CN111982692B - Long-term deformation testing method for rock under different stress components and application thereof - Google Patents
Long-term deformation testing method for rock under different stress components and application thereof Download PDFInfo
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Abstract
The invention discloses a long-term deformation testing method of a rock under different stress components, and belongs to the field of rock mechanical property testing. The method comprises the steps of respectively loading and maintaining confining pressure, axial pressure and pore water pressure of a test rock sample by using different motor servo pumps, realizing a constant internal pressure and constant external pressure loading mode under the conditions of triaxial stress and pore water pressure, simultaneously positioning the position of a piston in the confining pressure motor servo pump to record the oil volume in the pump, eliminating errors caused by the loss of oil volume in a triaxial chamber by piston displacement in the axial loading process to the volume deformation measurement of the test rock sample through the cross section area and the axial displacement of an axial pressure head, obtaining the volume strain data of the test rock sample under the conditions of constant internal pressure and constant external pressure by using the oil volume change data in the pump, and respectively obtaining the lower body volume strain and the partial strain relation of two stress states of a spherical stress component and a partial stress component along with time through formula calculation by combining the axial deformation data. The invention also discloses application of the long-term deformation testing method.
Description
Technical Field
The invention relates to a long-term deformation testing method of a rock under different stress components, and belongs to the field of rock mechanical property testing. The method is mainly used for researching the evolution rule of the volume strain and the partial strain of the surrounding rock along with time in two stress component states of a spherical stress component and a partial stress component, analyzing the long-term stability of the rock engineering and predicting the aging deformation of the rock engineering.
Background
Rock long-term deformation has been a direction of great concern in the field of rock mechanics. With the popularization of deep underground engineering in China, the long-term stability and safety of rock engineering are the most important of the engineering. Many underground construction rock masses undergo significant deformation over time during operational and even construction periods. The softer rock is shown as an obvious large deformation phenomenon, the harder rock is shown as gradually cracking from inside to outside along with the time, and finally generating larger displacement and even damage on the surface, for the reservoir rock with a pore structure, the reservoir rock shows the continuous change of compaction and expansion deformation along with the time under the combined action of external load and internal water pressure, and the continuous surface uplifting or collapse is reflected to the ground.
Mechanically, the phenomenon of long-term deformation of the rock is also called creep. Many scholars at home and abroad study the creep characteristics of the rock under different conditions by developing rock rheological mechanical property experiments and constitutive models. The long-term deformation rule of the rock is the key for researching the long-term stability and safety of rock engineering. In a traditional creep model, viscous deformation is generally considered to be caused by partial stress, deformation caused by ball stress only does not have time dependence, however, the rock serving as a natural material has a pore structure or microcracks (fissures), and the change of external load or the change of underground water conditions under engineering conditions can cause the change of the pore structure or the initiation, extension, opening and closing of the fissures. The natural defects of rock materials and the accumulated damage under different working conditions cause the rock volume deformation to change along with time, so that the rock material shows different creep characteristics under different stress components: exhibits volume creep under ball stress; exhibiting shear creep under the action of an offset stress.
At present, the long-term deformation test method of rock under different conditions is studied, for example, chinese patent publication no: 110346218A publication date: 2019.10.18 invention relates to a rock creep test method based on different mining stress paths, which considers the actual change situation of the stress environment after deep coal resource mining and adopts the way of increasing the axial pressure and discharging the confining pressure to perform creep testAnd (6) testing, and respectively obtaining axial displacement and transverse displacement through an axial sensor and a circumferential sensor. The patent does not consider the time dependence of volume deformation, and the annular sensor needs to apply enough pressure to clamp the outer layer of the rubber sleeve of the rock sample, so that the long-term deformation of the thermoplastic sleeve or the rubber sleeve caused by local extrusion of the obtained deformation data cannot be eliminated, the testing accuracy is not high enough, and particularly, the long-term deformation monitoring error of harder rock is large. Moreover, such a circumferential sensor can only acquire a local deformation, which is not equivalent to the full-height deformation of the sample measured by an axial sensor, and the radial deformation measured by the sensor is not representative. Therefore, the circumferential deformation data also needs to take account of the heterogeneous deformation characteristic of the rock to obtain the full-height circumferential deformation data of the rock sample. Direct measurement of the volumetric deformation of a rock sample is key to solving this problem. In the aspect of rock long-term volume deformation measurement, Chinese patent publication No.: 111272562A publication date: 2020.06.12 entitled device and method for measuring rock high temperature creep volume deformation, provides a method for monitoring and calculating creep volume deformation by using a magnetostrictive liquid level meter. The method needs to switch gas and liquid modes for loading confining pressure for many times so as to ensure the range of measuring range, the process is complicated and difficult to operate, and the axial pressure loading process has certain influence on maintaining the constancy of the confining pressure. The deformation measurement precision is less than 0.1mm3And the requirement of high-precision measurement under the condition of small deformation of hard rock cannot be met. In addition, the invention patent does not consider the influence of the internal pore water pressure of the rock sample on the volume deformation. Therefore, the device cannot test the volume deformation data of the rock sample under the conditions of constant internal pressure and constant external pressure, and further cannot obtain the relation between the volume strain and the offset strain of the rock under two stress states of a spherical stress component and an offset stress component in the environment of constant internal pressure and constant external pressure along with time.
