CN112504870A - Test system and method for directly measuring interface shear strength at different temperatures - Google Patents

Test system and method for directly measuring interface shear strength at different temperatures Download PDF

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CN112504870A
CN112504870A CN202011291970.3A CN202011291970A CN112504870A CN 112504870 A CN112504870 A CN 112504870A CN 202011291970 A CN202011291970 A CN 202011291970A CN 112504870 A CN112504870 A CN 112504870A
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horizontal
sample
sensor
side frame
water bath
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于龙
扈晓飞
杨庆
杨钢
韩云瑞
王泽明
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Dalian University of Technology
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N3/00Investigating strength properties of solid materials by application of mechanical stress
    • G01N3/24Investigating strength properties of solid materials by application of mechanical stress by applying steady shearing forces
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01LMEASURING FORCE, STRESS, TORQUE, WORK, MECHANICAL POWER, MECHANICAL EFFICIENCY, OR FLUID PRESSURE
    • G01L11/00Measuring steady or quasi-steady pressure of a fluid or a fluent solid material by means not provided for in group G01L7/00 or G01L9/00
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2203/00Investigating strength properties of solid materials by application of mechanical stress
    • G01N2203/0014Type of force applied
    • G01N2203/0025Shearing
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2203/00Investigating strength properties of solid materials by application of mechanical stress
    • G01N2203/02Details not specific for a particular testing method
    • G01N2203/022Environment of the test
    • G01N2203/0222Temperature
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2203/00Investigating strength properties of solid materials by application of mechanical stress
    • G01N2203/02Details not specific for a particular testing method
    • G01N2203/026Specifications of the specimen
    • G01N2203/0298Manufacturing or preparing specimens
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2203/00Investigating strength properties of solid materials by application of mechanical stress
    • G01N2203/02Details not specific for a particular testing method
    • G01N2203/06Indicating or recording means; Sensing means
    • G01N2203/067Parameter measured for estimating the property
    • G01N2203/0676Force, weight, load, energy, speed or acceleration

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Abstract

The invention discloses a test system and a test method for directly measuring interface shear strength at different temperatures, and belongs to the technical field of research on rock soil, geology, environment and the like. The invention provides a system and a method for directly measuring interface shear strength at different temperatures, aiming at the problems of insufficient precision, poor anti-interference capability, limited measurement parameters and the like of the existing direct shear test testing technology. The device provided by the invention mainly comprises a lower shearing box-measuring device, a constant-temperature water bath, a heating and refrigerating circulator and a loading device, wherein a tension and compression stress sensor and a pore water pressure sensor are used as internal high-precision measuring components of the structure, a method for testing and calculating the properties of the structure-soil interface at different temperatures and roughness is provided, the method can be used for measuring the interface strength and the pore water pressure of the structure-soil interface, and the relationship between the cohesive force and the friction angle of the structure-soil interface, the temperature and the roughness as well as the shearing rate can be obtained through calculation and analysis.

Description

Test system and method for directly measuring interface shear strength at different temperatures
Technical Field
The invention belongs to the research fields of rock and soil, geology, environment and the like, and relates to a test system and a test method for directly measuring interface shear strength at different temperatures.
Background
The structure foundation of ocean engineering inevitably produces complicated interact with the seabed soil body in installation and in-service process. The structure-soil interface problem is frequent in geotechnical engineering, and the discontinuous deformation phenomena of local separation, dislocation, sliding and the like of the contact surface of the structure-soil interface are caused by the generation of larger shear stress, so that the bearing performance and the stability of the structure are seriously influenced. Therefore, accurately grasping the properties of the structure-soil interface is important for the structural stability and safety of ocean engineering.
The direct shear test is used as an indoor test means, and the test result can obtain an experimental parameter for evaluating the soil body and structure-soil interface property, namely shear strength, so as to judge the bearing performance and stability of the seabed foundation. At present, the direct shear test testing technology is widely applied to engineering design and evaluation, but simultaneously, the direct shear test testing technology has some defects, such as the continuous reduction of the contact surface of a structure and soil in the shearing process, the incapability of measuring the pore water pressure of the shearing surface, the incapability of performing shear tests under different temperature conditions, and the like. On the other hand, in addition to the structure-soil interface, there are interfaces between the various instrument components in the direct shear test equipment, which results in higher than actual shear strength of the measured structure-soil interface. In order to solve the above problems, it is important to provide a testing system and method capable of directly measuring the interface shear strength at different temperatures.
The invention provides a system and a method for directly measuring interface shear strength at different temperatures, which utilize friction plate measuring devices with different roughness to carry out a direct shear test of a structure-soil, can directly obtain the real shear strength of the structure-soil interface and the development rule of pore water pressure at the interface, and can neglect the influence of the friction force between instrument components on the measurement result. Meanwhile, the direct shear test of the structure-soil sample at different temperatures is carried out by utilizing the heat exchange technology, so that the method has important significance for improving the precision of the test result and accurately reflecting the property of the structure-soil interface under different test environments.
Disclosure of Invention
The invention aims to provide a test system and a test method for directly measuring interface shear strength at different temperatures, so as to overcome the defects of the existing means. The direct measurement of the shear strength of the structure-soil interface and the pore water pressure under different temperature and roughness conditions can be realized, and the measurement result can accurately reflect the property of the structure-soil interface.
