RU2592038C2 - Khrustalev method of determining mechanical parameters of material medium in mass - Google Patents

Abstract

FIELD: physics.

SUBSTANCE: invention relates to "Physics of material contact interaction" of ponderable medium in its mass and at edges of slopes in natural and disturbed state. At depth h in ponderable material mass, determining on collected samples of medium in laboratory conditions parameters angle φ_str internal friction, c_str - specific adhesion and γ_str - specific weight of medium. Calculating based on relationships

$${\gamma }_h=\frac{p_{b}tg{\phi }_h+c_h}{h}$$

- respectively parameters for internal friction, specific adhesion and specific weight of medium at depth of testing in structurally disturbed state, where p_b=(γ_strh-c_str)ctgφ_str - natural pressure at depth h. Determining value of tangential natural pressure at depth h as p_x=p_y=γ_strh or p_x=p_y=γ_h(h). Determining parameters of coefficient of total lateral pressure of medium at rest $${\zeta }_0^{str}=tg{\phi }_{str},$$

at failure of natural structure of mass $${\zeta }_0^h=tg{\phi }_h,$$

in walls of open basin

and in walls of an open basin with a deformed structure

Coefficients of total relative transverse deformation of medium in mass are respectively defined by relationship

and side walls of open basin,

where p_atm=1.033 kg/cm² - normal atmospheric pressure on material medium $${\gamma }_h=\frac{p_{b}tg{\phi }_h+c_h}{h}$$

- specific weight of medium with a deformed structure.

EFFECT: increased reliability and accuracy of determining physical parameters of soils.

1 cl, 2 dwg

Description

The invention relates to the field of “Physics of material contact interaction”, and specifically to a method for determining the mechanical parameters of a coherent material medium — its total lateral pressure coefficient ζ ₀ and its total relative transverse deformation ν ₀ (similar to the Poisson's ratio for an elastic medium).

A known method for determining the coefficient of total lateral pressure ζ _{0 of the} material array, which consists in the fact that at a given depth h of the array determine the value of the vertical gravitational (household) pressure p _b = p _z of the own weight of the overlying layers of the medium and the value of the lateral horizontal pressure p _x = p _y, for example, using crushing flat pressure sensors - force cell, common side medium pressure ratio is determined through the expression of ζ _{0 = p x / p z = p} y / p z and gaining statistical significance of the data oeffitsienta ζ ₀ for different types of material of the medium, and the coefficient of the total relative transverse deformation of the material of the medium is determined from the dependence of ν ₀ = ε _x / ε _z = ε _y / ε _z = ζ ₀ / (1 + ζ _0), where ε _x = ε _y and ε _z are the relative deformations of the medium at the point of the array in the horizontal and vertical directions [1, 2].

Testing the material environment in the array with the help of pressure sensors for pressure measurement - vertical and horizontal pressure doses is a laborious operation that does not allow reliable data on the pressures at the point of the material array in the vertical and horizontal directions due to disturbances in the natural state of the array when the pressure sensors are crushed and when drilling, if necessary, the tested well.

The statistical data for the calculation of the coefficients ζ ₀ and ν ₀ are very remote from the real ones and have a wide spread for one kind of medium.

для песчаных грунтовых сред с удельным сцеплением с_стр≈0 и по зависимости Г.А. Спальвинга для связных глинистых грунтовых сред - ζ₀=[1+2(tgφ_стр+с_стр/р_б)]^-1, где р_б - гравитационное (бытовое) давление, при этом коэффициент общего бокового давления среды определяют как отношение горизонтального к вертикальному давлению ζ₀=p_x/p_z=p_y/p_z на заданной глубине h материального массива, а значение коэффициента общей относительной поперечной деформации материальной среды определяют по зависимости ν₀=ε_x/ε_z=ε_y/ε_z=ζ₀/(1+ζ₀), где ε_x=ε_y и ε_z - относительные деформации среды в точке массива в горизонтальном и вертикальном направлении [3].A known method for determining the mechanical parameters of the material medium in the array at a given depth h, which consists in the fact that according to the results of preliminary studies at an depth h of the medium array of the undisturbed structure, the angle parameter φ _{p of} its internal friction and specific adhesion with _p are obtained, characterized in that the coefficient value total lateral pressure is determined by the dependence of Y. Yaki $${\zeta }_0=\frac{\mathrm{one}-\sin {\phi }_{ctp}}{\mathrm{one}+\sin {\phi }_{ctp}}(\mathrm{one}+\frac{2}{3}\sin {\phi }_{ctp})$$

