CN106525297A - Mini three dimensional effective stress box and test method of the same - Google Patents

Abstract

The invention provides a mini three dimensional effective stress box. The mini three dimensional effective stress box is characterized in that a skeleton of the stress box is in an upper-middle-lower structural form; the middle structure is an eight-prism which is formed by means of enclosure of eight squares; the upper and lower structures are formed by five squares or four equilateral triangles; the upper structure and the lower structure are symmetrical with the middle structure; an inclinometer is arranged on any surface of the inner wall of the skeleton; bearing diaphragms are respectively arranged on each surface, with round holes, of the skeleton; a foil gauge is pasted on the inner wall of the round surface which is formed after combination of the bearing diaphragms and the skeleton; and a foil gauge wire and an inclinometer wire are led out through a data wire hole by means of a data wire, and then are connected with a data acquisition instrument so as to form a mini three dimensional effective stress box. And at the same time, the invention also provides a test method of the mini three dimensional effective stress box. The mini three dimensional effective stress box and the test method of the same have the advantages of reducing the error caused by rotation of the mini three dimensional effective stress box, reducing the test error caused by unequal range finding, being able to reflect the bearing state of soil because of improvement of accuracy, improving the safety stock during the soil construction process.

Description

Miniature three-dimensional effective stress box and its method of testing

Technical field

The invention belongs to Geotechnical Engineering effective stress field tests, specially a kind of miniature three-dimensional effective stress box and its survey Method for testing, it is adaptable to the measure of Geotechnical Engineering saturation soil body effective stress.

Background technology

The too husky basic conception for proposing principle of effective stress based on nineteen twenty-three, illustrates granular material and continuous solid body material Significant difference in stress-strain relation.Therefore, principle of effective stress is so that soil mechanics is different from Solid Mechanics and forms For the important symbol of an independent educational project.

For saturated soil, soil particle hole is full of water, and the stress that outer lotus is produced in the soil body is by intergranular Contact with pore water to transmit.The stress transmitted by interparticle contact causes soil particle to produce displacement, so as to cause the soil body strong Degree and problem on deformation, it is this to act on intergranular contact stress and be referred to as effective stress.Hole in saturated soil is by continuous hole Gap water is filled, and pore water pressure obeys the hydrostatic pressure regularity of distribution, and this stress by hole Water transport is referred to as pore water pressure.

The mode of conventional determination soil strength and deformation mainly has the indoor examination with direct shear test, triaxial test as representative Test, and the on-the-spot test that plate, vane shear test are representative.Due to laboratory test exist loading border and Film imbedding problem, test accuracy has to be hoisted；On-the-spot test cannot cause pore water pressure to dissipate completely because the time limits, thus It is determined that not authentic and valid stress, and determine not Three-dimensional Effective Stress.The deep foundation of routine, seabed tunnel, cross a river are big The design and construction of the facilities such as bridge is both needed to determine the effective stress of its ground place soil layer, with reasonable definition soil deformation to structure The impact of thing.Therefore, rationally determine that the Three-dimensional Effective Stress of the saturation soil body seems most important.

The content of the invention

It is an object of the invention to provide a kind of miniature three-dimensional effective stress box and its method of testing, have effect to solve three-dimensional Force test device because deviateing the larger error problem that predetermined angle causes, overcomes pressure containing disk and measuring center in use The test error that distance etc. does not cause, and then lift the accuracy in measurement to soil body Three-dimensional Effective Stress.