The technical scheme of the invention is as follows:
a test system for directly measuring interface shear strength at different temperatures comprises a lower shear structure-measuring device, a constant-temperature water bath 1, a heat conduction pipe 2, a heating and refrigerating circulator 3, a water bath cover plate 4, a lower shear box force transmission beam 5, a sample loading top plate 6, a sample pressurizing cap 7, a force transmission rod 8, a normal displacement sensor 9, a spring frame 10, a normal stress applying device 11, a sample 12, an electric signal demodulator 13, a temperature sensor 14, a first sealing ring 15, a second sealing ring 16, a normal stress sensor 17, a horizontal displacement applying device 18, a horizontal displacement sensor 19, a slide way 20, a lower shear box bearing platform 21, a first cable 22, a computer 23, a pore water pressure sensor 30, a horizontal actuating shaft 37, a horizontal fixing shaft 38, a sample shear box 40, a sample box force transmission beam 41, a third sealing ring 42, a horizontal fixing device 43, a second shear box force transmission rod 8, A horizontal stress sensor 44, a drain valve 45, a first valve 46 and a second valve 47;
the lower shearing structure-measuring device comprises a structure top plate 24, a side frame structure I25, a side frame structure II 26, a friction plate 27, a tension-compression sensor I28, a tension-compression sensor II 29, a metal hose 31, a structure bottom plate 32, a linear guide rail I33, a silica gel sealing ring 34, a side frame structure III 35, a side frame structure IV 36, a permeable stone 39, a linear guide rail II 48, a groove 49 and a cable II 50; the first side frame structure 25, the second side frame structure 26, the third side frame structure 35 and the fourth side frame structure 36 enclose a frame body with a space structure in the middle, the fourth side frame structure is positioned on a uniform horizontal plane, the first side frame structure 25 and the second side frame structure 26 have the same structure, the third side frame structure 35 and the fourth side frame structure 36 have the same structure, and the third side frame structure 35 and the fourth side frame structure 36 are clamped between the first side frame structure 25 and the second side frame structure 26; the structure top plate 24 and the structure bottom plate 32 are respectively fixed at the upper part and the lower part of the frame body, a square through hole is arranged at the center of the upper surface of the structure top plate 24, and friction surfaces are arranged around the square through hole; the section of the friction plate 27 is convex, and the upper surface of the friction plate is a rough surface, so that the upper surface of the friction plate 27 is ensured to be in contact with the lower surface of the test sample 12; the friction plate 27 is arranged in the space structure inside the frame body, and the upper surface of the friction plate is level with the upper surface of the structure top plate 24; a certain gap is formed between the structural top plate 24 and the friction plate 27 and is filled by a silica gel sealing ring 34; the left side surface and the right side surface of the friction plate 27 are respectively connected with one end of a first pull-press sensor 28 and one end of a second pull-press sensor 29; the friction plate 27 is respectively connected with the first linear guide rail 33 and the second linear guide rail 48, so that the lower surface of the friction plate 27 and the upper surfaces of the first linear guide rail 33 and the second linear guide rail 48 are in the same horizontal plane; the first linear guide rail 33 and the second linear guide rail 48 are positioned in a space structure inside the frame body; a groove 49 is arranged at the center of the upper surface of the friction plate 27 to ensure that the permeable stone 39 is fixed therein; a through hole is formed in the center of the bottom of the groove 49, so that the metal hose 31 can conveniently penetrate through the through hole, the lower surface of the permeable stone 39 and the top of the metal hose 31 are ensured to be in the same horizontal plane, and the upper surface of the permeable stone 39 and the upper surface of the friction plate 27 are ensured to be in the same horizontal plane;
the first tension and compression sensor 28 and the second tension and compression sensor 29 are positioned in the space structure in the frame body, and the other ends of the first tension and compression sensor and the second tension and compression sensor are respectively connected with the inner side surfaces of the first side frame structure 25 and the second side frame structure 26; the first side frame structure 25 and the second side frame structure 26 are provided with threaded through holes for the second cable 50 to pass through; the first tension and compression sensor 28 and the second tension and compression sensor 29 are both connected with the electric signal demodulator 13 through a second cable 50;
the metal hose 31 is connected with a pore water pressure sensor 30 outside the constant temperature water bath 1; the pore water pressure sensor 30 is connected with the electric signal demodulator 13 through a first cable 22;
the lower shearing structure-measuring device is embedded into the lower shearing box bearing platform 21; the lower shear box bearing platform 21 is connected with a horizontal actuating shaft 37 through a lower shear box force transmission beam 5; the sample shearing box 40 is connected with the horizontal fixed shaft 38 through a sample box force transmission beam 41; the horizontal fixing shaft 38 is fixed on the horizontal fixing device 43;
the outer wall of the constant-temperature water bath tank 1 is provided with two through holes which are respectively positioned at the top and the bottom of the outer wall of the constant-temperature water bath tank 1 and are respectively connected with a first valve 46 and a second valve 47; the first valve 46 and the second valve 47 are respectively connected with the heating and refrigerating circulator 3 through the heat conducting pipe 2;
the water bath cover plate 4 is covered on the constant-temperature water bath 1, two through holes are formed in the upper surface of the water bath cover plate, and a cable II 50 can conveniently penetrate through one through hole to ensure the sealing performance of the cable II; the other through hole is positioned at the center of the upper surface of the water bath cover plate 4, so that the dowel bar 8 can conveniently pass through the through hole; the third sealing ring 42 is fixed at the intersection of the water bath cover plate 4 and the dowel bar 8;
the top end of the dowel bar 8 is connected with the spring frame 10, so that the base shafts of the dowel bar 8 and the spring frame 10 are ensured to be in a vertical state; the top end of the spring frame 10 is connected with a normal stress applying device 11; the spring frame 10 can only vertically move up and down under the action of the normal stress applying device 11 and cannot move left and right or rotate;
the bottom end of the dowel bar 8 is contacted with the sample pressurizing cap 7, so that the axle center of the dowel bar 8 and the axle center of the sample pressurizing cap 7 are ensured to be positioned on the same vertical line; the bottom end of the sample pressurizing cap 7 is contacted with the top end of the sample loading top plate 6, and the sample loading top plate 6 can only vertically move up and down under the action of the normal stress applying device 11 and cannot move left and right or rotate;
the sample 12 is positioned in the sample shearing box 40, the top end of the sample 12 is contacted with the bottom end of the sample loading top plate 6, and the top end of the sample 12 and the bottom end of the sample loading top plate 6 are ensured to be positioned on the same horizontal plane;