Disclosure of Invention
The invention aims to solve the technical problem that the conventional rock creep testing device cannot test the volume deformation data of a rock sample under the conditions of constant internal pressure and constant external pressure for a long time, and provides a long-term deformation testing method of a rock under different stress components. Loading and maintaining confining pressure and axis of test rock sample respectively through different motor servo pumpsAnd the pressure and the pore water pressure realize a constant internal pressure and constant external pressure loading mode under the conditions of triaxial stress and the pore water pressure. Considering that the creep loading mode is a constant confining pressure state, the confining pressure motor servo pump is proposed to adopt a motor servo pump which is manufactured by French TOP industrie and is of model number PMHP50-1000, the piston position in the confining pressure motor servo pump can be simultaneously positioned to record the volume of oil in the pump, and the scale is accurate to 10-3mm3. In the testing process, the volume of the oil quantity in the pump recorded by the servo pump of the confining pressure motor not only comprises the volume change of the oil quantity caused by the volume deformation of the rock sample, but also comprises the volume change of the oil quantity in the triaxial chamber caused by the displacement of the piston of the upper pressure head. In order to obtain accurate volume deformation data of the test rock sample under the conditions of constant internal pressure and constant external pressure, the error caused by the volume of oil in a triaxial chamber consumed by piston displacement in the axial loading process on the volume deformation measurement of the test rock sample can be eliminated through the cross section area and the axial displacement of the axial pressure head. And finally, calculating the relationship of the lower volume strain and the offset strain of the two stress states of the spherical stress component and the offset stress component along with time by combining the axial deformation data through a formula.
In order to achieve the purpose, the technical scheme and the test method adopted by the invention are carried out according to the following steps:
a. the method comprises the following steps of (1) loading a cylindrical rock sample with the diameter of H and the height of D into a sealing sleeve, placing permeation gaskets on the upper end surface and the lower end surface of the cylindrical rock sample, fixing the sealing sleeve between a pressure head and a base in a triaxial chamber, and uniformly installing at least two LVDTs between the pressure head and the base around the periphery of the sealing sleeve, so that the LVDTs can acquire axial deformation data in the loading process of the cylindrical rock sample, namely the displacement of a piston on the upper part of the pressure head;
b. after the pressure head and the base are tightly combined up and down, oil and air are pumped out from the three-axis chamber by using a vacuum pump, the vacuum degree is kept, the three-axis chamber is filled with oil, and a first motor servo pump capable of filling oil into the three-axis chamber is filled with oil;
c. filling oil into a bias chamber which applies pressure to the upper end of a piston at the upper part of the pressure head, and filling oil into a second motor servo pump which can fill oil into the bias chamber;
d. enabling a third motor servo pump which can fill water to the upper end face and the lower end face of the cylindrical rock sample from the pressure head and the base to be full of water;
e. the first motor servo pump is used for filling oil to the three-axis chamber, and the confining pressure is loaded to a set value sigma3Keeping the constant, and recording the oil volume corresponding to the position of the piston in the first motor servo pump;
f. filling water to the upper end face and the lower end face of the cylindrical rock sample through a third motor servo pump, loading the pore pressure p to a set value and maintaining the pore pressure p constant;
g. charging oil into the bias chamber via a second motor servo pump, loading the bias force (σ)1-σ3) Axial pressure σ1The compression strength of the cylindrical rock sample is 50-80% and is kept constant;
h. acquiring axial deformation initial data L of cylindrical rock sample0And initial oil volume V in the servo pump of the first motor0；
Acquiring axial deformation data L of cylindrical rock sample at i-moment to t-momenttAnd the current oil volume V in the servo pump of the first motort
Rock sample long-term axial strain epsilon at time t1And volume strain εvRespectively as follows:
ε1＝(Lt-L0)/H
wherein D ispistonThe diameter of the piston at the upper part of the pressure head,
According to the definition of the strain component, obtaining the axial offset strain e1Comprises the following steps:
e1＝ε1-εv/3
plotting the volume strain epsilon of a cylindrical rock samplevTime dependence and axial offset strain e1A time-dependent curve is obtainedAnd (3) long-term deformation rule of the rock sample under different stress components.