The technical solution used in the present invention is to provide a kind of miniature three-dimensional effective stress box, the stress box and data collecting instrument It is connected, wherein：The stress box includes skeleton, pressure containing disk, foil gauge, high permeable stone, data conductor, band circular hole slab, poly- With thing glue, obliquity sensor.Version of the skeleton for upper, middle and lower, central structure is that eight squares enclose the eight of composition Prism form, upper and lower structure is the form being made up of five squares and four equilateral triangles, superstructure with Substructure is symmetrical with regard to central structure；Five of three square surfaces and skeleton central structure of the skeleton superstructure The center of one square surface of square surface and skeleton substructure is equipped with circular port；Obliquity sensor is arranged at bone On frame inwall arbitrary face, pressure containing disk is consistent with each surface size of skeleton；Pressure containing disk is respectively arranged into each band circle in skeleton The surface in shape hole, and the rounded face inwall for being combined rear formation with skeleton in pressure containing disk pastes foil gauge；By pressure containing disk and bone Gap between frame waterproof gasket cement fills closely knit；Choose under two square surfaces and skeleton of the skeleton central structure One square surface of portion's structure and the surface of pressure containing disk is provided with, will be pasted onto with circular hole slab by polymer latex described Three are provided with the square surface of pressure containing disk, and circular high permeable stone is arranged in the circular hole position with circular hole slab；It is logical Cross data conductor foil gauge wire and obliquity sensor wire are connected with data collecting instrument Jing after the extraction of data conductor hole, i.e., Form miniature three-dimensional effective stress box.

There is provided a kind of method of testing of miniature three-dimensional effective stress box simultaneously.

The effect of the present invention is that the device is reduced because of the device error that causes of rotation, is reduced because range finding etc. does not cause Test error, reduces the error of unidirectional pore water pressure test based on the pore water pressure average computation method of orthogonal direction. In the case where there is no angle rotational case, if the measuring accuracy of single group foil gauge is θ, the average test precision of effective stress is 2.25θ.The stress of the more actual response soil body is capable of in the raising of precision, lifts the safety stock in soil body work progress.

Description of the drawings

Fig. 1 is the miniature three-dimensional effective stress box design sketch of the present invention；

Fig. 2 is skeleton design sketch according to the present invention；

Fig. 3 is a kind of rectangular coordinate system in space that the miniature three-dimensional effective stress box of the present invention is set up；

Fig. 4 is the miniature three-dimensional effective stress box assembling schematic diagram of the present invention；

Fig. 5 is layout drawing of the foil gauge according to the present invention on pressure containing disk；

Fig. 6 to Fig. 9 is carcasing flow chart according to the present invention.

In figure：

1. 2. pressure containing disk of skeleton, 3. foil gauge, 4. high permeable stone

5. data conductor 6. is with 7. data conductor hole of circular hole slab, 8. poly- and thing glue

9. 10. rounded face of circular port, 11. lead point, 12. obliquity sensor

13. waterproof gasket cements

Specific embodiment

Miniature three-dimensional effective stress box of the invention and its method of testing are illustrated with reference to accompanying drawing.

The miniature three-dimensional effective stress box of the present invention and its method of testing design principle：Electricity is converted into based on mechanical strain amount The method of amount, as member stress deforms, the foil gauge sensitive grid for being arranged in component surface also deforms therewith, causes its resistance value Change.The change of this resistance value is proportional to component surface strain, between the stress and strain according to foil gauge placement-face Relation, you can the anti-size for releasing the power for putting on placement-face.Matrix relationship between conventional stress state and principal stress, with And the mathematical relationship in principle of effective stress between total stress and effective stress is the enforcement of Three-dimensional Effective Stress box and provides May.

The Three-dimensional Effective Stress box structure of the present invention is that the stress box is connected with data collecting instrument, and the stress box includes Skeleton 1, pressure containing disk 2, foil gauge 3, high permeable stone 4, data conductor 5, band circular hole slab 6, poly- and thing glue 8, obliquity sensor 12. Version of the skeleton 1 for upper, middle and lower, central structure are the eight prism forms that eight squares enclose composition, and top is with Portion's structure is the form being made up of five squares and four equilateral triangles, and superstructure is with substructure with regard to middle part knot Structure is symmetrical.Five square surfaces of 1 central structure of three square surfaces and skeleton of 1 superstructure of the skeleton and skeleton The center of one square surface of 1 substructure is equipped with circular port 9.Inclination angle sensing is provided with 1 inwall arbitrary face of skeleton Device 12, pressure containing disk 2 is respectively arranged in each surface with circular port 9 of skeleton 1, and after pressure containing disk 2 is combined with skeleton 1 10 inwall of rounded face of formation pastes foil gauge 3, and the gap filling between pressure containing disk 2 and skeleton 1 has waterproof gasket cement 13.Choosing Take a square surface of 1 substructure of two square surfaces and skeleton of 1 central structure of the skeleton and be provided with and hold The surface of pressuring film plate 2, will be pasted onto described three with circular hole slab 6 by polymer latex 8 and is provided with the surface of pressure containing disk 2, And circular high permeable stone 4 is arranged on into the circular hole position with circular hole slab 6,3 wire of foil gauge and inclination angle are passed by data conductor 5 12 wire Jing data conductors hole 7 of sensor is drawn and is connected with data collecting instrument, that is, form miniature three-dimensional effective stress box.It is described Rigidity of the rigidity of pressure containing disk 2 less than 1 each face of skeleton, and the size of pressure containing disk 2 is consistent with 1 each surface size of skeleton； The consistency of thickness of the thickness with circular hole slab 6 and high permeable stone 4.