the normal displacement sensor 9 is fixed on the side surface of the dowel bar 8, so that the base shaft of the normal displacement sensor 9 is ensured to be in a vertical state; the normal displacement sensor 9 is connected with the electric signal demodulator 13 through a first cable 22; the temperature sensor 14 is fixed on the water bath cover plate 4, so that the effective testing section of the temperature sensor 14 is ensured to be positioned below the heat exchange liquid level in the constant-temperature water bath 1 and is connected with the electric signal demodulator 13 through a cable I22;
a pair of through holes are formed in the transverse axis of the bottom end of the constant-temperature water bath 1, so that the horizontal actuating shaft 37 and the horizontal fixing shaft 38 can conveniently penetrate through the through holes; the right end of the horizontal actuating shaft 37 is connected with the force transmission beam 5 of the lower shear box, and the left end of the horizontal actuating shaft is connected with the horizontal displacement application device 18, so that the horizontal actuating shaft 37 can only horizontally move under the action of the horizontal displacement application device 18 and cannot move up and down or rotate; the left end of the horizontal fixed shaft 38 is connected with a force transmission beam 41 of the sample box, and the right end is connected with a horizontal stress sensor 44; ensuring that the base shafts of the lower shear box force transfer beam 5, the horizontal actuating shaft 37, the horizontal fixed shaft 38, the sample box force transfer beam 41 and the horizontal stress sensor 44 are in the same horizontal line;
the horizontal stress sensor 44 is fixed on the horizontal fixing device 43, so that the horizontal fixing shaft 38, the horizontal stress sensor 44 and the horizontal fixing device 43 are ensured not to move or rotate;
the first sealing ring 15 is fixed at the intersection of the horizontal actuating shaft 37 and the constant-temperature water bath 1; the second sealing ring 16 is fixed at the intersection of the horizontal fixing shaft 38 and the constant-temperature water bath 1;
the horizontal displacement sensor 19 is fixed on the upper surface of the horizontal actuating shaft 37, and the base axis of the horizontal displacement sensor 19 is ensured to be parallel to the base axis of the horizontal actuating shaft 37;
the lower shear box bearing platform 21 is fixed on the slideway 20, so that the lower surface of the lower shear box bearing platform 21 and the upper surface of the slideway 20 are in the same horizontal plane; the lower surface of the slideway 20 is contacted with the bottom surface of the constant-temperature water tank 1, moves left and right under the action of the horizontal displacement applying device 18 and cannot move up and down or roll, and the friction between the contact surfaces is rolling friction;
the pore water pressure sensor 30 is connected with the drain valve 45 and the metal hose 31 through a three-way joint;
the normal stress sensor 17 and the horizontal stress sensor 44 are respectively connected with the electric signal demodulator 13 through a first cable 22; the electric signal demodulator 13 is connected to the computer 23.
The friction surfaces of the structural top plate 24 have different roughness, the roughness of the position close to the friction plate 27 is consistent with the roughness of the upper surface of the friction plate 27, and the upper surface of the structural top plate 24 far away from the friction plate 27 is smooth.
A test method for directly measuring interface shear strength at different temperatures comprises the following steps:
s1, selecting different types of soil bodies, different materials and structures with different roughness according to requirements, and manufacturing a sample 12, a replacement structure top plate 24 and a friction plate 27;
s2, adjusting the rigidity and the installation position of the spring frame 10 to ensure that the spring frame 10 is stable and vertical;
s3, adjusting the positions of the lower shearing structure object-measuring device and the sample shearing box 40 to ensure that the vertical basic shafts of the lower shearing structure object-measuring device and the sample shearing box 40 and the vertical basic shafts of the dowel bar 8 and the spring frame 10 are on the same vertical line;
s4, connecting the cables of the normal displacement sensor 9, the normal stress sensor 17, the horizontal displacement sensor 19, the horizontal stress sensor 44 and the pore water pressure sensor 30 to the electric signal demodulator 13, connecting the electric signal demodulator to the computer 23, operating the test control platform and clearing the readings of the normal displacement sensor 9, the normal stress sensor 17, the horizontal displacement sensor 19 and the horizontal stress sensor 44;
s5, closing the valve of the pore water pressure sensor 30, opening the drain valve 45, injecting water into the metal hose 31, stopping injecting water after the water overflows from the permeable stone 39, and clearing the reading of the pore water pressure sensor 30 to zero;
s6, placing the sample 12 into the sample shearing box 40, adjusting the vertical positions of the sample loading top plate 6, the sample pressurizing cap 7, the dowel bar 8 and the normal displacement sensor 9, ensuring that the basal axes of the sample loading top plate 6, the sample pressurizing cap 7 and the dowel bar 8 are positioned on the same vertical line, ensuring that the sample loading top plate 6 is in contact with the sample 12 and the bottom end of the normal displacement sensor 9 is in contact with the water bath cover plate 4, and covering and fixing the water bath cover plate 4;
s7, applying a normal load to the sample 12 through the normal displacement sensor 9, after the normal load reaches a target value, performing heat exchange on the cooling liquid in the constant-temperature water bath 1 through the heating and refrigerating circulator 3 to apply a temperature load to the sample, and after the sample reaches the target temperature and is stabilized for 12 hours, applying horizontal displacement through the horizontal displacement applying device 18 to perform a direct shear test;
s8, performing interface strength shear tests at different temperatures, reading and recording test data through the computer 23, and further calculating the interface shear strength tau;
Figure BDA0002784050710000071
in the formula: τ is the shear strength of the structure-soil interface; q. q.s1The stress measured for the tension and compression sensor one 28; q. q.s2The stress measured for the second tension and compression sensor 29; a is the area of the upper surface of the friction plate 27;
the area of the upper surface of the friction plate 27 is:
A=W×L
in the formula: w is the width of the upper surface of the friction plate 27; l is the length of the upper surface of the friction plate 27;
the shear strength parameters of the structure-soil interface are expressed as:
Figure BDA0002784050710000072
in the formula: c is the cohesive force of the structure-soil interface;
Figure BDA0002784050710000073
is the rubbing angle of the structure-soil interface; σ is the normal stress acting on the structure-soil interface by the normal stress applying device 11; mu is a through-pore water pressure sensor 30Measuring the pore water pressure of the structure-soil interface;
the cohesive force c of the structure-soil interface is related to the ambient temperature, the roughness of the structure and the shear rate of the structure-soil, and is expressed as:
c=f(Rn,T,v,…)
friction angle of structure-soil interface
Figure BDA0002784050710000074
The temperature of the environment, the roughness of the structure and the shear rate at which the structure-soil is located are related and are expressed as:
Figure BDA0002784050710000075
the pore water pressure μ at the structure-soil interface is related to the ambient temperature, structure roughness and shear rate at which the structure-soil is located and is expressed as:
μ=h(Rn,T,v,…)
s9, analyzing the test reliability through the reading of the horizontal stress sensor 44;
F=τA+f
in the formula: f is the result of the horizontal stress sensor 44 test; τ is the shear strength of the structure-soil interface; a is the area of the upper surface of the friction plate; f is the friction between the test system structures.