for sandy soil environments with specific adhesion with _p ≈ 0 and according to G.A. Spalving for cohesive clayey soil is ζ ₀ = [1 + 2 (tgφ _p + s _p / p _b )] ^-1 , where p _b is gravitational (household) pressure, and the coefficient of the total lateral pressure of the medium is determined as the ratio of horizontal to vertical pressure ζ ₀ = p _x / p _z = p _y / p _z at a given depth h of the material array, and the value of the coefficient of the total relative transverse deformation of the material medium is determined by the dependence ν ₀ = ε _x / ε _z = ε _y / ε _z = ζ ₀ / (1 + ζ ₀ ), where ε _x = ε _y and ε _z are the relative deformations of the medium at the array point in the horizontal and vertical directions and [3].

The disadvantage of this method of determining the coefficient ζ ₀ is the limited use of the dependencies J. Yaki and G.L. Spalving, respectively, only for clean sands and clayey soil. These dependencies do not take into account the true value of gravitational (everyday) pressure in the mass of the material medium, which should be obtained first on the basis of additional thorough experiments.

при p_z=р_б+c_cтpctφ_стр, где гравитационное бытовое давление р_б=(γ_cтph-с_стр)ctgφ_стр, а для массива материальной среды с нарушенной структурой от динамического или статического воздействия определяют удельный вес среды нарушенной структуры $${\gamma }_{н}=\frac{p_{б}tg{\phi }_{н}+c_{н}}{h}$$

, боковое давление р_х=p_y=γ_нh, коэффициент общего бокового давления определяют по зависимости $${\zeta }_0^{н}=tg{\phi }_{н}$$

, где φ_н=arcsin[2sinφ_стр/(1+sin²φ_стр)]-φ_стр, с_н=с_стр[2-tgφ_н/tgφ_стр] - соответственно угол внутреннего трения и удельное сцепление среды с нарушенной структурой при вертикальном давлении p_z=р_б+с_нctgφ_н; при этом замеряют атмосферное давление р_атм или его принимают нормальным по величине р_атм=1,033 кГ/см² и в стенках открытой вертикальной выработки в массиве структурированной среды коэффициент общего бокового давления определяют по зависимости

, а в стенках открытой вертикальной выработки в массиве среды с нарушенной структурой коэффициент общего бокового давления определяют по зависимости

, при этом определяют удельный вес структурированной среды γ_стр, а коэффициент общей относительной поперечной деформации структурированной среды в массиве рассчитывают по зависимости

, коэффициент общей относительной поперечной деформации материальной среды с нарушенной структурой рассчитывают по зависимости

, на открытой боковой поверхности выработки в массиве структурированной среды определяют ее удельный вес γ_стр и рассчитывают коэффициент ее общей относительной поперечной деформации по зависимости

, а в стенках открытой вертикальной выработки в массиве с нарушенной структурой определяют коэффициент общей относительной поперечной деформации по зависимости