The miniature three-dimensional effective stress box method of testing step of the present invention is as follows：

First, skeleton 1 makes and obliquity sensor 12 is arranged.The square that each rib length as shown in Figure 6 is a is chosen, In square OABC-DEFG, point M, N, P, Q are located on rib ED, FG, EA, FB respectively, andEntity is simultaneously split by connection MN, MP, PQ, NQ along face MNPQ, referred to as square Two adjacently situated surfaces guide face of body, as shown in Figure 7；Respectively by square any two adjacently situated surfaces guide face, as shown in Figure 8, Figure 9.In Fig. 3 Shown A₁、A₂、A₃、A₄、A₅、A₆、u₁、u₂、u₃The circular port 9 that radius is r is opened in face respectively, and data conductor hole 7 is opened in and A₁And u₃ On adjacent surface；Obliquity sensor 12 is arranged in and u₂And u₃On the inwall of adjacent surface；The skeleton 1 of this fermentation is formed, is such as schemed Shown in 2.

Second, make pressure containing disk 2.Pressure containing disk 2 is the length of sideSquare.

3rd, paste foil gauge 3.The above-mentioned pressure containing disk 2 made is taken, and radius is drawn with foursquare center as the center of circle is The circle of r, that is, form rounded face 10, as shown in Figure 5；Foil gauge 3, wherein foil gauge 3 is pasted in rounded face 10 according to four wall full-bridge methods Center 0.577r of the position of form center away from pressure containing disk 2, and draw 4 single data wires 5 from lead point 11 respectively.

4th, assemble the miniature three-dimensional effective stress box of the present invention.The data of the pressure containing disk 2 of foil gauge 3 will be pasted with The circular port 9 of 5 Jing skeletons 1 of wire is simultaneously passed from data conductor hole 7, and foil gauge 3 is located facing to 1 side of skeleton, as shown in Figure 4. Operate A more than repeating₁、A₂、A₃、A₄、A₅、A₆、u₁、u₂、u₃The pressure containing disk 2 in face is installed；Then by pressure containing disk 2 and bone Gap between frame 1 and the gap waterproof gasket cement 13 between data conductor hole 7 and data conductor 5 fill closely knit；With poly- Compound glue 8 will be pasted onto u with circular hole slab 6₁、u₂、u₃2 top of pressure containing disk in face, and circular high permeable stone 4 is arranged in into band circle The circular hole position of orifice plate 6, as shown in Figure 4；The miniature three-dimensional effective stress box of the present invention is formed, as shown in Figure 1.

5th, the miniature three-dimensional effective stress box of the present invention is demarcated.Relation between nominal pressure and strain is obtained, And demarcate relation between hydraulic pressure and strain；Determine the angle initial error of obliquity sensor.

6th, Three-dimensional Effective Stress box it is embedded.The space coordinates direction of the saturation soil body is defined, and by Fig. 3 institutes The coordinate direction of the parallel soil body of coordinate direction of the miniature three-dimensional effective stress box for showing is buried.

