CN112284902A - Conversion method from triaxial creep test result of graded loading rock soil to respective loading - Google Patents

Conversion method from triaxial creep test result of graded loading rock soil to respective loading Download PDF

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CN112284902A
CN112284902A CN202011175527.XA CN202011175527A CN112284902A CN 112284902 A CN112284902 A CN 112284902A CN 202011175527 A CN202011175527 A CN 202011175527A CN 112284902 A CN112284902 A CN 112284902A
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sample
creep
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CN112284902B (en
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汤爱平
渠海港
朱世界
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Harbin Institute of Technology
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N3/00—Investigating strength properties of solid materials by application of mechanical stress
    • G01N3/08—Investigating strength properties of solid materials by application of mechanical stress by applying steady tensile or compressive forces
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
    • G01N2203/0058—Kind of property studied
    • G01N2203/0069—Fatigue, creep, strain-stress relations or elastic constants
    • G01N2203/0071—Creep
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
    • G01N2203/0058—Kind of property studied
    • G01N2203/0069—Fatigue, creep, strain-stress relations or elastic constants
    • G01N2203/0075—Strain-stress relations or elastic constants
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
    • G01N2203/02—Details not specific for a particular testing method
    • G01N2203/025—Geometry of the test
    • G01N2203/0256—Triaxial, i.e. the forces being applied along three normal axes of the specimen

Abstract

The invention discloses a method for converting triaxial creep test results of graded loading rock soil to respective loading, which comprises the steps of expressing graded loading in a column mode and respectively loading to a certain moment of a certain total load value, accumulating total energy input to a triaxial sample by the outside, enabling the total energy input by the outside in two loading modes to be equal, establishing an equation about creep deformation of the sample, solving creep deformation of the sample under respective loading according to creep deformation data of graded loading and integrating initial sizes of the sample and external conditions thereof, and drawing a creep deformation-time curve under respective loading by combining test time corresponding to each equation. The invention considers the influence of nonlinear deformation during the conversion of two loading modes from the energy perspective, so that the conversion process has clearer physical and mechanical significance, reasonably considers the nonlinear factors of deformation, analyzes the problem possibly implied by researching the creep of the rock and soil by graded loading, and provides a new idea for reasonably and accurately researching the creep of the rock and soil.

Description

Conversion method from triaxial creep test result of graded loading rock soil to respective loading
Technical Field
The invention belongs to the technical field of geotechnical engineering, relates to a method for analyzing and processing geotechnical triaxial creep test result data, and particularly relates to a processing method for converting triaxial vertical creep deformation data obtained by a graded loading mode of a geotechnical sample into vertical creep deformation data obtained by a respective loading mode.
Background
The basic subject of rheology is to study the law of stress-strain state and its change with time, and to solve the problems related to rheology encountered in engineering practice according to the established law of structure.
In the indoor rheological test of soil, the test has two modes of separate loading and graded loading. Respectively loading can meet the conditions required by the rheological test in theory, and the whole rheological process curve of the soil can be directly obtained, but the actual and strict respective loading is not easy, so that on one hand, the condition that a plurality of completely same test conditions are unlikely to be ensured, and the obtained test result is often discrete; on the other hand, it is difficult to have such many sets of instruments simultaneously for long-term rheological tests. Therefore, the indoor rheological test at home and abroad at present is generally carried out by adopting a graded loading method instead of the method. The change in stress level with time under graded loading and the resulting creep curve show a stepped profile with an increase. In the study of the soil rheology, it is common to adopt the form of a rheology curve loaded separately, and the form of the rheology curve loaded in stages must be converted into the form loaded separately.
The conversion of separate loading into step loading usually adopts a "coordinate translation" method, that is, the time of each loading is taken as the initial time of the creep curve under the load of the step, and the later time is calculated from the time, that is, the time is pushed forward. The method is based on a Boltzmann linear superposition method for rock linear visco-elastic bodies, namely, the soil body is considered to be a linear rheological body, and the flow variable at any moment is the sum of the flow variables of each stage of load increment at the moment in the previous moment. The method has the following disadvantages: the test conditions to be met are more, the time for applying the load level of each stage must be kept consistent, and the creep deformation rate at the load level must be kept close to 0 to carry out the next stage of loading. The "coordinate translation" method is only applicable to linear rheology.
The Chen base provides a Chen's loading method for rock creep, which is called a Chen's method for short: the Chen method is to extend the dotted line of the previous stage creep curve under the stage loading, the creep increment caused by the next stage load is the difference value between the real curve and the dotted line, the difference value is extracted, the curve is drawn, and the curve starting point is translated to the coordinate zero point like the coordinate translation method. The Chen's method generally admits that the influence of nonlinear factors on a creep curve can be considered, but the creep deformation mechanism of rock soil is not completely clear at present, so that the deformation after a certain time point is artificially predicted, and the extension of a broken line of the deformation curve is not necessarily proper. The Chen method requires that the loading time of each level is the same, and after the load of the previous level is loaded, the next level of loading is carried out after the sample achieves stable deformation. In the process of a large number of rock-soil triaxial creep tests, along with the increase of the loading stage, the longer the time for each stage of sample to reach creep stability is, usually, researchers take the deformation smaller than a certain speed such as 0.01mm/d as the standard for judging to enter the next stage of test, and therefore, the time interval is difficult to determine at the initial stage of the test.
Disclosure of Invention
The invention aims to provide a method for converting triaxial creep test results of graded loading rock and soil to respective loading, which considers the influence of nonlinear deformation in the conversion of two loading modes from the energy perspective, so that the conversion process has clearer physical and mechanical significance, reasonably considers the nonlinear factor of deformation, breaks through the limitation that the loading time lengths of various levels of the Chen's method are equal, analyzes the problem possibly implied by the graded loading to research the creep of the rock and soil, and provides a new idea for reasonably and accurately researching the creep of the rock and soil.