Further, the scale of the first motor servo pump is accurate to 10-3mm3And the volume data of the oil in the pump can be read through the position of the piston in the pump.
Preferably, an oil filling pipe in the inner wall of the triaxial chamber is respectively communicated with the vacuum pump and the oil tank through a first three-way valve, wherein when the first three-way valve is closed, the oil filling pipe is communicated with the vacuum pump to form a vacuum pumping loop; when the first three-way valve is opened, the oil filling pipe is communicated with the oil tank to form a downstream oil filling loop.
Preferably, a pressurized oil pipe in the upper end of the three-shaft chamber is communicated with an oil tank through a first valve, a first motor servo pump and a second valve in sequence to form a confining pressure loading loop.
Preferably, the biasing chamber is communicated with the oil tank through a third valve, a second motor servo pump and a fourth valve in sequence to form a biasing loading loop.
Preferably, the permeation channels of the pressure head and the base are respectively communicated with a second three-way valve and a third motor servo pump, the second three-way valve is also respectively communicated with a fifth valve and a third motor servo pump, the fifth valve is also communicated with a water tank, the second three-way valve is closed, and when the fifth valve is opened, the water tank is communicated with the third motor servo pump; and when the second three-way valve is opened and the fifth valve is closed, the permeation channels of the pressure head and the base are respectively communicated with the third motor servo pump to form a pore pressure loading loop.
The long-term deformation testing method of the rock under different stress components is applied to the long-term stability analysis and the aging deformation prediction of rock engineering: and respectively obtaining creep model parameters of the spherical stress component and the offset stress component according to evolution curves of the lower volume strain and the axial offset strain of the cylindrical rock sample in two stress states of the spherical stress component and the axial offset stress component along with time, and applying the creep model parameters to long-term stability analysis and aging deformation prediction of rock mass engineering.
The application of the invention comprises the following specific steps:
1) according to the initial volume strain and the initial axial partial strain in the evolution curve of the volume strain and the axial partial strain, the axial pressure loaded in the step g, the confining pressure loaded in the step e and the pore pressure loaded in the step f at the initial moment are brought into an initial equation of a creep model, and elastic parameters are obtained: bulk and shear moduli;
2) according to N groups of volume strain data at the starting moment on an evolution curve of the volume strain along with time and a volume strain calculation value obtained by model calculation, a creep model parameter under a spherical stress component in a model is taken as an unknown parameter, and a creep model parameter under the spherical stress component is obtained by using a target function and a least square method;
3) and according to N groups of axial partial strain data at the starting moment on the evolution curve of the axial partial strain along with the time and an axial partial strain calculation value obtained by model calculation, taking a creep model parameter under a partial stress component in the model as an unknown parameter, and solving a creep model parameter under the partial stress component by using a target function and a least square method.
Due to the adoption of the technical scheme, the invention has the following advantages and positive effects:
(1) the method provides a new method for long-term deformation measurement of the rock under different stress components, and can automatically acquire rock sample volume deformation data simply, conveniently and accurately, wherein the volume data is accurate to 10-3mm3. And expressing the error of the volume loss of the oil in the triaxial chamber caused by the displacement of the piston in the axial loading process on the volume deformation measurement of the test rock sample by the product of the cross section area of the axial pressure head and the axial displacement.
(2) The stress condition of the rock sample also considers the water pressure effect in the pore space besides the confining pressure and the axial pressure.