7th, data acquisition.Reading equipment is surveyed by ess-strain and obtains miniature three-dimensional effective stress box skeleton superstructure Three square surfaces and three square surfaces of skeleton central structure can obtain 6 stress readings, i.e. σ₁、σ₂、σ₃、 σ₄、σ₅、σ₆；Can obtain according to two square surfaces of skeleton central structure and a square surface of skeleton substructure Take 3 pore water pressure readings, i.e. u₁、u₂、u₃；Miniature three-dimensional effective stress box can be obtained by obliquity sensor receiving device 3 tilt readings, i.e. α, β, γ.

8th, three-dimensional stress constraint is calculated.The 6 stress readings obtained according to step the seven and 3 tilt readings, according to public affairs Formula (1) calculates the inside soil body conventional stress state of a bit, and formula (1) is

{σ_ij}=A^-1{σ_i} (1)

In formula (1), { σ_ij}={ σ_x, σ_y, σ_z, σ_xy, σ_yz, σ_zx}^T, wherein σ_x、σ_y、σ_z、σ_xy、σ_yz、σ_zxFor conventional stress shape 3 direct stress components and 3 shear stress components of state；{σ_i}={ σ₁, σ₂, σ₃, σ₄, σ₅, σ₆}^T, wherein σ₁、σ₂、σ₃、σ₄、σ₅、σ₆ For three square tables of three square surfaces and skeleton central structure of miniature three-dimensional effective stress box skeleton superstructure 6 stress readings that face obtains；A^-1For the inverse matrix of matrix A, A^-1Can be calculated by linear algebra theory according to matrix A, square Battle array A is shown in formula (2)

In formula (2), α, β, γ are the angle of the miniature three-dimensional effective stress box rotation that obliquity sensor is obtained, and M, N, P are shown in Formula (3)

In formula (3), α, β, γ are the miniature three-dimensional effective stress box rotation that obliquity sensor is obtained described in step the seven Angle.

9th, pore water pressure is calculated.According to 3 pore water pressure readings that step the seven is obtained, calculate according to formula (4) Go out the inside soil body pore water pressure of a bit, formula (4) is

In formula (4), u is the pore water pressure of a bit；u₁、u₂、u₃The miniature three-dimensional effective stress box bone described in step the seven 3 pore water pressures that one square surface of two square surfaces of frame central structure and skeleton substructure is obtained are read Number.

Tenth, effective stress is calculated.The Three-dimensional Effective Stress of test point is calculated according to formula (5)

In formula (5), σ '_x、σ'_y、σ'_z、σ'_xy、σ'_yz、σ'_zx3 direct stress components for Three-dimensional Effective Stress state and 3 Shear stress component；σ_x、σ_y、σ_z、σ_xy、σ_yz、σ_zxExpression (1) calculates 3 direct stress of the test point routine stress state for obtaining Component and 3 shear stress components；U is that formula (4) calculates the pore water pressure for obtaining.

The strain system-computed of the miniature three-dimensional effective stress box derives as follows：

Based on the circular slab that the radius under elastic theory, Uniform Load is r, on plate, each point stress state can be according to meter Obtain.Be computed, hoop strain piece is pasted in the range of x=0.577r, can effectively measure the strain of evenly load, Ji Jiangtu Foil gauge shown in 5 is centrally disposed at the center of circle 0.577r of rounded face.

The formula proving of miniature three-dimensional effective stress box is as follows：

This device is the miniature three-dimensional effective stress box for being converted to electric quantity test method by mechanical strain amount, as shown in Figure 1. Based on principle of effective stress, the total stress of the saturation soil body is by effective stress and pore water pressure shared.According to six direction Separate principal stress can calculate the conventional stress state of a bit, according to the pore water pressure of three coordinate directions, after weighting The pore water pressure force value of any can be obtained；Conventional stress state is the effective stress shape of any with the difference of pore water pressure force value State.