The purpose of the invention is realized by the following technical scheme:
a method for converting triaxial creep test results of graded loading rock and soil to respective loading comprises the following steps:
step 1: when the columnar expression is loaded to the nth level load in a grading way, the integral expression of the total work done by the outside on the triaxial sample is recorded, and the total work of the outside is W n1,2,3, then:
Figure BDA0002748589440000031
in the formula, n is the axial external load stage number reached by the current loading or the external force work pair required to be calculatedThe corresponding axial external load stage number; fiThe ith stage of axial external loading (single stage loading under step loading, not cumulative); t is ti-1、tiThe time for the initial loading of the i-th stage of the axially external load and the time for the loading to steady creep, respectively, where t 00, unit: min; lj-the j-th level of load under graded loading is loaded to a stable rule, the vertical deformation of the soil sample compared with the previous level of load is increased, unit: mm; lxjLoading the j-th level load of the triaxial rock-soil sample under graded loading until the j-th level load meets the set creep stability rule, wherein the average radial expansion amount of the soil sample is increased compared with the previous level load, and the unit is as follows: mm; sigma3-confining pressure, unit: MPa; a. thet-area of top surface of triaxial test piece under graded loading, unit: mm is2；As-side area of triaxial test piece under graded loading, unit: mm is2(ii) a Q (t) -energy input during the test due to the change of the external environment (when the sample releases energy due to the influence of the external environment, the energy is negative), and the specific value corresponds to the time variable and is in units of energy form, for example, the unit of the input energy due to the change of the external temperature is joule; note: i and j are positive integers, the value closed interval is 1-n, and the specific value is determined according to the formula meaning;
step 2: considering the physical quantities loaded in stages to the creep stabilization time of the nth stage load, setting the rules for taking out these physical quantities, and simplifying the integral expression in step 1, the following are provided:
Figure BDA0002748589440000032
in the formula, Ati-the area of the top surface of the triaxial creep specimen when it reaches steady creep under graded loading when a total of i-grade loads are added, in units of: mm is2；AsiThe side area of the triaxial creep test sample when the triaxial creep test sample reaches stable creep under the step loading and the separate loading when the total i-step loading is added is as follows: mm is2(ii) a Note: confining pressure sigma3Since the test instrument or test design may not be constant, it is placed in parentheses in the summation formula;
and step 3: when the column expression is respectively loaded to a certain level of load (the axial external load of a certain numerical value grade is loaded at one time), the integral expression of the total work of the external world on the triaxial sample is recorded, and the total work of the external world is W'i1,2,3, then there are:
Figure BDA0002748589440000041
of formula (II) F'iA total of i-level axial external loads corresponding to the step loading are applied to the triaxial sample at once, i.e. the i-th level of axial external loads applied separately ("first" is for a series of separate loadings of the test, relative to the other axial external load levels), in units of: n; t'i-one-time load F'iTime taken for load to creep stability, unit: min; t is t 00, unit: min; l'i-separate load, one-time load F'iCumulative vertical deformation of the load to the stability rule, unit: mm; l'xi-separately loading a lower triaxial test piece applying F'iAverage radial expansion to steady regular accumulation, unit: mm; sigma'3-confining pressure, unit: MPa; a't-loading the top surface area, A 'of the lower triaxial test piece respectively'sLoading the lateral surface area of the lower triaxial specimen, unit: mm is2；
And 4, step 4: taking into account the physical quantities at the steady creep time, which are respectively applied to the loads of this stage, a rule for taking out these physical quantities is set, for example σ'3＝σ3And simplifying the integral expression in the step 3, namely:
W′i＝F′i·l′i+σ3·A′ti·l′1-σ3·A′si·l′xi+Q(t)；
of formula (II) to'ti-area of the top surface when the triaxial creep specimen reaches steady creep under respective loading, unit: mm is2；A′si-the area of the side when the triaxial creep specimen reaches steady creep under respective loading, in units: mm is2；
And 5: aiming at a normal-temperature consolidation and non-drainage triaxial creep test, assuming that the volume of a soil sample in the test is kept unchanged, a cylinder is always kept in the deformation process of the soil sample, and the value and unit magnitude of Q (t) are not large and can be ignored under the normal-temperature test;
step 6: step 1 to step 4, calculating external force work to obtain a radial deformation value of the triaxial sample, and deducing the relation between vertical deformation and radial deformation of the triaxial sample caused by applying different axial loads at two levels front and back in a graded loading mode according to the test condition and hypothesis in step 5:
Figure BDA0002748589440000051
in the formula, hj-1The initial height of the triaxial test sample when the j level load is applied, namely the height when the j-1 level load is applied to the test sample to reach creep stability, is expressed as the unit: mm, obviously, j is 1, h0Is the initial height of the sample; dj-1The initial diameter of the cylindrical triaxial sample when the j-th level load is applied, namely the diameter when the j-1-th level load is applied to the sample to achieve creep stability, is expressed as the unit: mm, obviously, when j is 1, d0Is the initial diameter of the sample;
deducing the relation between vertical deformation and radial deformation of the triaxial sample caused by applying a certain level of axial load compared with the initial size of the sample without applying any axial external load in a respective loading mode:
Figure BDA0002748589440000052
and 7: substituting the working condition data of the triaxial test: the specific data of axial force, confining pressure, initial size of sample, etc. are calculated and loaded in grades, and are counted up
Figure BDA0002748589440000053
When the axial external load acts on the soil sample until the creep deformation is stable, the external world faces the soilSample accumulated input external force work Wn：
Figure BDA0002748589440000054
In the formula, Asi＝πdjhj；
Figure BDA0002748589440000055
hj＝hj-1-lj；
Figure BDA0002748589440000056
When the above formula is substituted into a numerical value, i is equal to j, i and j represent the same number of load steps, and hjRepresents the height of the sample when creep stability is achieved by applying the j-th order load, unit: mm; djRepresents the diameter at which the grade j load is applied until creep stability of the specimen is achieved, in units of: mm;
and 8: substituting the relational expression of the vertical deformation and the radial deformation under the respective loading in the step 6 and the three-axis test working condition data in the step 7 into W 'in the step 4'iFor further integration in the expression:
W′i＝F′i·l′i+σ3·A′ti·l′1-σ3·A′si·l′xi；
of formula (II) to'si＝πd′ih′i；
Figure BDA0002748589440000061
h′i＝h0-l′i；
Figure BDA0002748589440000062
h′iRepresents the height of the sample when creep stability is achieved by applying the j-th order load, unit: mm; d'iRepresents the diameter at which the i-th order load is applied until creep stability of the specimen is achieved, in units of: mm;
and step 9:corresponding to axial loads of the same magnitude and grade, i.e. order
Figure BDA0002748589440000063
So that Wn＝W′iThe equation for creep vertical deformation is listed:
Figure BDA0002748589440000064
introducing a xi amount which is an expression amount related to vertical deformation, and then:
Figure BDA0002748589440000065
namely, it is
Figure BDA0002748589440000066
The equation is arranged into a unitary quartic equation about xi, and the coefficient expressions from the quartic to the zero power are sequentially arranged and summarized into a, b, c, d and e;
Figure BDA0002748589440000067