.From the provisions of the “Physics of Material Contact Interaction” it is known that any material medium is characterized through the physical parameters of its angle “φ” of internal friction and specific adhesion “c” both in a structured and broken state, then the technical result is by the method of determining the mechanical parameters of the material of the medium in the array, which consists in preliminarily determining at a given depth h of the array the physical parameters of the strength of the medium of the undisturbed structure — the angle φ _{p of} internal friction and specific adhesion - with _p , the coefficient of the total lateral pressure of the medium is determined by the dependence ζ ₀ = p _x / p _z = p _y / p _z , where p _x = p _y is the lateral horizontal pressure and p _z is the vertical pressure at depth h, the coefficient of relative transverse deformation of the medium is determined by the dependence ν ₀ = ε _x / ε _z = ε _y / ε _z = ζ ₀ / (1 + ζ ₀ ), where ε _x = ε _y and ε _z is the relative deformation of the medium at the point of the array in horizontal and vertical direction is achieved in that at a predetermined depth h of material of the array define the proportion γ _p and structured medium calcd yvayut value her side as a horizontal gravitational pressure p _x = p _y = γ _pg h, the total lateral structured medium pressure coefficient is determined depending on $${\zeta }_0^{ctp}=tg{\phi }_{ctp}$$

when p _z = p _b + c _{pg p} ctφ where gravitational domestic pressure p _b = (γ _pg with _h-p) ctgφ _page, and the array material medium with broken structure of a dynamic or static exposure determined proportion of the disturbance structure $${\gamma }_n=\frac{p_{b}tg{\phi }_n+c_n}{h}$$

, lateral pressure p _x = p _y = γ _n h, the coefficient of total lateral pressure is determined by the dependence $${\zeta }_0^n=tg{\phi }_n$$

, where φ _n = arcsin [2sinφ _p / (1 + sin ² φ _p )] - φ _p , s _n = s _p [2-tgφ _n / tgφ _p ] - respectively, the angle of internal friction and the specific adhesion of the medium with the broken structure at vertical pressure p _z = p _b + s _n ctgφ _n ; in this case, atmospheric pressure p _atm is measured or it is assumed to be normal in value p _atm = 1.033 kg / cm ² and in the walls of an open vertical working out in an array of structured medium, the coefficient of total lateral pressure is determined by the dependence

, and in the walls of open vertical excavation in an array of medium with a disturbed structure, the coefficient of total lateral pressure is determined by the dependence

, while determining the specific gravity of the structured medium γ _p , and the coefficient of the total relative transverse deformation of the structured medium in the array is calculated according to

, the coefficient of the total relative transverse deformation of a material environment with a broken structure is calculated according to

, on the open side surface of the mine in the array of structured medium, determine its specific gravity γ _p and calculate the coefficient of its total relative transverse deformation according to

, and in the walls of the open vertical excavation in an array with a disturbed structure, the coefficient of the total relative transverse deformation is determined by the dependence

.

The invention is illustrated by graphic materials, where in FIG. 1 is a graph p = ƒ (τ) of the limiting state of a cohesive elastoplastic material medium, in FIG. 2 is a graph of p = ƒ (τ) of the limiting state of a connected elastically elastic medium with pronounced compressibility anisotropy.

Considering the graph p = ƒ (τ) of the limiting state of S. Coulomb a cohesive elastoplastic material medium (Fig. 1) in a natural (natural) stress-strain state, we determine the vertical gravitational (household) pressure at a point at a depth h of the medium array as p _b = (γ _pg with _h-p) ctgφ _p and the pressure p _in the connected medium = -c _pg ctgφ _page which counteracts stretching of the medium-edged point.

.Thus, natural vertical pressure at a point at a depth h is equal to p _z = p _a p _b = γ _pg h · ctgφ _p. The tangential natural pressure at a point at a depth of h is τ _b = p _x = p _y = γ _ctp h, then the coefficient of the total lateral pressure of the elastoplastic medium is defined as

.

Based on the dependence ν ₀ = ζ ₀ / (1 + ζ ₀ ) we find that the coefficient of the total relative transverse deformation of the material medium in the array is ν = tgφ _p / (1 + tgφ _p ).