According to elastic-plastic mechanics theory, the conventional stress state of 1 point of P (x, y, z) of media interior can the used point it is small The components of stress on cube are representing.Assume that the conventional stress state of any is by σ in space_x、σ_y、σ_z、σ_xy、σ_yz、σ_zxSix The components of stress represent, then the direct stress σ of any direction_k

Wherein, k=1,2,3,4,5,6；L, m, n represent direct stress and x, y, z axle clamp cosine of an angle value respectively.By formula (6) It is expressed in matrix as

The direct stress in inside soil body 6 directions of a bit, i.e. σ can be calculated according to formula (7)₁、σ₂、σ₃、σ₄、σ₅、σ₆；If this six The direct stress in individual direction is known and ensures that inverse of a matrix is present, then tangent stress σ_x、σ_y、σ_z、σ_xy、σ_yz、σ_zxCan be according to Matrix inversion operation is obtained.

Formula (7) can be sketched and be

{σ_i}=A { σ_ij} (8)

In formula (8), { σ_i}={ σ₁, σ₂, σ₃, σ₄, σ₅, σ₆}^T, wherein σ₁、σ₂、σ₃、σ₄、σ₅、σ₆6 directions are represented respectively Direct stress；{σ_ij}={ σ_x, σ_y, σ_z, σ_xy, σ_yz, σ_zx}^T, wherein σ_x、σ_y、σ_z、σ_xy、σ_yz、σ_zxFor 3 of conventional stress state just The components of stress and 3 shear stress components；Matrix A is

Due to the granular characteristic of the soil body, during load-bearing, its internal microstructure rearranges meeting to the saturation soil body in addition Change the position of embedded device.Thus, in the skeletal internal arrangement obliquity sensor of this device, to obtain Three-dimensional Effective Stress box The relative angle for rotating in use.The anglec of rotation of this device around x, y, z direction is represented respectively with α, β, γ, then because of dress The direction cosines change that the angle rotation put causes is shown in Table 1.

The direction cosines change that the rotation of 1 angle of table causes

Note：In table 1, M, N, P value is shown in formula (3)

With reference to formula (9) and table 1, matrix A is

A^-1Can be obtained by linear algebra theoretical calculation according to matrix A, more then conventional stress state is

{σ_j}=A^-1{σ} (11)

In formula (11), { σ_ij}={ σ_x, σ_y, σ_z, σ_xy, σ_yz, σ_zx}^T, wherein σ_x、σ_y、σ_z、σ_xy、σ_yz、σ_zxFor conventional stress shape 3 direct stress components and 3 shear stress components of state；{σ_i}={ σ₁, σ₂, σ₃, σ₄, σ₅, σ₆}^T, wherein σ₁、σ₂、σ₃、σ₄、σ₅、σ₆ For three square tables of three square surfaces and skeleton central structure of miniature three-dimensional effective stress box skeleton superstructure 6 stress readings that face obtains；A^-1For the inverse matrix of matrix A, A^-1Can be calculated by linear algebra theory according to matrix A, square Battle array A is shown in formula (10).

As relative angle α, β, γ that the miniature three-dimensional effective stress box that obliquity sensor is obtained rotates in use When being 0, the conventional stress state of any can be calculated according to formula (12)

In formula (12), { σ_ij}={ σ_x, σ_y, σ_z, σ_xy, σ_yz, σ_zx}^T, wherein σ_x、σ_y、σ_z、σ_xy、σ_yz、σ_zxFor conventional stress shape 3 direct stress components and 3 shear stress components of state；{σ_i}={ σ₁, σ₂, σ₃, σ₄, σ₅, σ₆}^T, wherein σ₁、σ₂、σ₃、σ₄、σ₅、σ₆ For three square tables of three square surfaces and skeleton central structure of miniature three-dimensional effective stress box skeleton superstructure 6 stress readings that face obtains.

The effect of the present invention is that the device is reduced because of the device error that causes of rotation, is reduced because range finding etc. does not cause Test error, reduces the error of unidirectional pore water pressure test based on the pore water pressure average computation method of orthogonal direction. In the case where there is no angle rotational case, if the measuring accuracy of single group foil gauge is θ, the average test precision of effective stress is 2.25θ.The stress of the more actual response soil body is capable of in the raising of precision, lifts the safety stock in soil body work progress

The foregoing is only and illustrate with reference to this manufacturing process, be not intended to limit this structure, for the technology of this area For personnel, the present invention can have various change and change, such as substituted foil gauge, changed foil gauge mounting surface etc. with firm string. All any modification, equivalent substitution and improvements within the spirit and principles in the present invention, made etc., should be included in the present invention's Within protection domain.