step 10: determining a, b, c, d and e according to the stress condition of the soil sample and the geometric dimension of the soil sample, solving a unitary quartic equation, taking a real number slightly larger than 1 in four solutions, and further calculating to obtain respectively loaded variables from the ξ value
Figure BDA0002748589440000071
The amount of deformation until creep is stabilized;
Figure BDA0002748589440000072
step 11: according to the steps 1-10, the loading cut-off time t is taken for each level of load under the graded loadingk＝α·2kK is 0,1,2,3. (unit: min) which is the temporary stabilization time under the stage creepAlgebraically calculating the total work accumulated by the external force at these moments
Figure BDA0002748589440000073
Figure BDA0002748589440000074
After simplification, the method comprises the following steps:
Figure BDA0002748589440000075
wherein α -is the first value in a selected series of cutoff time points;
Figure BDA0002748589440000076
when load acts on the soil sample, the load is stopped to tkThe external force work accumulated on the sample by the external force at any moment is as follows, unit: n.mm;
Figure BDA0002748589440000077
when acting on a soil sample, is stopped at tkThe unit of the single-stage vertical deformation of the sample relative to the previous stage load at any moment is as follows: mm;
Figure BDA0002748589440000078
when acting on a soil sample, is stopped at tkThe moment the sample is relative to the single-stage radial deformation under the previous stage load, unit: mm;
Figure BDA0002748589440000079
when load acts on the soil sample, the load is stopped to tkTop surface area of the sample at time, unit: mm is2；
Figure BDA00027485894400000710
When load acts on the soil sample, the load is stopped to tkSide area of the sample at time, unit: mm is2；
Step 12: similarly, according to step 11, the pairs are loaded respectively withTaking the loading cut-off time tk＝α·2kK is 0,1,2,3. (unit: min) is the temporary stabilization time under the stage creep, and the total external force accumulated at the time is calculated algebraically
Figure BDA0002748589440000081
Figure BDA0002748589440000082
Taking into account the physical quantities at the steady creep time, which are respectively applied to the loads of this stage, a rule for taking out these physical quantities is set, for example σ'3＝σ3The simplified integral expression includes:
Figure BDA0002748589440000083
in the formula, under the condition of respectively loading,
Figure BDA0002748589440000084
when load acts on the soil sample, the load is stopped to tkThe external force work accumulated on the sample by the external force at any moment is as follows, unit: n.mm;
Figure BDA0002748589440000085
when acting on a soil sample, is stopped at tkThe unit of the single-stage vertical deformation of the sample relative to the previous stage load at any moment is as follows: mm;
Figure BDA0002748589440000086
when acting on a soil sample, is stopped at tkThe moment the sample is relative to the single-stage radial deformation under the previous stage load, unit: mm;
Figure BDA0002748589440000087
when load acts on the soil sample, the load is stopped to tkTop surface area of the sample at time, unit: mm is2；
Figure BDA0002748589440000088
When load acts on the soil sample, the load is stopped to tkSide area of the sample at time, unit: mm is2；
Step 13: corresponding to axial loads of the same magnitude and grade, i.e. order
Figure BDA0002748589440000089
For the same tkSo that
Figure BDA00027485894400000810
The equation for creep vertical deformation is listed:
Figure BDA00027485894400000811
introduction of a
Figure BDA00027485894400000812
Amount of (a) to
Figure BDA00027485894400000813
The quantity is an expression quantity related to vertical deformation, and then:
Figure BDA0002748589440000091
namely, it is
Figure BDA0002748589440000092
The equation is arranged to relate to
Figure BDA0002748589440000093
The coefficient expressions from the fourth power to the zero power are sequentially summarized as a, b, c, d and e:
Figure BDA0002748589440000094
step 14: according to the soil sampleDetermining a, b, c, d and e according to the force condition and the geometric size of the soil sample, solving a unitary quartic equation, taking a real number slightly larger than 1 in four solutions, and calculating the real number according to the real number
Figure BDA0002748589440000095
Further calculation of the values results in separate loading
Figure BDA0002748589440000096
To tkAmount of deformation in the case of (2):
Figure BDA0002748589440000097
in the formula (I), the compound is shown in the specification,
Figure BDA0002748589440000098
denotes the sample at t under respective loadingkDiameter of time, unit: mm;
Figure BDA0002748589440000099
denotes the sample at t under respective loadingkHeight of time, unit: mm;
step 15: drawing different axial loads according to the data obtained in the step 14
Figure BDA00027485894400000910
And testing the creep deformation curve cluster under other corresponding working conditions. Thus, the conversion of the graded loading creep test curve to the separately loaded creep test curve is completed.
In the above method, another preferred embodiment of the steps 11 to 14 is as follows:
in the creep process, the specific vertical deformation at each moment is limited by the delta (t) of the soil body at the moment from the energy perspective, and the delta (t) represents the instant conversion and dissipation capacity of the soil sample to external force work and changes along with the change of time and the state of the soil body.
The research is carried out on the conversion and consumption process of the soil sample to the external force work under the graded loading, and the research is carried out on the conversion and consumption process of the soil sample to the external force work
Figure BDA00027485894400000911
The entire process of loading to the steady creep time can be expressed as the following equation:
Figure BDA0002748589440000101
in the formula, tnN-1, 2,3.. denotes the total time taken for the staged loading until the nth stage of load to creep-stabilize (from the moment of loading start of the 1 st stage of load), respectively, in units of: min;
subtracting the two adjacent stages of loading creep processes can obtain the following equation:
Figure BDA0002748589440000102
in the formula In-step-load loading of the nth level of load to the creep stability rule with increased vertical deformation of the sample compared to the previous level of load, in units: mm; lxnLoading the nth level load of the triaxial rock-soil sample under graded loading until the nth level load meets the set creep stability rule, wherein the average radial expansion amount of the soil sample is increased compared with the previous level load, and the unit is as follows: mm; a. thetn-the area of the top surface of the triaxial test piece when the nth level load is loaded to the creep stability rule under the graded loading, unit: mm is2；Asn-the lateral area of the triaxial test piece when the nth level load is loaded to the creep stability rule under the graded loading, unit: mm is2。
The nature of the integration is summation. For faster calculation and considering that actually drawing a curve does not necessarily result in all points on the curve, but results in several distinct points to join a curve, the pair
Figure BDA0002748589440000103
Dt step in (1) is taken t according to step 11k＝α·2kK is 0,1,2,3. (unit: min) until the stable moment of the test of this stage under the stage loading (the last moment value is taken according to the test and may not meet tk＝α·2kK is 0,1,2, 3.) the integral equation is converted to a sum equation, the left side of which corresponds to tk＝α·2kAnd k is 0,1,2,3. the external work is calculated in the same way as the step 11, so that a conversion and dissipation efficiency delta (t) curve of the soil sample to the external work along with time under the test working condition is obtained. After obtaining the change rule of delta (t), the following are:
Figure BDA0002748589440000104
selecting delta within a segment according to time periodiAnd (t) integrating the time, and summing the integrals according to the cut-off time (same as step 12) to obtain the external force work at the corresponding time so as to obtain the instant deformation, thereby drawing deformation-time curves of the respective loaded creep tests, and also drawing a strain-time curve by deducing the strain.