Considering the graph (Fig. 2) p = ƒ (τ) of the limiting state of a connected elastically elastic material medium, for example, an undried peat deposit with a high degree of anisotropy A _Е = Е _в / Е _г = 0.4 compressibility in the vertical and horizontal direction, we determine the vertical natural gravitational (household) pressure at a depth h like p _b = R = c _ctp cosφ _p / (1-sinφ _p ) with the corresponding tangential stress at a point at the same depth τ = p _x = p _y = p _b tgφ _p + s _page

Connected _to the pressure medium p = -c _pg ctgφ _page, then the natural vertical pressure at a point at a depth h is equal to p p _z = _b = c cosφ _{pg p} / (1-sinφ _p) + c _pg ctgφ _p = c _{p pg} ctgφ / (1-sinφ _pg .). The coefficient of the total lateral pressure of an elastic medium is defined as

and the coefficient ν ₀ = ζ ₀ / (1 + ζ ₀ ) = tgφ _p / (1 + tgφ _p ).

, а коэффициент общей относительной поперечной деформации суглинка определяем по зависимости

. Статистические справочные данные имеют значения ζ₀=0,11…0,82, ν₀=0,30…0,40 для текучепластичных суглинков [1]. На глубине h₃=с_стр/γ_стр=0,20/0,002=100 см при бытовом давлении р_б=(γ_cтph₃-с_стр)ctgφ_стр=(0,002·100-0.2)ctg23°=0, значение ζ₀₃=tg23°=0,4245, ν₀₃=tg23°/(1+tg23°)≈0,3.Example 1 of the implementation of the method. 1) In the process of drilling a well in a soil material massif, consisting of loam, soil samples were taken from depths h ₁ = 90 cm and h ₂ = 280 cm, laboratory analysis of which made it possible to establish the angle of their internal friction φ _str1 = φ _str2 = 23 ° and specific adhesion with _str1 = with _str2 = 0.2 kg / cm ² with a specific gravity of γ _str1 = γ _str2 = 0.002 kg / cm ³ . The magnitude of the gravitational (domestic) pressure at the depth of 90 cm and 280 cm is set to p _b1 = (γ _pg h ₁ -c _p) ctgφ _p = (0,002 · 90-0,2) ctg23 ° = -0,0471 kg / cm ² , p _b2 = (γ _ctp h ₂ -s _pg ) ctgφ _pg = (0.002 · 280-0.2) ctg23 ° = -0.8481 kg / cm ² . The coefficient of total household pressure is calculated according to

, and the coefficient of the total relative transverse deformation of loam is determined by the dependence

. Statistical reference data have values ζ ₀ = 0.11 ... 0.82, ν ₀ = 0.30 ... 0.40 for fluid-plastic loam [1]. At a depth h ₃ = c _p / γ _p = 0.20 / 0.002 = 100 cm at the household pressure p _b = (γ _pg h ₃ -c _p) ctgφ _p = (0,002 · 100-0.2) ctg23 ° = 0, the value ζ ₀₃ = tg23 ° = 0.4245, ν ₀₃ = tg23 ° / (1 + tg23 °) ≈ 0.3.

теоретическое значение ν₀₁=ζ₀₁/(1+ζ₀₁)=0,4245/(1+0,4245)=0,3, что соответствует результатам расчетов.We will verify the results. At $${\zeta }_{01}^{ctp}={\zeta }_{02}^{ctp}=0.4245$$

theoretical value ν ₀₁ = ζ ₀₁ / (1 + ζ ₀₁ ) = 0.4245 / (1 + 0.4245) = 0.3, which corresponds to the calculation results.

. Коэффициент общего бокового давления становится равным $${\zeta }_{01}^{н}=tg{\phi }_{н}=tg\mathrm{19,6843}°=\mathrm{0,3577}$$

, а коэффициент общей относительной поперечной деформации среды $${\nu }_{01}^{н}=tg{\phi }_{н}/(1+tg{\phi }_{н})=tg\mathrm{19,6843}°/(1+tg\mathrm{19,6843}°)=\mathrm{0,2561}$$