Claims (2)

1. a kind of miniature three-dimensional effective stress box, the stress box are connected with data collecting instrument, be it is characterized in that：The miniature three-dimensional has Efficacy box is included：Skeleton (1), pressure containing disk (2), foil gauge (3), high permeable stone (4), data conductor (5), band circular hole slab (6), gather and thing glue (8), obliquity sensor (12)；Described skeleton (1) for upper, middle and lower version, central structure be eight just The square eight prism forms for enclosing composition, upper and lower structure are respectively and are made up of with four equilateral triangles five squares Form, superstructure is corresponding to substructure and central structure symmetrical；The square table of three of skeleton (1) superstructure The center of one square surface of five square surfaces and skeleton (1) substructure of face and skeleton (1) central structure is equal It is provided with circular port (9)；Be provided with obliquity sensor (12) on skeleton (1) inwall arbitrary face, by pressure containing disk (2) be respectively arranged in Each surface with circular port (9) of skeleton (1), and in the rounded face (10) that pressure containing disk (2) combines rear formation with skeleton (1) Wall pastes foil gauge (3), and the gap filling between pressure containing disk (2) and skeleton (1) has waterproof gasket cement (13)；

Choose two square surfaces of the skeleton (1) central structure and a square surface of skeleton (1) substructure And the surface of pressure containing disk (2) is provided with, described three will be pasted onto with circular hole slab (6) by polymer latex (8) and be provided with and be held On the surface of pressuring film plate (2), and circular high permeable stone (4) are arranged on into the circular hole position with circular hole slab (6), by data conductor (5) foil gauge (3) wire and obliquity sensor (12) wire Jing data conductors hole (7) are drawn and is connected with data collecting instrument Connect, form miniature three-dimensional effective stress box；

Rigidity of the rigidity of pressure containing disk (2) less than each face of skeleton (1), and the size of pressure containing disk (2) is each with skeleton (1) Surface size is consistent；The consistency of thickness of the thickness with circular hole slab (6) and high permeable stone (4).

2., using the method for testing of miniature three-dimensional effective stress box described in claim 1, the method is comprised the following steps：

1) the miniature three-dimensional effective stress box is imbedded into saturation inside soil body, according to miniature three-dimensional effective stress box skeleton top Three square surfaces of three square surfaces and skeleton central structure of structure can obtain 6 stress readings, i.e. σ₁、σ₂、 σ₃、σ₄、σ₅、σ₆；One square surface of two square surfaces and skeleton substructure according to skeleton central structure can Obtain 3 pore water pressure readings, i.e. u₁、u₂、u₃；3 inclination angles of miniature three-dimensional effective stress box are obtained according to obliquity sensor Reading, i.e. α, β,；

2) according to step 1) 6 stress readings obtaining and 3 tilt readings, inside soil body any normal is calculated according to formula (1) Stress state is advised, formula (1) is

{σ_ij}=A^-1{σ_i} (1)

In formula (1), { σ_ij}={ σ_x, σ_y, σ_z, σ_xy, σ_yz, σ_zx}^T, wherein σ_x、σ_y、σ_z、σ_xy、σ_yz、σ_zxFor the 3 of conventional stress state Individual direct stress component and 3 shear stress components；{σ_i}={ σ₁, σ₂, σ₃, σ₄, σ₅, σ₆}^T, wherein σ₁、σ₂、σ₃、σ₄、σ₅、σ₆For miniature Three square surfaces of three square surfaces and skeleton central structure of Three-dimensional Effective Stress box skeleton superstructure are obtained 6 stress readings；A^-1For the inverse matrix of matrix A, A^-1Can be calculated by linear algebra theory according to matrix A, matrix A is shown in Formula (2)