(3) According to the definition of the strain component, the evolution curves of the volume strain and the partial strain of the rock sample in two stress states of the spherical stress component and the partial stress component along with time are obtained by combining the axial deformation data.
Drawings
FIG. 1 is a schematic representation of the test method of the present invention;
FIG. 2 is an axial strain ε obtained by a test method of the present invention1An evolution curve;
FIG. 3 is a diagram of the testing method of the present inventionSystem of volume strain epsilonvAn evolution curve;
FIG. 4 is an axial offset strain e plotted by the test method of the present invention1A plot of time;
Detailed Description
The invention is further described below in conjunction with specific implementations and computational methods.
Sandstone with porosity of about 21.5% is used as a case object, a sandstone creep test is carried out under the conditions of confining pressure, axial pressure and pore water pressure, and volume strain epsilon of a sample under a ball stress component is obtainedvTime dependence and axial offset strain e under offset stress component1The test method is carried out according to the following steps of the relation curve along with time:
a, a standard cylindrical rock sample with the diameter D of 49.70mm and the height H of 100.02mm is loaded into a sealing sleeve 18, permeation gaskets are respectively arranged on the upper end surface and the lower end surface of the sealing sleeve 18, the sealing sleeve 18 is fixed between a pressure head 1 and a base 2 in a triaxial chamber 19, two LVDTs (linear variable differential transformers) 3 are arranged between the pressure head 1 and the base 2, axial deformation data in the loading process of the standard cylindrical rock sample are collected, and the data also reflect the displacement of a piston 4 on the upper portion of the pressure head;
b, after the installation is finished, lifting the base 2 of the three-axis chamber 19, closing the three-axis chamber 19 up and down tightly, closing the first three-way valve 5, communicating the three-axis chamber 19 with the vacuum pump 6, starting the vacuum pump 6 to exhaust oil and air in the three-axis chamber 19, opening the first three-way valve 5, opening the first valve 7 and the second valve 8, connecting the three-axis chamber 19 with the first motor servo pump 9 and the oil tank 10, filling oil into the three-axis chamber 19, closing the first valve 7 after the oil is filled, filling oil into the first motor servo pump 9, and closing the second valve 8 after the oil is filled;
c, opening the third valve 11 and the fourth valve 12, connecting the bias chamber 20 with the second motor servo pump 13 and the oil tank 10, filling oil into the bias chamber 20, closing the third valve 11 after the bias chamber is filled with the oil, filling the second motor servo pump 13 with the oil, and closing the fourth valve 12 after the bias chamber is filled with the oil;
d, closing the second three-way valve 14, opening the fifth valve 15, connecting the third motor servo pump 16 with the water tank 17, and filling the third motor servo pump 16 with water;
e opening the first valve 7, starting the first motor servo pump 9, loading the confining pressure to the set value sigma3Recording the oil volume corresponding to the position of a piston in the first motor servo pump 9 when the pressure is 6MPa and is kept constant; the motor servo pump mentioned in the embodiment is suggested to adopt a motor servo pump which is produced by TOP industrie of France and has the model number of PMHP 50-1000;
f, closing the fifth valve 15, opening the second three-way valve 14, starting the third motor servo pump 16, and loading the pore pressure to a set value p of 1MPa and keeping the pore pressure constant;
g opening the third valve 11, starting the second motor-driven servo pump 13, and applying a biasing force (σ)1-σ3) At 18MPa and held constant, i.e. axial pressure σ1＝24MPa；
h at the moment, the data acquisition instrument automatically acquires axial deformation initial data L0And the initial volume V of oil in the first motor servo pump 90
The i data acquisition instrument automatically acquires axial deformation data L of 160 hourstAnd the current volume V of oil in the first motor servo pump 9t
The long-term axial strain epsilon of the rock sample is obtained1And volume strain εvRespectively as follows:
ε1＝(Lt-L0) The formula is
Wherein H is the height of the standard cylindrical rock sample of 100.02mm,
d is the diameter of a standard cylindrical rock sample of 49.70mm,
Dpistonthe diameter of the piston at the upper part of the pressure head is 50mm,
As shown in FIG. 3, the axial strain ε is plotted1And volume strain εvAn evolution curve over time;
from the definition of the strain component, the axial offset strain e is obtained as shown in FIG. 41Comprises the following steps:
e1＝ε1-εv/3
thereby drawing axial offset strain e1Curve over time:
the long-term deformation rule of the rock sample under different stress components is obtained. Based on the curves of the volume strain and the partial strain of the rock along with time in two stress states of the spherical stress component and the partial stress component, the mechanical parameters suitable for the creep model can be obtained, and the method is applied to long-term stability analysis and aging deformation prediction of rock engineering. According to the three-dimensional constitutive relation of a viscoelastic part under a ball stress state, the three-dimensional constitutive relation is as follows:
wherein σm，
Mean stress and its first and second derivatives, εv，
Respectively the volume strain and its first and second derivatives, KM、KK、
All are ball stress viscoelasticity parameters.