The invention has the beneficial effects that:
the invention relates to a test system for directly measuring interface shear strength at different temperatures, and provides a test system and a test method for directly measuring the property of a structure-soil interface under different temperatures and roughness conditions;
the invention can measure the change rule of pore water pressure of the structure-soil interface in the shearing process;
the device has the advantages of novel structure, convenient use, low manufacturing cost and simple operation, can accurately measure the shear strength and pore water pressure change rule of the structure-soil interface under different temperature and roughness conditions, and greatly improves the safety of ocean engineering design;
the test system formed by the equipment and the test method can effectively overcome the corrosion and high pressure action of the soil body of the ocean engineering.
Drawings
Fig. 1 is a schematic diagram of a testing system for directly measuring interfacial shear strength at different temperatures according to an embodiment of the present invention.
Fig. 2 is a longitudinal sectional view a-a' of a measuring device in a testing system according to an embodiment of the present invention.
Fig. 3 is a longitudinal sectional view a-a' of the inside of a constant temperature water bath in a test system according to an embodiment of the present invention.
FIG. 4 is a top view of a measurement device in a test system according to an embodiment of the present invention.
Fig. 5 is a schematic diagram of a shear-down structure-measuring device in a test system according to an embodiment of the present invention.
Fig. 6 is a longitudinal sectional view a-a' of a shear-down structure-measuring device in a test system according to an embodiment of the present invention.
FIG. 7 is a side cross-sectional view B-B' of a shear-down structure-measuring device in a testing system according to an embodiment of the present invention.
In the figure: 1, a constant-temperature water bath; 2, a heat conduction pipe; 3 heating the refrigeration circulator; 4 water bath cover plate; 5, a shearing box force transfer beam is arranged below the shearing box; 6, loading a top plate on the sample; 7, a sample pressurizing cap; 8 a dowel bar; 9 a normal displacement sensor; 10 a spring frame; 11 a normal stress applying device; 12, testing the sample; 13 an electric signal demodulator; 14 a temperature sensor; 15, sealing the ring I; 16, a second sealing ring; 17 a normal stress sensor; 18 horizontal displacement application means; 19 a horizontal displacement sensor; 20 slideways; 21, a shear box bearing platform; 22, a first cable; 23, a computer; 24 a structural top panel; 25 side frame structure one; 26 a second side frame structure; 27 a friction plate; 28, pulling and pressing the first sensor; 29, pulling and pressing a second sensor; 30 pore water pressure sensors; 31 a metal hose; 32 a structural backing plate; 33, linear guide rail I; 34 a silica gel sealing ring; 35 side frame structure three; 36 side frame structure four; 37 horizontally acting the moving shaft; 38 a horizontal fixed shaft; 39 a permeable stone; 40 sample shearing box; 41 a sample box force transfer beam; 42, a sealing ring III; 43 horizontal fixing means; 44 horizontal stress sensors; 45 a drain valve; 46, a first valve; 47, valve two; 48 linear guide rails II; 49 grooves; and 50, a second cable.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention. It is to be understood that the embodiments described are only some of the embodiments of the invention, and not all of them. The components of the embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations.
Thus, the detailed description of the embodiments of the present invention provided in the following drawings is not intended to limit the scope of the invention as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments of the present invention without making any creative effort, shall fall within the protection scope of the present invention.
It should be noted that like reference numerals and letters refer to like items in the following figures, and thus, once an item is defined in one figure, it need not be further defined and explained in subsequent figures.
The positional relationships indicated by "upper", "lower", "left", "right", and the like in the description of the present invention are based on the orientations and positional relationships shown in the drawings, or the orientations and positional relationships which are usually placed when the product of the present invention is used, or the orientations and positional relationships which are usually understood by those skilled in the art, and are only for convenience of description in the present examples, and do not indicate or imply that the devices and elements which are indicated must have specific orientations, and therefore, the present invention should not be construed as being limited.
Examples
The embodiment is a test system and a method for directly measuring the interface shear strength at different temperatures, the experimental method provided by the embodiment is simple, the direct measurement of the shear strength of the structure-soil interface and the pore water pressure under different temperatures and roughness conditions can be realized, the measurement result can accurately reflect the property of the structure-soil interface, and the system and the method can be used for the design and construction of underwater pipelines, pile foundations and other structures.