$A=\left\{\begin{array}{cccccc}1& {\sin }^2\mathrm{\β}& {\sin }^2\mathrm{\γ}& -2\sin \mathrm{\β}& 2\sin \mathrm{\β}\sin \mathrm{\γ}& -2\sin \mathrm{\γ}\\ {\sin }^2\mathrm{\α}& 1& {\sin }^2\mathrm{\γ}& -2\sin \mathrm{\α}& -2\sin \mathrm{\γ}& 2\sin \mathrm{\α}\sin \mathrm{\γ}\\ {\sin }^2\mathrm{\α}& {\sin }^2\mathrm{\β}& 1& 2\sin \mathrm{\α}\sin \mathrm{\β}& -2\sin \mathrm{\β}& -2\sin \mathrm{\α}\\ M^2& N^2& {\sin }^2\mathrm{\γ}& 2MN& -2N\sin \mathrm{\γ}& -2M\sin \mathrm{\γ}\\ {\sin }^2\mathrm{\α}& N^2& P^2& -2N\sin \mathrm{\α}& 2NP& -2P\sin \mathrm{\α}\\ M^2& {\sin }^2\mathrm{\β}& P^2& -2M\sin \mathrm{\β}& -2P\sin \mathrm{\β}& 2MP\end{array}\right\}---\left(2\right)$

In formula (2), α, β, γ are the angle of the miniature three-dimensional effective stress box rotation that obliquity sensor is obtained；M, N, P are shown in formula (3)

$\left\{\begin{array}{c}M=\frac{\sqrt{2}}{2}(\frac{1+cos\mathrm{\α}}{2}-\frac{\sqrt{6+2cos\mathrm{\α}}}{2}\×sin\frac{\mathrm{\α}}{2})\\ N=\frac{\sqrt{2}}{2}(\frac{1+\cos \mathrm{\β}}{2}-\frac{\sqrt{6+2cos\mathrm{\β}}}{2}\×\sin \frac{\mathrm{\β}}{2})\\ P=\frac{\sqrt{2}}{2}(\frac{1+\cos \mathrm{\γ}}{2}-\frac{\sqrt{6+2\cos \mathrm{\γ}}}{2}\×\sin \frac{\mathrm{\γ}}{2})\end{array}\right.---\left(3\right)$

In formula (3), α, β, γ be step 1) described in obliquity sensor obtain miniature three-dimensional effective stress box rotation angle；

3) according to step 1) 3 pore water pressure readings obtaining, the inside soil body pore water pressure of any is calculated according to formula (4) Power, formula (4) is

$u=\frac{1}{3}(u_1+u_2+u_3)---\left(4\right)$

In formula (4), u is the pore water pressure of a bit；u₁、u₂、u₃For step 1) in the middle part of the miniature three-dimensional effective stress box skeleton 3 pore water pressure readings that one square surface of two square surfaces of structure and skeleton substructure is obtained；

4) Three-dimensional Effective Stress of test point is calculated according to formula (5)

$\left\{\begin{array}{c}{\mathrm{\σ}}_x^{\′}\\ {\mathrm{\σ}}_y^{\′}\\ {\mathrm{\σ}}_z^{\′}\\ {\mathrm{\σ}}_{xy}^{\′}\\ {\mathrm{\σ}}_{yz}^{\′}\\ {\mathrm{\σ}}_{zx}^{\′}\end{array}\right\}=\left\{\begin{array}{c}{\mathrm{\σ}}_x\\ {\mathrm{\σ}}_y\\ {\mathrm{\σ}}_z\\ {\mathrm{\σ}}_{xy}\\ {\mathrm{\σ}}_{yz}\\ {\mathrm{\σ}}_{zx}\end{array}\right\}-\left\{\begin{array}{c}u\\ u\\ u\\ u\\ u\\ u\end{array}\right\}---\left(5\right)$

In formula (5), σ '_x、σ'_y、σ'_z、σ'_xy、σ'_yz、σ'_zx3 direct stress components for Three-dimensional Effective Stress state and 3 cut should Force component；σ_x、σ_y、σ_z、σ_xy、σ_yz、σ_zxExpression (1) calculates 3 direct stress components of the test point routine stress state for obtaining With 3 shear stress components；U is that formula (4) calculates the pore water pressure for obtaining.