In practice it has been found that even if delta is calculatedi(t), δ under step loading and separate loadingi(t) is not necessarily the same, how to convert and use, whether the conversion process is to deltaiSimple integration of the sum of the integrals (t) is still to be investigated, preferably by further experimental determination of the delta in both loading modesi(t) difference and correlation between the two.
Another extremely simplified alternative is: the final creep deformation obtained by deduction and calculation in the steps 1-10 is compared with the creep final deformation obtained by a coordinate translation method to obtain a ratio, all displacement values of a certain level of accumulated creep curve are multiplied by the ratio, the coordinate translation method is used for the reduced curves, and the obtained curve cluster is regarded as a graded load creep final deformation curve obtained by converting the creep displacement curve under the level of accumulated load.
Note: in all the steps, all the average radial expansion parameters are calculated by subtracting the diameter after deformation from the diameter before deformation.
The central idea of steps 1 to 15 in the above method is to establish a transformation relationship between creep deformation curves obtained by two loading modes, i.e. data, by ensuring that the energy accumulated and input to the creep sample from the outside is equal in the step loading and the respective loading modes, wherein:
the accumulated input energy of the external environment to the creep sample refers to: neglecting the part of gravity acting in the deformation process of the sample, namely the change of the gravitational potential energy of the sample, neglecting the part of the friction force between soil at two ends of the soil sample and the filter paper, and between the filter paper and the permeable stone, which does work on the external force of the soil sample, and taking the value of the energy input by the change of the external environment according to the test working condition, for example, neglecting the energy input by the change of the temperature under the normal temperature test, and mainly considering the energy input by the accumulation of the axial pressure and the confining pressure on the creep.
The method for calculating the accumulated input energy of the axial pressure and the confining pressure to the creep sample is as follows: the force multiplied by the corresponding displacement of the point of application of force, the displacement being obtained including, but not limited to, the following: directly measuring by a sensor; the sensor indirectly measures other quantities, such as the volume of the drained water, and then converts the volume into the required displacement; in the embodiment of the invention, the vertical displacement is directly measured by a creep instrument sensor, and the radial displacement is obtained by deduction and calculation of the vertical displacement based on certain geometric assumption.
The invention uses a pseudo-triaxial creep test, i.e. sigma2＝σ3The triaxial creep test not equal to 0 is an example, and the skilled person can easily develop a uniaxial compression creep test (σ) according to the solution of the present invention2＝σ3Creep test of 0), σ3(confining pressure) creep test with constant change in test process implements curve conversion method with same principle, and can also be used for true triaxial creep test, i.e. sigma1≠σ2≠σ3The same principle of curve transformation was performed for the three-axis test of (1).
In the present invention, creep tests are generally carried out for a single stage load of 24 hours or more, and compression tests conforming to this characteristic are also within the scope of the present invention, although compression tests are not entitled "creep".
In the invention, the original curve to be converted is taken from a hierarchical loading mode, and the new curves to be converted are respectively loaded. The step loading means that in each test aiming at one soil sample, a first-stage load is firstly applied to the sample, and the next-stage load is applied when the sample reaches the artificially established standard that the next-stage load can be applied. The respective loading means that load is applied to the sample at one time, and the load is not changed in the middle of the test until the test is finished. The load value and the number of stages of the graded loading and the load value of the respective loading are determined by testers, under the graded loading, the numerical value change trends of the axial pressure and the confining pressure can be from small to large, from large to small or alternatively from increasing to decreasing, and the direction can be changed.
In the invention, the curve is drawn by connecting a plurality of points, each point represents a (deformation, time) data pair, and the vertical deformation and the radial and annular deformation can be obtained. For deformation, other physical quantities characterizing deformation besides displacement are also within the scope of the invention, such as overall strain, real-time strain, etc.
In the present invention, the central idea of another preferred variant of steps 11-14 is that the external energy input to which the sample is subjected in the creep test is equal to the energy transferred and dissipated inside the sample over time, subject to such criteria both in grading and under separate loading.
In the invention, in the whole calculation process, each quantity participating in the calculation has a respective unit, and the change of the formula and the result value caused by the change of the unit is also within the protection scope of the invention.
Compared with the prior art, the invention has the following advantages:
1. the invention reasonably explains the creep deformation process of the rock-soil triaxial sample from the aspects of geometry and physical mechanics, and provides a new idea for respectively loading the creep deformation sample by the graded loading creep deformation curve.
2. The invention can directly deduce the radial and circumferential deformation of the sample from the vertical creep deformation, and reduces the rigid requirement of the conversion calculation method on the measurement function of the rock-soil triaxial creep test instrument.
3. The invention carries out curve transformation by the fact that the external force and work of the rock-soil triaxial sample under grading and separate loading are equal, has no relation with the linearity or nonlinearity of the sample deformation, and has wider applicability.
4. The invention carries out curve transformation by the fact that the external force and work of the rock-soil triaxial sample under grading and separate loading are equal, and the requirement that the load time of each grade is equal during grading loading by the Chen's method is removed.
5. The transformation method of the invention is not limited to rock-soil materials in practice, and any material which does not generate large-width cracks or crumbles in sample deformation under the triaxial creep test which limits the upper limit of load can be applied.
6. The computer technology is increasingly improved, the transformation method is suitable for programming integrated computation, and the development of the method can reduce the workload of manually processing the graph in the creep research process.
7. The method of the invention contains a path considering the hydro-thermal coupling, aiming at a rock-soil body, external force, temperature change, moisture seepage and other external energy which is input and taken away by the soil body and influences the structure and volume change of the rock-soil body are introduced, a hydro-thermal coupling model related to the rock-soil body can be established by obtaining delta (t) of the soil body through some tests, and the method is provided for the research of the time effect of the rock-soil because the delta (t) is introduced and even reflects the time variable in the established model.
Drawings
FIG. 1 is F1And F1+F2The schematic diagram of the stress and deformation of the test sample under the load grading loading and separate loading modes is shown on the left, the stress and deformation of the test sample under the grading loading is shown on the right, and the stress and deformation of the test sample under the separate loading is shown in the diagram: f1First stage axial outward load, unit: n; fi-an i-th stage axial external load, i ═ 1,2, 3.; l, lx-real-time vertical deformation and average radial expansion under graded loading, in units: mm; liLoading the ith load to a stable rule under graded loading, the vertical deformation of the soil sample increased compared to the previous load, not the total cumulative deformation, in units: mm, i ═ 1,2, 3.; l'i-cumulative vertical deformation of the i-class load once loaded to the stability rule in units of: mm, i ═ 1,2, 3.; lxiLoading the ith level load of the triaxial rock-soil sample under graded loading until the ith level load meets the set creep stability rule, wherein the soil sample is compared with the previous level loadIncreased average radial expansion, in units: mm, i ═ 1,2, 3.; l'xiLoading the total i-level load of the triaxial test piece under the respective loading to the average radial expansion amount accumulated by the stability rule, unit: mm, i ═ 1,2, 3.; sigma3-confining pressure, unit: MPa.