The test system for directly measuring the interface shear strength at different temperatures provided by the embodiment can be used for directly measuring the structure-soil interface shear strength and the pore water pressure. A test system for directly measuring interface shear strength at different temperatures comprises a constant-temperature water bath 1, a heat conduction pipe 2, a heating and refrigerating circulator 3, a water bath cover plate 4, a lower shear box force transmission beam 5, a sample loading top plate 6, a sample pressurizing cap 7, a force transmission rod 8, a normal displacement sensor 9, a spring frame 10, a normal stress applying device 11, a sample 12, an electric signal demodulator 13, a temperature sensor 14, a first sealing ring 15, a second sealing ring 16, a normal stress sensor 17, a horizontal displacement applying device 18, a horizontal displacement sensor 19, a slideway 20, a lower shear box bearing platform 21, a first cable 22, a computer 23, a structural top plate 24, a first side frame structure 25, a second side frame structure 26, a friction plate 27, a first tension and compression sensor 28, a second tension and compression sensor 29, a pore water pressure sensor 30, a metal hose 31, a structural bottom plate 32, a first temperature sensor 14, a second side frame structure, The device comprises a first linear guide rail 33, a silica gel sealing ring 34, a third side frame structure 35, a fourth side frame structure 36, a horizontal actuating shaft 37, a horizontal fixed shaft 38, a permeable stone 39, a sample shearing box 40, a sample box force transmission beam 41, a third sealing ring 42, a horizontal fixing device 43, a horizontal stress sensor 44, a drain valve 45, a first valve 46, a second valve 47, a second linear guide rail 48, a groove 49 and a second cable 50;
the constant-temperature water bath 1 is filled with silicon oil, is connected with the heating and cooling circulator 3 through a first valve 46, a second valve 47 and the heat conduction pipe 2, and is used for changing the temperature of the sample 12 so as to simulate different temperature environments; heat conduction pipe 2 for transferring liquid required for heat exchange; a heating and refrigerating circulator 3 for heating or refrigerating, the bottom end of which is connected to the heat transfer pipe 2; a water bath cover plate 4 for sealing and heat preservation; the lower shear box transfer beam 5 is used for enabling the connected lower shear box bearing platform 21 to horizontally move left and right so as to realize shearing and returning; the sample loading top plate 6 is an acrylic glass plate and is used for preventing the overflow of the 12 soil particles of the sample; the sample pressurizing cap 7 is used for connecting the dowel bar 8 to apply normal load to the sample 12; a normal displacement sensor 9 for measuring normal deformation of the specimen 12; the spring frame 10 is used for changing the application mode of normal stress and can realize the application mode of load by a constant stress and constant rigidity method; the normal stress applying device 11 is used for applying and unloading normal loads and can realize the applying modes of constant stress and constant strain normal stress; a sample 12, a soil sample for performing an indoor test; the electric signal demodulator 13 is used for collecting, restoring and processing the electric signal transmitted by the sensor; the temperature sensor 14 is used for measuring the temperature in the constant-temperature water bath 1 so as to control the temperature of the sample 12; the first sealing ring 15, the second sealing ring 16 and the third sealing ring 42 are metal floating sealing rings; a normal stress sensor 17 for measuring a normal stress of the sample; a horizontal displacement applying device 18 for providing a power for shearing and returning; a horizontal displacement sensor 19 for measuring the magnitude of shear strain; the slideway 20 is used for bearing the lower shearing box bearing platform 21 and enabling the lower shearing box bearing platform to horizontally move left and right so as to realize shearing and returning; a lower shear box bearing platform 21 for bearing a lower shear structure, namely a measuring device; the first cable 22 and the second cable 50 are used for transmitting electric signals obtained by the sensor; a computer 23 for test control and data reading and saving; a structural top plate 24 for carrying the sample shear box 40 and the sample 12; the side frame structure I25, the side frame structure II 26, the side frame structure III 35, the side frame structure IV 36 and the structural bottom plate 32 are frame structures of a lower shearing structure object-measuring device so as to achieve the purposes of fixing the sensor and penetrating through a cable; the friction plate 27 is a structure in a structure-soil interface direct shear test; the tension and compression sensor I28 and the tension and compression sensor II 29 are used for measuring the shear stress of the structure-soil interface; a pore water pressure sensor 30 for measuring the pore water pressure of the structure-soil interface; the metal hose 31 is used for connecting the permeable stone 39 and the pore water pressure sensor 30 at the structure-soil interface so as to measure the pore water pressure of the structure-soil interface; the first linear guide rail 33 and the second linear guide rail 48 reduce the friction force between the friction plate 27 and the structural bottom plate so as to realize the accurate measurement of the shearing stress of the structure-soil interface; the silica gel sealing ring 34 is a non-standard O-shaped sealing ring to prevent the sample soil particles from falling; a horizontal actuating shaft 37 for making the connected lower shear box transfer beam 5 horizontal and left-right fixed and return; the horizontal fixing shaft 38, the sample box force transmission beam 41 and the horizontal fixing device 43 are used for fixing the sample shearing box so as not to move or rotate; a porous stone 39 for measuring pore water pressure to prevent the soil particles of the sample 12 from falling down to block the metal hose 31; a sample shear box 40 for containing the sample 12; a horizontal stress sensor 44 for checking the reliability of the test; a drain valve 45 for discharging and injecting water into the metal hose 31; the first valve 46 and the second valve 47 are used for controlling the switch of the heat exchange; a groove 49 for fixing the permeable stone 39;
the upper surface of the friction plate 27, which is in contact with the lower surface of the sample 12, is a rough surface, the left side surface and the right side surface are respectively provided with a threaded hole and are respectively connected with a first tension and compression sensor 28 and a second tension and compression sensor 29, the top surfaces of the front side surface and the rear side surface are respectively provided with two pairs of threaded through holes and are respectively connected with a first linear guide rail 33 and a second linear guide rail 48 through bolts, and the lower surfaces of the friction plate and the upper surfaces of the first linear guide rail 33 and the second linear guide rail;
the friction plate 27 passes through a large square through hole in the middle of the structural top plate 24; a groove 49 is formed at the center of the upper surface of the friction plate 27, and a permeable stone 39 is fixed in the groove 49; the metal hose 31 passes through a through hole in the center of the bottom of the groove 49; the lower surface of the permeable stone 39 is contacted with the top of the metal hose 31, and the upper surface of the permeable stone 39 and the upper surface of the friction plate 27 are in the same horizontal plane;
the structure top plate 24 is of a central square opening structure, the upper surface of the structure top plate has different roughness, the roughness of the position close to the friction plate is consistent with that of the upper surface of the friction plate 27, and the upper surface of the structure top plate 24 far away from the friction plate 27 is smooth; the gap between the structural top plate 24 and the friction plate 27 is filled by a silica gel sealing ring 34;
the metal hose 31 is connected with a pore water pressure sensor 30 outside the constant temperature water bath 1; the lower shear structure object-measuring device is embedded into a lower shear box bearing platform 21, and the lower shear box bearing platform 21 is connected with a horizontal actuating shaft 37 through a lower shear box transmission beam 5;
the horizontal fixing shaft 38 is connected with a sample box 40 through a sample box force transmission beam 41 and is fixed on a horizontal fixing device 43; the outer wall of the constant-temperature water bath tank 1 is provided with two through holes which are respectively positioned at the top and the bottom of the outer wall of the constant-temperature water bath tank 1 and are respectively connected with a first valve 46 and a second valve 47; the first valve 46 and the second valve 47 are respectively connected with the heating and refrigerating circulator 3 through the heat conducting pipe 2;
the top end of the dowel bar 8 is connected with the spring frame 10, and the bottom end of the dowel bar is contacted with the sample pressurizing cap 7; the bottom end of the sample pressurizing cap 7 is contacted with the top end of the sample loading top plate 6; the sample 12 is positioned in the sample box 40, and the top end of the sample 12 is contacted with the bottom end of the sample loading top plate 6; the top end of the spring frame 10 is connected with a normal stress applying device 11; the devices form a set of loading system, and the whole set of normal loading system can only vertically move up and down under the action of the normal stress applying device 11 and cannot move left and right or rotate;
the first tension and compression sensor 28 and the second tension and compression sensor 29 are respectively fixed at two ends of the horizontal central axis of the friction plate 27; a normal displacement sensor 9 is fixed on the side surface of the dowel bar 8, a temperature sensor 14 is fixed on the water bath cover plate 4, and a horizontal displacement sensor 19 is fixed on the upper surface of the horizontal actuating shaft 37; the sensors are respectively connected with an electric signal demodulator 13, and the electric signal demodulator 13 is connected with a computer 23.