The three-dimensional constitutive relation of the viscoelastic part in the biased stress state can be expressed as:
wherein S isij，
The partial stress tensor and its first and second derivatives, eij，
The partial strain tensor and its first and second derivatives, G, respectivelyM、GK、
All are bias stress viscoelasticity parameters.
Thus, the σ in the experiment1，σ3Constitutive equation under the condition of p constant:
wherein σ1Axial pressure, σ, applied for step g3Confining pressure applied in step e, and pore pressure applied in step f, σm＝(σ1+2σ3)/3. According to the initial equation at the time when t is 0:
the axial strain epsilon of the measured data1And volume strain εvSubstituting the initial equation of the creep model to obtain an elastic parameter: bulk modulus KMAnd shear modulus GM。
N groups (N) of start time on the evolution curve of the volume strain with time>3) Measured data epsilonvAnd calculating the value
With KK，
As unknown parameters, using the objective function:
least square method for obtaining creep model parameter K under spherical stress componentK，
Wherein the volume is measured by a strain calculation
The following equation is obtained:
similarly, according to N groups (N) of the initial time on the evolution curve of the axial partial strain along with the time>3) Measured data e1And calculating the value
With GK、
As unknown parameters, using the objective function:
least square method for obtaining creep model parameter G under partial stress componentK、
Wherein the axial offset strain is calculated
The following equation is obtained:
and obtaining creep model parameters in numerical calculation.
Claims (7)
1. A long-term deformation test method of a rock under different stress components is characterized by comprising the following steps:
a. the method comprises the following steps of (1) putting a cylindrical rock sample with the diameter of H and the height of D into a sealing sleeve, placing permeation gaskets on the upper end surface and the lower end surface of the cylindrical rock sample, fixing the sealing sleeve between a pressure head (1) and a base (2) in a triaxial chamber (19), and uniformly installing at least two LVDTs (3) between the pressure head (1) and the base (2) around the periphery of the sealing sleeve, so that the LVDTs (3) can acquire axial deformation data in the loading process of the cylindrical rock sample, namely the displacement of a piston (4) on the upper part of the pressure head, wherein the LVDTs are linear variable differential transformers;
b. after the pressure head (1) and the base (2) are tightly closed up and down, oil and air are pumped out from the three-axis chamber (19) by using the vacuum pump (6), the vacuum degree is kept, the three-axis chamber (19) is filled with oil, and the first motor servo pump (9) which can fill the oil into the three-axis chamber (19) is filled with the oil;
c. a bias pressure chamber (20) which applies pressure to the upper end of a piston (4) at the upper part of the pressure head is filled with oil, and a second motor servo pump (13) which can fill the bias pressure chamber (20) with oil is filled with oil;
d. a third motor servo pump (16) which can fill water to the upper end surface and the lower end surface of the cylindrical rock sample from the pressure head (1) and the base (2) is filled with water;
e. the first motor servo pump (9) is used for filling oil to the three-shaft chamber (19) and loading confining pressure to a set value
Keeping the constant, and recording the oil volume corresponding to the position of the piston in the first motor servo pump (9);
f. filling water to the upper end face and the lower end face of the cylindrical rock sample through a third motor servo pump (16), loading the pore pressure p to a set value and keeping the pore pressure p constant;
g. the bias chamber (20) is filled with oil by a second motor servo pump (13) and the bias force is loaded
Waiting for axial compression
The compression strength of the cylindrical rock sample is 50-80% and is kept constant;
h. acquiring axial deformation initial data of cylindrical rock sample
And the initial volume of oil in the first motor servo pump (9)
；
Acquiring axial deformation data of cylindrical rock sample at i-moment to t-moment
And the current oil volume in the first motor servo pump (9)
Long term axial strain of rock sample at time t
And volume strain
Respectively as follows:
wherein,
the diameter of the piston at the upper part of the pressure head,
according to the definition of the strain component, the axial offset strain is obtained as follows:
plotting volumetric strain of cylindrical rock sample
Time dependence and axial strain
And (3) obtaining a long-term deformation rule of the rock sample under different stress components by using a relation curve along with time.