FIG. 2 is an exemplary view of a three-axis creep specimen deformation failure mode.
FIG. 3 is a plot of triaxial creep vertical deformation versus time for sample number 14 under graded loading.
FIG. 4 is a hierarchical load (σ)1-σ3) Graph of values, in which: (sigma)1-σ3) In practice, it refers to the axial stress caused by the axial external load, in units: kPa.
FIG. 5 is F using EXCEL1+F2The results are computed from the conversion of the hierarchical loads to the separate loads.
FIG. 6 is a final creep vertical deformation curve cluster for the transformation of sample No. 14 from fractional loading to separate loading, where: f1The expression "n" means an axial external load of
Figure BDA0002748589440000141
Detailed Description
The technical solution of the present invention is further described below with reference to the accompanying drawings, but not limited thereto, and any modification or equivalent replacement of the technical solution of the present invention without departing from the spirit and scope of the technical solution of the present invention shall be covered by the protection scope of the present invention.
The invention provides a method for converting a triaxial creep test deformation curve of graded loading rock-soil into test curves under respective loading, so as to realize the consideration of linear or nonlinear deformation of a sample in the conversion of the deformation curves of two loading tests and improve the requirement on loading time of each level of load. The method comprises the steps of expressing the total energy input to a triaxial sample in a grading loading mode in a column mode and accumulating the total energy input to the triaxial sample by the outside at a certain moment when the total energy is loaded to a certain total load value respectively, enabling the total energy input to the outside in the two loading modes to be equal, establishing an equation about creep deformation of the sample, solving creep deformation of the sample under the respective loading according to the creep deformation data of the grading loading and integrating the initial size and the external conditions of the sample, and drawing a creep deformation-time curve under the respective loading by combining test time corresponding to each equation. The equation was established assuming that the specimen remained cylindrical and constant in volume during creep.
The present invention will be described in detail with reference to fig. 1, in which the results of the respective loading tests are estimated based on the results of the gradation loading tests based on the conservation of energy.
Under the first-level load, the total work of the sample accumulated by the external force applied to the sample when the sample is loaded in a column-type expression grading loading mode and the creep stability mode is respectively loaded (the energy of the sample input by the change of the external environment can be ignored for the tests with little change of the room temperature, and the like), and the total work of the accumulated external force of the two loading modes is equal.
Figure BDA0002748589440000151
In the formula, F1First stage axial outward load, unit: n; fi-an i-th stage axial external load; t is t0、t1-the time for the start of loading and the time for loading to steady creep, respectively, in units of: min; l, lx-real-time vertical deformation and average radial expansion under graded loading, in units: mm; liLoading the ith load to a stable rule under graded loading, the vertical deformation of the soil sample increased compared to the previous load, not the total cumulative deformation, in units: mm; l'i-cumulative vertical deformation if a total of i-class loads are loaded once to the stability rule, in units of: mm; lxiLoading the ith level load of the triaxial rock-soil sample under graded loading until the ith level load meets the set creep stability rule, wherein the average radial expansion amount of the soil sample increased compared with the previous level load is not the total accumulated radial expansion amount, unit: mm; l'xiLoading the total i-level load of the triaxial test piece under the respective loading to the average radial expansion amount accumulated by the stability rule, unit: mm; sigma3-confining pressure, unit: MPa; a. thet-area of top surface of lower triaxial test piece under graded loading, A'tLoading the area of the top surface of the lower triaxial test piece, A, respectivelys-area of side face of lower triaxial test piece under graded loading, A'sLoading the lateral surface area of the lower triaxial specimen, unit: mm is2。
Due to At、A′t、As、A′s、l、l′、lx、l′xAll are variables changing along with time, and the change process is difficult to determine by adopting integral calculation, so the simplification is realized. In order to ensure a certain degree of safety and set a certain redundancy for stabilizing the creep value, for the integral operation in the above formula, the area value, the vertical deformation value and the radial expansion amount at the time of stabilizing the creep are substituted to simplify the integral. Thus, the above formula is converted to the following formula:
W1＝F1l1+σ3·At1·l1-σ3·As1·lx1＝W′1＝F1l′1+σ3·A′t1·l′1-σ3·A′s·l′x1 (2)；
in the formula, Ati、A′ti-the area of the top surface when the triaxial creep test specimen reaches steady creep, unit, under step loading and under load respectively: mm is2。Asi、A′si-the lateral area when the triaxial creep test specimen reaches steady creep, unit, under step loading and under load respectively: mm is2. And step-by-step loading is carried out on the ith stage under the step-by-step loading, and the i-stage loads which are loaded at the next time are respectively loaded.
The purpose of "transformation" is to finally determine the stable creep deformation values under the respective loading, which can be obtained from equation (2):
Figure BDA0002748589440000161
the same reasoning shows that:
secondary loading:
Figure BDA0002748589440000162
third-level load:
Figure BDA0002748589440000171
the purpose of deriving these formulae from the external energy point of view is to hopefully convert the test results of the staged loading into test results of the separate loading, mainly solving for l'i. On the basis of the test results,/iAre known. In the above formula Ati、A′ti、Asi、A′si、lxi、l′xiIt is desirable to obtain it by other methods.
Note: in fact, Ati、A′ti、Asi、A′si、lxi、l′xiAre all related to the diameter of the three-axis sample, which relates to diDetermining and selecting the diameter of the triaxial soil sample. The possible solutions are as follows:
1. the test process is directly measured. It is too costly to measure each diameter value along the height, and the physical elements can be measured in layers by soil height. Finally taking the average value to calculate Ati、Asi、lxi。
2. And measuring the volume of water to be drained through the change of the pore water pressure, and converting the volume into a body change to obtain the transverse deformation.
3. Based on some geometrical assumptions, radial deformation is derived from the vertical deformation which can be directly measured, and the initial size of the sample is known to obtain the required diameter data. Particularly, in the three-axis test without consolidation and drainage, the volume of the three-axis sample becomes zero (on the premise of not considering the damage crack of the sample). After the vertical deformation of the triaxial sample is obtained, the radial deformation of the triaxial sample can be obtained by using the unchanged volume, and a conversion formula between the transverse deformation and the vertical deformation is constructed. Let lxAnd l'xThe same transformation relationship is found between vertical real-time deformations l and l' in the unconsolidated, undischarged state. In addition, to complete the conversion of the formula, it is also necessary to obtain AsiAnd A'siIs described in (1).
Geometrically deriving the transformation formula of vertical deformation and radial deformation, and the change formula of the side area of the triaxial sample, it is necessary to refer to the deformation state of the triaxial soil sample, and fig. 2 is a typical deformation failure form of the creep sample.
