damage caused by load circulation for the ith-level displacement, and is called circulation damage for short; d Ri The residual rate of the bearing capacity under the i-th level displacement control is called residual rate for short; the sum of the three is equal to 1.
The damage value of the ith displacement control is as follows:
Figure GDA0003739836840000081
Figure GDA0003739836840000082
Figure GDA0003739836840000083
example (c): in the 1 st stage displacement control, the displacement is Δ 1 The displacement damage is
Figure GDA0003739836840000084
The circulatory impairment is
Figure GDA0003739836840000085
The residual rate is
Figure GDA0003739836840000086
In the case of the 2 nd stage displacement control, the displacement is Δ 2 The displacement damage is
Figure GDA0003739836840000087
The circulatory impairment is
Figure GDA0003739836840000088
A residual rate of
Figure GDA0003739836840000089
And so on … …
The same applies to the calculation of negative loading.

Claims (7)

1. A deformation cycle damage calculation method is characterized by comprising the following steps:
step 1) establishing a first skeleton curve and a second skeleton curve; the first skeleton curve and the second skeleton curve are determined by a load displacement curve; in the anti-seismic test research, a loading system of first load control and second displacement control is adopted: loading once under the control of each level of load; under each stage of displacement control, cyclic loading is required for three times; loading the test piece according to the loading system to obtain a load displacement curve; in the displacement control stage, each stage of displacement control is circularly loaded for three times, so that three hysteresis loops are arranged under each stage of displacement control in a load displacement curve;
determining a connecting line of the highest point of the loading hysteresis loop in the load control stage and the highest point of the first hysteresis loop in each stage of displacement control loading as a first skeleton curve, wherein the function expression is P ═ f 1 (△ i ) (ii) a Determining a connecting line of the highest point of the loading hysteresis loop in the load control stage and the highest point of the third hysteresis loop in each stage of displacement control loading as a second skeleton curve, wherein the function expression is P ═ f 2 (△ i )；
Step 2) determining a damage starting point of the test piece, and determining a no-damage slope k according to the damage starting point 1 The non-destructive linear function expression is P ═ k 1 △ i (ii) a Determining a damage point of the test piece to obtain a load when the test piece is damaged;
step 3) determining the total residual load P under each stage of displacement control Ei Third cycle residual load P Ri Cyclic effective consumption load P Ci Displacement effective consumption load P △i ；P Ei The difference between the bearing capacity of the test piece without damage and the load of the test piece without damage in the same displacement state; p is Ri Loading the test piece to the difference between the bearing capacity of the test piece in the third cycle under the ith-level displacement control and the load of the test piece in the damage process; p Ci For the accumulation of the loss of bearing capacity caused by circulation, the difference between the first skeleton curve and the second skeleton curve under the control of displacement at each stage is accumulated, i.e. the difference is accumulated
Figure FDA0003739836830000011
P △i The loss of load bearing capacity for increased displacement is given by: p △i ＝P Ei －P Ri －P Ci (ii) a The values of the negative loading and the positive loading are the same;
step 4) determining a damage value D according to a damage calculation formula di 、D Ci And D Ri ；
The method adopts the concept of damage transmission, quantitatively describes the damage caused by displacement increase and the damage caused by load circulation, and has the following calculation formula:
Figure FDA0003739836830000012
Figure FDA0003739836830000013
Figure FDA0003739836830000014
in the formula: d di Controlling damage caused by 'displacement increase' for the ith-level displacement, and is called displacement damage for short; d Ci Damage caused by load circulation in the ith displacement control stage and the previous displacement control stage is referred to as circulation damage for short; d Ri The residual rate of the bearing capacity under the i-th level displacement control is called residual rate for short; the sum of the three is equal to 1.
2. The deformation cycle damage calculation method of claim 1, wherein: the failure point of the test piece in the step 2) is E (delta) u ，0.85P m )；P m The peak load is obtained; the breaking point is the load from the peak value P m Down to 0.85P m A point in time; taking the point O as a damage starting point, if the test piece is not damaged, developing a load displacement curve along a tangent line of the point O at the initial loading point, and calling the straight line as a damage-free straight line; the slope of the tangent line of the initial point of the positive loading, namely the initial slope of the skeleton curve is k 1 So the function expression of the intact line is P ═ k 1 △ i (ii) a If the completely damaged test piece is loaded, the load displacement curve of the test piece develops along a straight line OE, and the straight line is called a damage straight line; the slope of the damage line is k 2 ，k 2 ＝0.85P m /△ u Therefore, it isThe functional expression of the damage line is P ═ k 2 △ i (ii) a The initial slope, peak load, failure point and slope of the damage straight line of the negative skeleton curve are the same as those of the positive calculation method.
3. The deformation cycle damage calculation method of claim 2, wherein: p in said step 3) Ei ＝k 1 △ i －k 2 △ i ；P Ri ＝f 2 (△ i )－k 2 △ i 。
4. The deformation cycle damage calculation method according to claim 3, wherein: the damage value calculation of the ith-level displacement control in the step 4) is specifically as follows:
Figure FDA0003739836830000021
Figure FDA0003739836830000022
Figure FDA0003739836830000023
5. the deformation cycle damage calculation method according to claim 1, wherein: determining the peak load P of the skeleton curve in the step 2) m Breaking point E (. DELTA.. delta.) u ，0.85P m ) The failure point E is the load from the peak value P m Down to 0.85P m A point in time; making a horizontal line from the damage point to the ascending section of the skeleton curve at the damage starting point A (delta) 0 ，0.85P m ) If the test piece is not damaged, the load displacement curve develops a straight line OA, the straight line OA is called a damage-free straight line, and the functional expression of the straight line is P ═ k 1 △ i ，k 1 ＝0.85P m /△ 0 (ii) a The peak load, the damage starting point, the damage point and the slope of the linear elastic straight line of the negative skeleton curve are the same as those of the positive calculation method.
6. The deformation cycle damage calculation method of claim 5, wherein: p in said step 3) Ei ＝k 1 △ i －0.85P m ；P Ri ＝f 2 (△ i )－0.85P m 。
7. The deformation cycle damage calculation method of claim 6, wherein: the damage value of the ith level displacement control in the step 4) is as follows:
Figure FDA0003739836830000031
Figure FDA0003739836830000032
Figure FDA0003739836830000033
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Publication number Priority date Publication date Assignee Title
CN104020063A (en) * 2014-06-11 2014-09-03 西南交通大学 Method for measuring load threshold of geotechnical packing accumulated deformation state under cyclic loading
CN107703011A (en) * 2017-11-27 2018-02-16 东南大学 The evaluation method of Porous Elastic Road Surface accumulated damage
CN108920739A (en) * 2018-04-27 2018-11-30 天津大学 A kind of material constitutive model numerical analysis method considering damage cumulating effect

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104020063A (en) * 2014-06-11 2014-09-03 西南交通大学 Method for measuring load threshold of geotechnical packing accumulated deformation state under cyclic loading
CN107703011A (en) * 2017-11-27 2018-02-16 东南大学 The evaluation method of Porous Elastic Road Surface accumulated damage
CN108920739A (en) * 2018-04-27 2018-11-30 天津大学 A kind of material constitutive model numerical analysis method considering damage cumulating effect

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