A pair of through holes are formed at the transverse axis of the bottom end of the constant-temperature water bath 1, and a horizontal actuating shaft 37 and a horizontal fixing shaft 38 penetrate through the through holes; the right end of the horizontal actuating shaft 37 is connected with the force transmission beam 5 of the lower shear box, and the left end is connected with the horizontal displacement applying device 18; the left end of the horizontal fixed shaft 38 is connected with a force transmission beam 41 of the sample box, and the right end is connected with a horizontal stress sensor 44; the horizontal stress sensor 44 is fixed on the horizontal fixing device 43; the base shafts of the lower shear box force transmission beam 5, the horizontal actuating shaft 37, the horizontal fixed shaft 38, the sample box force transmission beam 41 and the horizontal stress sensor 44 are in the same horizontal line; the first sealing ring 15 and the second sealing ring 16 are respectively fixed at the intersection of the horizontal actuating shaft 37 and the horizontal fixing shaft 38 with the constant-temperature water bath 1; the third sealing ring 42 is fixed at the intersection of the water bath cover plate 4 and the dowel bar 8;
the lower shear box bearing platform 21 is fixed on the slideway 20; the lower surface of the slideway 20 is contacted with the bottom surface of the constant-temperature water tank 1, and the friction between the contact surfaces is rolling friction; the pore water pressure sensor 30 is connected with the drain valve 45 and the metal hose 31 through a three-way joint;
a test system for directly measuring interface shear strength at different temperatures comprises the following steps:
s1, selecting different types of soil bodies, different materials and structures with different roughness according to requirements, manufacturing a sample, and replacing the structural top plate 24 and the friction plate 27; s2, adjusting the rigidity and the installation position of the spring frame 10 to ensure the stability and the verticality of the spring frame; s3, adjusting the positions of the lower shearing structure-measuring device and the sample shearing box to ensure that the vertical basic shafts of the lower shearing structure-measuring device and the sample shearing box are on the same vertical line with the vertical basic shafts of the dowel bar 8 and the spring frame 10; s4, connecting the cables of the normal displacement sensor 9, the normal stress sensor 17, the horizontal displacement sensor 19, the horizontal stress sensor 44 and the pore water pressure sensor 30 to the electric signal demodulator 13, connecting the electric signal demodulator to the computer 23, operating the test control platform software, and clearing the readings of the normal displacement sensor 9, the normal stress sensor 17, the horizontal displacement sensor 19 and the horizontal stress sensor 44; s5, closing the valve of the pore water pressure sensor 30, opening the drainage valve 45, injecting water into the metal hose 31, stopping injecting water after the water overflows from the permeable stone 39, and resetting the reading of the pore water pressure sensor 30 through software; s6, placing a sample 12 into a sample box 40, adjusting the vertical positions of a sample loading top plate 6, a sample pressurizing cap 7, a dowel bar 8 and a normal displacement sensor 9, ensuring that the basal axes of the sample loading top plate 6, the sample pressurizing cap 7 and the dowel bar 8 are positioned on the same vertical line, ensuring that the sample loading top plate 6 is in contact with the sample 12 and the bottom end of the normal displacement sensor 9 is in contact with a water bath cover plate 4, and covering and fixing the water bath cover plate 4; s7, applying normal load to the sample 12 through the normal displacement sensor 9, after the normal load reaches a target value, performing heat exchange on the cooling liquid in the constant-temperature water bath 1 through the heating and refrigerating circulator 3 to apply temperature load to the sample, and after the sample reaches the target temperature and is stable for 12 hours, applying horizontal displacement through the horizontal displacement sensor 19 to perform direct shear test; s8, performing interface strength shear tests at different temperatures, reading and recording test data through the computer 23, and further calculating the interface shear strength tau;
Figure BDA0002784050710000151
the above is only a preferred example of the present invention and is not intended to limit the present invention, and various modifications and changes will occur to those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (3)

1. The utility model provides a test system of interface shear strength under direct measurement different temperatures, characterized in that, this test system includes shearing structure thing-measuring device down, constant temperature water bath (1), heat pipe (2), heating refrigeration circulator (3), water bath apron (4), shearing box biography power roof beam (5) down, sample loading roof (6), sample pressurization cap (7), dowel bar (8), normal displacement sensor (9), spring frame (10), normal stress application device (11), sample (12), signal of telecommunication demodulation appearance (13), temperature sensor (14), sealing ring one (15), sealing ring two (16), normal stress sensor (17), horizontal displacement application device (18), horizontal displacement sensor (19), slide (20), shearing box cushion cap (21) down, cable one (22), computer (23), The device comprises a pore water pressure sensor (30), a horizontal actuating shaft (37), a horizontal fixing shaft (38), a sample shearing box (40), a sample box force transmission beam (41), a sealing ring III (42), a horizontal fixing device (43), a horizontal stress sensor (44), a drain valve (45), a valve I (46) and a valve II (47);
the lower shearing structure-measuring device comprises a structure top plate (24), a side frame structure I (25), a side frame structure II (26), a friction plate (27), a tension-compression sensor I (28), a tension-compression sensor II (29), a metal hose (31), a structure bottom plate (32), a linear guide rail I (33), a silica gel sealing ring (34), a side frame structure III (35), a side frame structure IV (36), a permeable stone (39), a linear guide rail II (48), a groove (49) and a cable II (50); the side frame structure I (25), the side frame structure II (26), the side frame structure III (35) and the side frame structure IV (36) enclose a frame body with a space structure in the middle, the side frame structure I (25) and the side frame structure II (26) are located on a uniform horizontal plane, the side frame structure III (35) and the side frame structure IV (36) are identical in structure, and the side frame structure III (35) and the side frame structure IV (36) are clamped between the side frame structure I (25) and the side frame structure II (26); the structure top plate (24) and the structure bottom plate (32) are respectively fixed at the upper part and the lower part of the frame body, a square through hole is formed in the center of the upper surface of the structure top plate (24), and a friction surface is arranged around the square through hole; the section of the friction plate (27) is convex, the upper surface of the friction plate is a rough surface, and the upper surface of the friction plate (27) is ensured to be in contact with the lower surface of the sample (12); the friction plate (27) is arranged in a space structure in the frame body, and the upper surface of the friction plate is level with the upper surface of the structure top plate (24); a certain gap is formed between the structural top plate (24) and the friction plate (27) and is filled by a silica gel sealing ring (34); the left side surface and the right side surface of the friction plate (27) are respectively connected with one end of a first tension and compression sensor (28) and one end of a second tension and compression sensor (29); the friction plate (27) is respectively connected with the first linear guide rail (33) and the second linear guide rail (48) to ensure that the lower surface of the friction plate (27) and the upper surfaces of the first linear guide rail (33) and the second linear guide rail (48) are in the same horizontal plane; the linear guide rail I (33) and the linear guide rail II (48) are positioned in a space structure inside the frame body; a groove (49) is arranged at the center of the upper surface of the friction plate (27) to ensure that the permeable stone (39) is fixed therein; a through hole is formed in the center of the bottom of the groove (49) so that the metal hose (31) can conveniently penetrate through the through hole, the lower surface of the permeable stone (39) and the top of the metal hose (31) are ensured to be in the same horizontal plane, and the upper surface of the permeable stone (39) and the upper surface of the friction plate (27) are ensured to be in the same horizontal plane;