AsiAnd A'si、lxiAnd l'xiThe preferred calculation scheme is: carrying out a large amount of statistics on deformation damage forms of the soil sample, carrying out three-dimensional modeling according to the statistical deformation damage characteristics of the soil sample, layering the orthographic projection surface of the soil sample according to the height, and taking the midpoint l of each layer of all the layersxiAnd l'xiAverage value of (2)
Figure BDA0002748589440000181
And
Figure BDA0002748589440000182
and calculates A according to the two valuessiAnd A'si. According to the height layering integral (-sigma) of soil sample3·Asi·lxi+σ3·A′si·l′xi) Thereby resulting in a large amount of computation and high mathematical power.
The other scheme is that the three-dimensional geometric model of the soil sample can be simplified according to the deformation of the soil sample:
1. the cylinder plus drum type requires a detailed curve function due to the multiple integration required for drum shape, and is not used.
2. Two symmetrical round tables with bottom surfaces stuck together. The following calculations occur in the calculation process:
when the load is estimated from the first stage, the following occurs: the volume of the cylinder is equal to that of the two round tables by an equation R2+R·r+r2To solve the mathematical calculation of the exact value of (R + R), certainvalue is difficult.
3. Assuming that the sample is still cylindrical after deformation, a series of equations are added by using equal volumes, and the equation with W ═ W' is brought back to solve the deformation of the triaxial sample under the graded loading.
From the first stage of load loading to the time when creep is stable, the body becomes zero, and the following geometric relation can be obtained under the stage loading:
Figure BDA0002748589440000183
lx1＝d0-d1 (7)；
As1＝πd1h1＝πd1(h0-l1) (8)；
Figure BDA0002748589440000184
and the following equation can be obtained under the respective loading:
Figure BDA0002748589440000185
l′x1＝d0-d′1 (11)；
A′s1＝πd′1h′1＝πd′1(h0-l′1) (12)；
Figure BDA0002748589440000191
similarly, the second stage load loading begins until the creep stabilizer becomes zero, and the following relation is obtained:
Figure BDA0002748589440000192
lx2＝d1-d2 (15)；
As2＝πd2h2＝πd2(h1-l2) (16)；
Figure BDA0002748589440000193
and the following equation can be obtained under the respective loading:
Figure BDA0002748589440000195
l′x2＝d′1-d′2 (20)；
A′s2＝πd′2h′2＝πd′2(h′1-l′2) (21)；
Figure BDA0002748589440000194
and analogizing in sequence to obtain a geometric relational expression obtained by changing the soil sample into zero in the step-by-step loading process.
In the formula (d)0、diInitial diameter of the sample and the diameter of the sample under the i-th level load to the stable creep are respectively. h is0、hiThe initial height of the sample and the height of the sample from the i-th level load to the stable creep are respectively. The superscript notation is still to distinguish progressive loading from separate loading.
The invention adopts the 2 nd connection vertical and radial deformation mode and adopts the cylindrical assumption.
When solving, it is noted that the conditions of the first stage of the staged loading and the loading of the first stage load respectively are the same, so that the stable strain and the transverse expansion amount of the loading of the first stage load respectively are the same, and the condition that the vertical deformation is l 'can be solved by using the formulas (6), (7), (10) and (11)'1＝l1The radial expansion amount is:
Figure BDA0002748589440000201
and (3) second-stage load conversion:
for simplifying the calculation, the left side of the equation (4) can be directly calculated by using the existing data and combining the geometric relations (6) to (22), and the statistics is W substituted into the calculation:
Figure BDA0002748589440000202
order to
Figure BDA0002748589440000203
Then
Figure BDA0002748589440000204
Continue substituting into the above equation:
Figure BDA0002748589440000205
multiplying both sides simultaneously by xi2And simplifying to obtain:
Figure BDA0002748589440000206
l 'is to be solved'2Then, xi is obtained, and
Figure BDA0002748589440000207
and (5) obtaining the vertical deformation value of the stable creep in the respective loading modes.
l′iAll the solving processes can refer to l'2The main difference of the formula is that the formula mainly adopts variable parameters in application, and the main difference is that W is in a corresponding step-by-step loading mode2Will be changed into WnThe corresponding equation of the loads in different stages is not (F)1+F2) Instead, it is
Figure BDA0002748589440000208
Xi expression becomes
Figure BDA0002748589440000209
Solving the unitary quartic equation (26) by combining Fortran with Matlab. In fact, the above formula may also be solved in Matlab in an iterative manner if ξ reduction is not employed in the process.
Example 1
The transformation amount of the whole curve is large, and the transformation is only carried out on the deformation-time point reaching the stability criterion for the first time under each stage of load during the stage-by-stage loading.
The data for this example is taken from the graded loading creep test deformation curve for a sample numbered 14 in a series of triaxial creep tests, as shown in FIG. 3, which have physical indices: the silty clay has uniform gradation, the initial size d0 of a sample is 61.615mm, the initial size h0 of the sample is 122.240mm, the unsaturated soil sample has the water content of 22.38 percent and the maximum dry density of 1.55g/cm3And the degree of compaction is 0.95. The test working condition is preset to be confining pressure 200kPa, the loading stage number n is 11, the accumulated stepped shaft pressure load value is shown in figure 4, no solidification and no drainage are realized, the environmental temperature and humidity in the test process are small in floating, and the temperature influence is ignored.
The following code is run first under the Fortran compilation environment of Codeblock:
Figure BDA0002748589440000211
Figure BDA0002748589440000221
note: the program is to obtain the total external force W of i-level load under the step-by-step loading.
Then, a project is newly built, and the following programs are operated:
Figure BDA0002748589440000222
Figure BDA0002748589440000231
note: the program is used for solving five variables of a, b, c, d and e of a zeta unary quadratic equation.
The results of the calculations for the parameters of equation (26) in table 1 were obtained using sample No. 14 as an example:
TABLE 1
Figure BDA0002748589440000232
Note:
1. running program calculation, although the confining pressure is set to 200kPa during design test, the actual confining pressure of the test is difficult to stabilize, so the average confining pressure value is adopted
Figure BDA0002748589440000233
Substitution of sigma3(in the program, sigme 3).
Figure BDA0002748589440000234
2. In the conversion mode, in the final unary quartic equation, the cubic coefficient b is equal to 0, and a and c are always kept unchanged in calculation; l1＝l′1Therefore, it is not necessary to calculate a, b, c, d, and e when n is 1; and the deformation of the load sample at the last stage reaches the upper limit of the measurement of the instrument, and the data is not effective, so that the calculation is not carried out.
Starting from a load of order i-2 (or n-2), the resulting a, b, c, d, e are input into MATLAB, and a one-dimensional system of quartic equations is solved.