2. The method for long term deformation testing of a rock according to claim 1 under different stress components, characterized by: the scale of the first motor servo pump (9) is accurate to 10-3mm3And the volume data of the oil in the pump can be read through the position of the piston in the pump.
3. The method for long term deformation testing of a rock according to claim 1 under different stress components, characterized by: an oil filling pipe (22) in the inner wall of the triaxial chamber (19) is respectively communicated with the vacuum pump (6) and the oil tank (10) through a first three-way valve (5), wherein when the first three-way valve (5) is closed, the oil filling pipe (22) is communicated with the vacuum pump (6) to form a vacuum pumping loop; when the first three-way valve (5) is opened, the oil filling pipe (22) is communicated with the oil tank (10) to form a downstream oil filling loop.
4. The method for long term deformation testing of a rock according to claim 1 under different stress components, characterized by: and a pressurized oil pipe in the upper end of the triaxial chamber (19) is communicated with the oil tank (10) sequentially through the first valve (7), the first motor servo pump (9) and the second valve (8) to form a confining pressure loading loop.
5. The method for long term deformation testing of a rock according to claim 1 under different stress components, characterized by: the bias pressure chamber (20) is communicated with the oil tank (10) through a third valve (11), a second motor servo pump (13) and a fourth valve (12) in sequence to form a bias pressure loading loop.
6. The method for long term deformation testing of a rock according to claim 1 under different stress components, characterized by: the pressure head (1) and a permeation channel (23) of the base (2) are respectively communicated with a second three-way valve (14) and a third motor servo pump (16), the second three-way valve (14) is also respectively communicated with a fifth valve (15) and a third motor servo pump (16), the fifth valve (15) is also communicated with a water tank (17), the second three-way valve (14) is closed, and when the fifth valve (15) is opened, the water tank (17) is communicated with the third motor servo pump (16); when the second three-way valve (14) is opened and the fifth valve (15) is closed, the permeation channels (23) of the pressure head (1) and the base (2) are respectively communicated with the third motor servo pump (16) to form a pore pressure loading loop.
7. The application of the long-term deformation testing method of rock under different stress components in rock mass engineering long-term stability analysis and aging deformation prediction is characterized in that: respectively obtaining creep model parameters of the spherical stress component and the partial stress component according to evolution curves of the volume strain and the partial strain of the cylindrical rock sample in two stress states of the spherical stress component and the partial stress component along with time, and applying the creep model parameters to long-term stability analysis and aging deformation prediction of rock mass engineering;
the method specifically comprises the following steps:
1) according to the initial volume strain in the evolution curve of the volume strain and the axial offset strain
And initial axial strain
The axle pressure loaded in the step g at the initial moment
Step e loaded confining pressure
And f, substituting the pore pressure p loaded in the step f into an initial equation of the creep model to obtain an elastic parameter: bulk modulus
And shear modulus
；
Wherein, the initial equation at the time t =0 is:
2) according to N groups of volume strain data of the starting moment on the evolution curve of the volume strain along with the time
And the calculated value of the volume strain obtained by model calculation
Using the creep model parameters under the spherical stress component in the model
，
，
As unknown parameters, the creep model parameters under the spherical stress component are obtained by using an objective function and a least square method
，
，
；
Wherein the objective function is:
，N>3；
wherein the volume is measured by a strain calculation
The following equation is obtained:
3) according to N groups of axial partial strain data at the starting moment on the evolution curve of the axial partial strain along with the time
Axial deflection strain calculated value obtained by model calculation
Using the creep model parameters under the bias stress component in the model
，
，
As unknown parameters, the creep model parameters under the partial stress components are obtained by using an objective function and a least square method
，
，
；
Wherein the objective function is:
，N>3；
wherein the axial offset strain is calculated
The following equation is obtained:
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