.2) During an earthquake, the natural structure of loam at a depth of h ₁ = 90 cm is violated to the value of the indicators: φ _н = arsin [2sinφ _p / (1 + sin ² φ _p )] - φ _p = arcsin [2sin23 ° / (1 + sin ² 23 °)] - 23 ° = 42.6843 ° -23 ° = 19.6843 ° and with _n = c _{p [n-tgφ} 2 / tgφ _p] = 0.2 [2-tg19,6843 ° / tg23 °] = 0.2314 kg / cm ² , $${\gamma }_n=\frac{p_{b}tg{\phi }_n+{\mathrm{from}}_n}{h}=\frac{-0.0471\cdot tg19.6843°+0.2314}{90}=\mathrm{0,00238}{\text{kg / cm}}^{\text{3}}$$

. The coefficient of total lateral pressure becomes equal $${\zeta }_{01}^n=tg{\phi }_n=tg19.6843°=0.3577$$

, and the coefficient of the total relative transverse deformation of the medium $${\nu }_{01}^n=tg{\phi }_n/(\mathrm{one}+tg{\phi }_n)=tg19.6843°/(\mathrm{one}+tg19.6843°)=0.2561$$

.

Example 2 of the implementation of the method. 1) Almost vertical walls of the coastal cliffs of the Dnieper-Bug estuary near the city of Ochakov, Mykolayiv region with a height of h ₀ > 10 m are semi-solid clay and loam, which are covered with grass vegetation on the banks along the edges of the cliffs. Hidden and open cracks with a depth of more than 50 cm and a width of up to 1 cm are observed on the coastal soil surface of the cliffs, and the soil itself has a folded surface and a wavy line of ledges with a height difference> 30 cm at a distance l = 10 ... 15 m from the edge of the cliff, while on the lateral surface of the cliff coastline, closed cracks are observed to a depth of h≈0.5 ... 0.7 m from the horizontal surface and the soil repels the walls at a depth of h ₀₁ = 8 m.

With the specific gravity of the soil medium γ _p = 0.0027 kg / cm ^{3, the} depth of the cliff with which it is stretched to a horizontal surface is h _p = s _p / γ _p = 0.2403 / 0.0027 = 89 cm with a specific adhesion of the medium with _pp = 0.2403 kg / cm ² .

, $$p_x^{\mathrm{0,89}}=p_y^{\mathrm{0,89}}={\gamma }_{cтp}h=\mathrm{0,0027}\cdot 89=\mathrm{0,2403}{\text{ кГ/см}}^{\text{2}}$$

и $$p_{б}^{10}=({\gamma }_{cтp}h-c_{cтp})ctg{\phi }_{cтp}=(\mathrm{0,0027}\cdot 1000-\mathrm{0,2403})ctg31°=\mathrm{4,0936}{\text{ кГ/см}}^{\text{2}}$$

, $$p_x^{10}=p_y^{10}={\gamma }_{cтp}h=\mathrm{0,0027}\cdot 1000=\mathrm{2,7}{\text{ кГ/см}}^{\text{2}}$$

. При нормальном атмосферном давлении р_атм=1,033 кГ/см² на боковой поверхности стенок берегового обрыва коэффициент общего бокового давления будет равен $$\begin{array}{l}{\zeta }_{\mathrm{0,89}}^{атм}={\gamma }_{cтp}h\cdot tg{\phi }_{cтp}/({\gamma }_{cтp}h+p_{атм}tg{\phi }_{cтp}-c_{cтp})=\\ =\mathrm{0,0027}\cdot 89\cdot tg31°/(\mathrm{0,0027}\cdot 89+\mathrm{1,033}\cdot tg31°-\mathrm{0,2403})=\mathrm{0,2326,}\end{array}$$

$${\zeta }_{10}^{cтp}=\mathrm{0,0027}\cdot 1000\cdot tg31°/(\mathrm{0,0027}\cdot 1000+\mathrm{1,033}\cdot tg31°-\mathrm{0,2403})=\mathrm{0,5266}$$

The angle of internal friction of the soil environment of the coastal slopes is approximately φ _cp = arctan (h ₀₁ / l) = arctan (8 ... 10/15) = 28 ° ... 33.7 ° ≈31 °, then the coefficient of total relative deformation will be ν _0.89 = tg31 ° / (1 + tg31 °) = 0.3754 - at depths h _p = 89 cm and h = 10 m, and the coefficient of total lateral pressure, respectively, will be ζ _0.89 = ζ ₁₀ = tg31 ° = 0.6007 - respectively, at $$p_b^{0.89}=0$$