Example (c):
y＝roots([78647.87500261143.938-314591.500-27859.5957])
y＝-0.4611+2.0104i
y＝-0.4611-2.0104i
y＝1.0051+0.0000i
y＝-0.0828+0.0000i
obviously, it is reasonable to set y to 1.0051, i.e., when n is 2, ξ is 1.0051.
To give a cauchy value, then according to l'i＝h0-h0/ξ2L 'is calculated'iThe value is obtained.
Example (c): l'2＝h0-h0/ξ2＝122.240-122.240/1.00512＝1.2374mm。
All were calculated in the same manner to obtain l 'corresponding to sample No. 14 shown in Table 2 and loaded respectively'i：
TABLE 2
Cumulative axial force/N Number of load stages n ξ l′i/mm
113.954 1 - 1.210
227.909 2 1.0051 1.2374
327.986 3 1.0051 1.2374
428.064 4 1.0055 1.3336
504.034 5 1.0060 1.4538
578.945 6 1.0068 1.6457
653.856 7 1.0083 2.0042
753.816 8 1.0124 2.9761
853.776 9 1.0246 5.7993
966.790 10 1.0517 11.7229
1080.744 11 - -
Example 2
With F1+F2The hierarchical loading of (a) into (b) instances.
The external force work in the whole loading process in two different modes is equal, and the external force work in each moment in the loading process is equal. The method for applying the external force work is as follows:
Figure BDA0002748589440000251
Figure BDA0002748589440000252
the calculation process can be realized by using EXCEL, a series of coefficients a, b, c, d and e of standard unitary quartic equations corresponding to different total axial pressure loads at different loading moments are obtained, the equations are solved to obtain xi values, correct xi values are selected, and a series of l 'are further solved'iThe value is obtained. FIG. 5 is F using EXCEL1+F2The results are computed from the conversion of the hierarchical loads to the separate loads. Fig. 6 is a final creep vertical deformation curve cluster of sample No. 14 converted from fractional loading to separate loading.

Claims (3)

1. A method for converting triaxial creep test results of graded loading rock and soil to respective loading is characterized by comprising the following steps:
step 1: when the columnar expression is loaded to the nth level load in a grading way, the integral expression of the total work done by the outside on the triaxial sample is recorded, and the total work of the outside is Wn1,2,3, then:
Figure FDA0002748589430000011
in the formula, n is the axial external load grade reached by the current loading or the axial external load grade corresponding to the external force work needing to be calculated; fi-an i-th stage axial external load; t is ti-1、ti-the time for the initial loading of the i-th stage of axially external load and the time for the loading to steady creep, respectively; lj-staged additionLoading the j level load until the load is stable and regular, and increasing the vertical deformation of the soil sample compared with the previous level load; lxjLoading the j-th level load of the triaxial rock-soil sample under the grading loading until the j-th level load meets the set creep stability rule, wherein the average radial expansion amount of the soil sample is increased compared with the previous level load; sigma3-confining pressure; a. thet-the area of the top surface of the lower triaxial test piece under graded loading; a. thes-the area of the lateral surface of the triaxial test piece under graded loading; q (t) -energy input during the test by ambient environment changes;
step 2: the integral expression in step 1 is simplified:
Figure FDA0002748589430000012
in the formula, AtiThe top surface area of the triaxial creep test sample reaches the stable creep when the triaxial creep test sample is accumulated and loaded with i-level loads; a. thesiThe side surface area of the triaxial creep test sample reaches the stable creep when the triaxial creep test sample is subjected to graded loading and respectively loading and a total i-grade load is accumulated;
and step 3: when column expression is respectively loaded to a certain level of load, the integral expression of the total work of the outside on the triaxial sample is recorded as Wi1,2,3, then there are:
Figure FDA0002748589430000013
in the formula, Fi' -a total of i-level axial external loads corresponding to the graded loading are applied to the triaxial sample at one time, namely i-level axial external loads loaded respectively; t'iOne-time loading Fi' time taken to load to stabilize creep; t is t0＝0；l′iUnder separate loading, load F oncei' accumulate vertical deformation when loaded to a stable rule; l'xi-applying F under separate loading of the triaxial test piecesi' average radial expansion to steady regular accumulation; sigma'3-confining pressure; a'tSeparate loading of the lower triaxial test piece top surfaceFood of overstrain A's-loading the lateral surface areas of the lower triaxial test piece separately;
and 4, step 4: simplifying the integral expression in step 3:
Wi′＝Fi′·l′i+σ3·A′ti·l′1-σ3·A′si·l′xi+Q(t)；
of formula (II) to'tiRespectively loading the top surface area of the triaxial creep test sample when the triaxial creep test sample reaches stable creep; a'siRespectively loading the lateral surface area of the triaxial creep test sample when the triaxial creep test sample reaches stable creep;
and 5: aiming at a normal-temperature unconsolidated and undrained triaxial creep test, if the volume of a soil sample in the test is kept unchanged, a cylinder is always kept in the deformation process of the soil sample, and Q (t) is ignored;
step 6: according to the test working condition and hypothesis in the step 5, deducing the relationship between the vertical deformation and the radial deformation of the triaxial sample caused by applying different axial loads of two levels front and back in a graded loading mode:
Figure FDA0002748589430000021
in the formula, hj-1The initial height of the triaxial test sample when the jth level load is applied is shown, namely the height when the jth-1 level load is applied to the test sample to achieve creep stability; dj-1The initial diameter of the triaxial sample when the j-th level load is applied is shown;
deducing the relation between vertical deformation and radial deformation of the triaxial sample caused by applying a certain level of axial load compared with the initial size of the sample without applying any axial external load in a respective loading mode:
Figure FDA0002748589430000022
and 7: substituting the working condition data of the triaxial test, calculating and grading loading, totaling
Figure FDA0002748589430000031
When the axial external load acts on the soil sample until the creep is stable, the external work W input to the soil sample is accumulated by the outsiden：
Figure FDA0002748589430000032
In the formula, Asi＝πdjhj，
Figure FDA0002748589430000033
hj＝hj-1-lj，
Figure FDA0002748589430000034
i＝j，hjRepresenting the height of the specimen at which creep stability is achieved by applying a load of the j-th order, djThe diameter of the sample when the j-th load is applied until the sample reaches creep stability is shown;
and 8: substituting the relational expression of vertical deformation and radial deformation under the respective loading in the step 6 and the three-axis test working condition data in the step 7 into W in the step 4i' in the expression:
Wi′＝Fi′·l′i+σ3·A′ti·l′1-σ3·A′si·l′xi；
of formula (II) to'si＝πd′ih′i；
Figure FDA0002748589430000035
h′i＝h0-l′i；
Figure FDA0002748589430000036
h′iShowing the height of the sample when the grade j load is applied until the creep stability is achieved; d'iRepresents the diameter of the sample when the i-th load is applied until the sample reaches creep stability;
and step 9: order to
Figure FDA0002748589430000037
So that Wn＝Wi', column equation for creep vertical deformation:
Figure FDA0002748589430000038
introducing a xi amount which is an expression amount related to vertical deformation, and then:
Figure FDA0002748589430000041