the first tension and compression sensor (28) and the second tension and compression sensor (29) are positioned in a space structure in the frame body, and the other ends of the first tension and compression sensor and the second tension and compression sensor are respectively connected with the inner side surfaces of the first side frame structure (25) and the second side frame structure (26); the first side frame structure (25) and the second side frame structure (26) are provided with threaded through holes, so that a second cable (50) can conveniently pass through the threaded through holes; the first tension and compression sensor (28) and the second tension and compression sensor (29) are both connected with the electric signal demodulator (13) through a second cable (50);
the metal hose (31) is connected with a pore water pressure sensor (30) outside the constant-temperature water bath (1); the pore water pressure sensor (30) is connected with the electric signal demodulator (13) through a first cable (22);
the lower shearing structure-measuring device is embedded into a lower shearing box bearing platform (21); the lower shear box bearing platform (21) is connected with the horizontal actuating shaft (37) through a lower shear box force transmission beam (5); the sample shearing box (40) is connected with the horizontal fixed shaft (38) through a sample box force transmission beam (41); the horizontal fixed shaft (38) is fixed on the horizontal fixing device (43);
the outer wall of the constant-temperature water bath (1) is provided with two through holes which are respectively positioned at the top and the bottom of the outer wall of the constant-temperature water bath (1) and respectively connected with a first valve (46) and a second valve (47); the first valve (46) and the second valve (47) are respectively connected with the heating and refrigerating circulator (3) through the heat conduction pipe (2);
the water bath cover plate (4) is covered on the constant-temperature water bath (1), two through holes are formed in the upper surface of the water bath cover plate, one through hole is convenient for the second cable (50) to penetrate through, and the sealing performance of the second cable is ensured; the other through hole is positioned in the center of the upper surface of the water bath cover plate (4) and is convenient for a dowel bar (8) to pass through; a third sealing ring (42) is fixed at the intersection of the water bath cover plate (4) and the dowel bar (8);
the top end of the dowel bar (8) is connected with the spring frame (10) to ensure that the base shafts of the dowel bar (8) and the spring frame (10) are in a vertical state; the top end of the spring frame (10) is connected with a normal stress applying device (11); the spring frame (10) can only vertically move up and down under the action of the normal stress applying device (11) and cannot move left and right or rotate;
the bottom end of the dowel bar (8) is contacted with the sample pressurizing cap (7), so that the axle center of the dowel bar (8) and the axle center of the sample pressurizing cap (7) are ensured to be positioned on the same vertical line; the bottom end of the sample pressurizing cap (7) is in contact with the top end of the sample loading top plate (6), and the sample loading top plate (6) can only vertically move up and down under the action of the normal stress applying device (11) and cannot move left and right or rotate;
the sample (12) is positioned in the sample shearing box (40), the top end of the sample (12) is contacted with the bottom end of the sample loading top plate (6), and the top end of the sample (12) and the bottom end of the sample loading top plate (6) are ensured to be positioned at the same horizontal plane;
the normal displacement sensor (9) is fixed on the side surface of the dowel bar (8) to ensure that the base shaft of the normal displacement sensor (9) is in a vertical state; the normal displacement sensor (9) is connected with the electric signal demodulator (13) through a first cable (22); the temperature sensor (14) is fixed on the water bath cover plate (4), so that the effective testing section of the temperature sensor (14) is positioned below the heat exchange liquid level in the constant-temperature water bath (1) and is connected with the electric signal demodulator (13) through a first cable (22);
a pair of through holes are formed in the transverse axis of the bottom end of the constant-temperature water bath (1) so that a horizontal actuating shaft (37) and a horizontal fixing shaft (38) can conveniently penetrate through the through holes; the right end of the horizontal actuating shaft (37) is connected with the force transmission beam (5) of the lower shear box, and the left end of the horizontal actuating shaft is connected with the horizontal displacement application device (18), so that the horizontal actuating shaft (37) can only horizontally move under the action of the horizontal displacement application device (18) and cannot move up and down or rotate; the left end of the horizontal fixed shaft (38) is connected with a force transfer beam (41) of the sample box, and the right end of the horizontal fixed shaft is connected with a horizontal stress sensor (44); ensuring that the base shafts of the lower shear box force transfer beam (5), the horizontal actuating shaft (37), the horizontal fixed shaft (38), the sample box force transfer beam (41) and the horizontal stress sensor (44) are in the same horizontal line;
the horizontal stress sensor (44) is fixed on the horizontal fixing device (43) to ensure that the horizontal fixing shaft (38), the horizontal stress sensor (44) and the horizontal fixing device (43) cannot move or rotate;
the first sealing ring (15) is fixed at the intersection of the horizontal actuating shaft (37) and the constant-temperature water bath (1); the second sealing ring (16) is fixed at the intersection of the horizontal fixed shaft (38) and the constant-temperature water bath (1);
the horizontal displacement sensor (19) is fixed on the upper surface of the horizontal actuating shaft (37) to ensure that the base shaft of the horizontal displacement sensor (19) is parallel to the base shaft of the horizontal actuating shaft (37);
the lower shear box bearing platform (21) is fixed on the slideway (20), and the lower surface of the lower shear box bearing platform (21) and the upper surface of the slideway (20) are ensured to be in the same horizontal plane; the lower surface of the slideway (20) is contacted with the bottom surface of the constant-temperature water tank (1), moves left and right under the action of the horizontal displacement application device (18) and cannot move up and down or roll, and the friction between contact surfaces is rolling friction;
the pore water pressure sensor (30) is connected with the drain valve (45) and the metal hose (31) through a three-way joint;
the normal stress sensor (17) and the horizontal stress sensor (44) are respectively connected with the electric signal demodulator (13) through a first cable (22); the electric signal demodulator (13) is connected with a computer (23).