namely, it is
Figure FDA0002748589430000042
The equation is organized as a quartic unitary equation about ξ:
Figure FDA0002748589430000043
coefficient expressions from fourth power to zero power are sequentially sorted and summarized as a, b, c, d and e;
step 10: determining a, b, c, d and e according to the stress condition of the soil sample and the geometric dimension of the soil sample, solving a unitary quartic equation, taking a real number slightly larger than 1 in four solutions, and further calculating to obtain respectively loaded variables from the ξ value
Figure FDA0002748589430000044
Amount of deformation until creep stabilization:
Figure FDA0002748589430000045
step 11: according to the steps 1-10, taking the time when the load is cut off for each level of load under the graded loadingTime tk＝α·2kK is 0,1,2,3. the temporary stable time under the stage creep, and the total external force accumulated at the time is calculated algebraically
Figure FDA0002748589430000046
Figure FDA0002748589430000047
After simplification, the method comprises the following steps:
Figure FDA0002748589430000048
wherein α -is the first value in a selected series of cutoff time points;
Figure FDA0002748589430000049
when load acts on the soil sample, the load is stopped to tkThe external force work done by the external force on the sample is accumulated at any moment;
Figure FDA00027485894300000410
when acting on a soil sample, is stopped at tkThe sample is vertically deformed relative to a single stage generated under the previous stage load at any moment;
Figure FDA0002748589430000051
when acting on a soil sample, is stopped at tkThe sample is subjected to single-stage radial deformation relative to the previous stage load at any moment;
Figure FDA0002748589430000052
when load acts on the soil sample, the load is stopped to tkThe area of the top surface of the sample at that moment;
Figure FDA0002748589430000053
when load acts on the soil sample, the load is stopped to tkSide area of time sample；
Step 12: according to the step 11, the loading cut-off time t is taken for each level of load loaded respectivelyk＝α·2kK is 0,1,2,3. the temporary stable time under the stage creep, and the total external force accumulated at the time is calculated algebraically
Figure FDA0002748589430000054
Figure FDA0002748589430000055
The simplified integral expression then has:
Figure FDA0002748589430000056
in the formula, under the condition of respectively loading,
Figure FDA0002748589430000057
when load acts on the soil sample, the load is stopped to tkThe external force work done by the external force on the sample is accumulated at any moment;
Figure FDA0002748589430000058
when acting on a soil sample, is stopped at tkThe sample is vertically deformed relative to a single stage generated under the previous stage load at any moment;
Figure FDA0002748589430000059
when acting on a soil sample, is stopped at tkThe sample is subjected to single-stage radial deformation relative to the previous stage load at any moment;
Figure FDA00027485894300000510
when load acts on the soil sample, the load is stopped to tkThe area of the top surface of the sample at that moment;
Figure FDA00027485894300000511
when load acts on the soil sample, the load is stopped to tkThe lateral area of the sample at the moment;
step 13: order to
Figure FDA00027485894300000512
For the same tkSo that
Figure FDA00027485894300000513
The equation for creep vertical deformation is listed:
Figure FDA0002748589430000061
introduction of a
Figure FDA0002748589430000062
Amount of (a) to
Figure FDA0002748589430000063
The quantity is an expression quantity related to vertical deformation, and then:
Figure FDA0002748589430000064
namely, it is
Figure FDA0002748589430000065
The equation is arranged to relate to
Figure FDA0002748589430000066
A one-dimensional quadratic equation of (a):
Figure FDA0002748589430000067
coefficient expressions from fourth power to zero power are sequentially sorted and summarized as a, b, c, d and e;
step (ii) of14: determining a, b, c, d and e according to the stress condition of the soil sample and the geometric dimension of the soil sample, solving a unitary quartic equation, taking a real number slightly larger than 1 in four solutions, and calculating the real number according to the real number
Figure FDA0002748589430000068
Further calculation of the values results in separate loading
Figure FDA0002748589430000069
To tkAmount of deformation in the case of (2):
Figure FDA00027485894300000610
in the formula (I), the compound is shown in the specification,
Figure FDA00027485894300000611
denotes the sample at t under respective loadingkThe diameter of the moment;
Figure FDA00027485894300000612
denotes the sample at t under respective loadingkThe height of the moment;
step 15: drawing different axial loads according to the data obtained in the step 14
Figure FDA00027485894300000613
And testing the creep deformation curve cluster under other corresponding working conditions.
2. The method for converting triaxial creep test results of graded loading geotechnical engineering according to claim 1, wherein the steps 11-14 are replaced by:
the research is carried out on the conversion and consumption process of the soil sample to the external force work under the graded loading, and the research is carried out on the conversion and consumption process of the soil sample to the external force work
Figure FDA0002748589430000071
The entire process of loading to the steady creep time is expressed as the following equation：
Figure FDA0002748589430000072
In the formula, tnN 1,2,3.. denotes the total time taken for the staged loading until the nth stage load creep stabilization, respectively;
subtracting the creep processes of two adjacent stages to obtain the following equation:
Figure FDA0002748589430000073
in the formula In-the nth level of load under graded loading to creep stability rule, increased vertical deformation of the sample compared to the previous level of load; lxnLoading the nth level load of the triaxial rock-soil sample under graded loading until the nth level load meets the set creep stability rule, wherein the average radial expansion amount of the soil sample is increased compared with the previous level load; a. thetn-the area of the top surface of the triaxial test piece when the nth level load is loaded to the creep stability rule under the graded loading; a. thesn-loading the nth level load to the lateral surface area of the triaxial test piece when the creep stability rule is reached under the graded loading;
to pair
Figure FDA0002748589430000074
Dt step size in (1) is taken as tk＝α·2kUntil the stabilization moment of the test of the current stage under the stage loading, the integral expression is converted into an addition expression, the left side of the above expression corresponds to tk＝α·2kK is 0,1,2,3. external force work, so as to obtain a curve of the conversion and dissipation efficiency delta (t) of the soil sample to the external force work along with time under the test working condition; after obtaining the change rule of delta (t), the following are:
Figure FDA0002748589430000075
selecting delta within a segment according to time periodi(t) and integrated over time,and (4) obtaining the external force work under corresponding time according to the sum of the integral of the cut-off time, thus obtaining the instant deformation, drawing deformation-time curves of the loading creep tests respectively, deducing the strain and drawing a strain-time curve.
3. The method for converting the triaxial creep test result of the graded loaded rock-soil to the separate loading according to claim 1, wherein i and j are both positive integers, and the value closed interval is 1-n.
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