2. The system for directly measuring the shear strength of an interface at different temperatures according to claim 1, wherein the friction surfaces of the structural top plate (24) have different roughness, the roughness of the position close to the friction plate (27) is consistent with the roughness of the upper surface of the friction plate (27), and the upper surface of the structural top plate (24) far away from the friction plate (27) is smooth.
3. A test method for directly measuring interface shear strength at different temperatures is characterized by comprising the following steps:
s1, selecting different soil bodies, different materials and structures with different roughness according to requirements, and manufacturing a sample (12), a structure top plate (24) and a friction plate (27) to be replaced;
s2, adjusting the rigidity and the installation position of the spring frame (10) to ensure that the spring frame (10) is stable and vertical;
s3, adjusting the positions of the lower shearing structure-measuring device and the sample shearing box (40) to ensure that the vertical basic shafts of the lower shearing structure-measuring device and the sample shearing box (40) are on the same vertical line with the vertical basic shafts of the dowel bar (8) and the spring frame (10);
s4, connecting cables of the normal displacement sensor (9), the normal stress sensor (17), the horizontal displacement sensor (19), the horizontal stress sensor (44) and the pore water pressure sensor (30) to an electric signal demodulator (13), connecting the electric signal demodulator to a computer (23), operating a test control platform, and resetting readings of the normal displacement sensor (9), the normal stress sensor (17), the horizontal displacement sensor (19) and the horizontal stress sensor (44);
s5, closing a valve of the pore water pressure sensor (30), opening a drain valve (45), injecting water into the metal hose (31), stopping injecting water after the water overflows from the permeable stone (39), and resetting the reading of the pore water pressure sensor (30);
s6, a sample (12) is placed in a sample shearing box (40), the vertical positions of a sample loading top plate (6), a sample pressurizing cap (7), a dowel bar (8) and a normal displacement sensor (9) are adjusted, the base shafts of the sample loading top plate (6), the sample pressurizing cap (7) and the dowel bar (8) are ensured to be positioned on the same vertical line, the sample loading top plate (6) is ensured to be in contact with the sample (12), the bottom end of the normal displacement sensor (9) is ensured to be in contact with a water bath cover plate (4), and the water bath cover plate (4) is covered and fixed;
s7, applying a normal load to the sample (12) through the normal displacement sensor (9), after the normal load reaches a target value, performing heat exchange on cooling liquid in the constant-temperature water bath (1) through the heating and refrigerating circulator (3) so as to apply a temperature load to the sample, and after the sample reaches a target temperature and is stable for 12 hours, applying horizontal displacement through the horizontal displacement application device (18) to perform a direct shear test;
s8, performing interface strength shear tests at different temperatures, reading and recording test data through a computer (23), and further calculating the interface shear strength tau;
Figure FDA0002784050700000061
in the formula: τ is the shear strength of the structure-soil interface; q. q.s1Stress measured for the tension and compression sensor one (28); q. q.s2Stress measured for the second tension and compression sensor (29); a is the area of the upper surface of the friction plate (27);
the area of the upper surface of the friction plate (27) is:
A=W×L
in the formula: w is the width of the upper surface of the friction plate (27); l is the length of the upper surface of the friction plate (27);
the shear strength parameters of the structure-soil interface are expressed as:
Figure FDA0002784050700000062
in the formula: c is the cohesive force of the structure-soil interface;
Figure FDA0002784050700000063
is the rubbing angle of the structure-soil interface; sigma is the normal stress acted on the structure-soil interface by the normal stress applying device (11); mu is the pore water pressure of the structure-soil interface measured by the pore water pressure sensor (30);
the cohesive force c of the structure-soil interface is related to the ambient temperature, the roughness of the structure and the shear rate of the structure-soil, and is expressed as:
c=f(Rn,T,v,…)
friction angle of structure-soil interface
Figure FDA0002784050700000064
The temperature of the environment, the roughness of the structure and the shear rate at which the structure-soil is located are related and are expressed as:
Figure FDA0002784050700000065
the pore water pressure μ at the structure-soil interface is related to the ambient temperature, the structure roughness and the shear rate at which the structure-soil is located, and is expressed as:
μ=h(Rn,T,v,…)
s9, analyzing the test reliability through the reading of the horizontal stress sensor (44);
F=τA+f
in the formula: f is the result of the horizontal stress sensor 44 test; τ is the shear strength of the structure-soil interface; a is the area of the upper surface of the friction plate; f is the friction between the test system structures.
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