, $$p_x^{0.89}=p_y^{0.89}={\gamma }_{ctp}h=0.0027\cdot 89=0.2403{\text{kg / <figure-callout id="2" label="cm" filenames="00000062.png" state="{{state}}">cm</figure-callout>}}^{\text{2}}$$

and $$p_b^{10}=({\gamma }_{ctp}h-c_{ctp})ctg{\phi }_{ctp}=(0.0027\cdot 1000-0.2403)ctg31°=4.0936{\text{kg / <figure-callout id="2" label="cm" filenames="00000062.png" state="{{state}}">cm</figure-callout>}}^{\text{2}}$$

, $$p_x^{10}=p_y^{10}={\gamma }_{ctp}h=0.0027\cdot 1000=2.7{\text{kg / <figure-callout id="2" label="cm" filenames="00000062.png" state="{{state}}">cm</figure-callout>}}^{\text{2}}$$

. At normal atmospheric pressure p _atm = 1,033 kg / cm ² on the lateral surface of the walls of the coastal cliff, the coefficient of total lateral pressure will be equal to $$\begin{array}{l}{\zeta }_{0.89}^{\mathrm{but}tm}={\gamma }_{ctp}h\cdot tg{\phi }_{ctp}/({\gamma }_{ctp}h+p_{\mathrm{but}tm}tg{\phi }_{ctp}-c_{ctp})=\\ =0.0027\cdot 89\cdot tg31°/(0.0027\cdot 89+\mathrm{1,033}\cdot tg31°-0.2403)=\mathrm{0.2326,}\end{array}$$

$${\zeta }_{10}^{ctp}=0.0027\cdot 1000\cdot tg31°/(0.0027\cdot 1000+\mathrm{1,033}\cdot tg31°-0.2403)=0.5266$$

with ν _0.89 = ζ ₀ / (1 + ζ ₀ ) = 0.2326 / (1 + 0.2326) = 0.1887 and ν ₁₀ = 0.5266 / 1.5266 = 0.3449.

, где гравитационное (бытовое) давление р_б=(γ_cтph-с_стр)ctgφ_стр=(0,002·89-0,2403)ctg31°=-0,1037 кГ/см². Коэффициент общего бокового давления становится равным $$\begin{array}{l}{\zeta }_{01атм}^{н}={\gamma }_{н}h\cdot tg{\phi }_{н}/({\gamma }_{н}h+p_{атм}tg{\phi }_{н}-{с}_{н})=\\ =\mathrm{0,003}\cdot 89\cdot tg23°\mathrm{,5004}/(\mathrm{0,003}\cdot 89+\mathrm{1,033}\cdot tg23°\mathrm{,5004}-\mathrm{0,3067})=\mathrm{0,2836,}\end{array}$$

а коэффициент общей относительной поперечной деформации $$\begin{array}{l}{\nu }_{01атм}^{н}={\gamma }_{н}h\cdot tg{\phi }_{н}/\left[{\gamma }_{н}h(1+tg{\phi }_{н})+p_{атм}tg{\phi }_{н}-{с}_{н}\right]=\\ =\mathrm{0,003}\cdot 89\cdot tg23°\mathrm{,5004}/[\mathrm{0,003}\cdot 89(1+tg23°\mathrm{,5004})+\mathrm{1,033}\cdot tg23°\mathrm{,5004}-\mathrm{0,3067}]=\mathrm{0,2209.}\end{array}$$

2) In case of earthquakes the natural structure of the soil breakage coastline will be broken up to the values of its parameters at the depth h = 89 cm: φ _n = arcsin [2sinφ _p / (1 + sin ² φ _p)] - φ _p = arcsin [2sin31 ° / (1 + sin ² 31 °)] - 31 ° = 54,5004 ° -31 ° = 23,5004 °, s _n = s _p [2-tgφ _n / tgφ _p ] = 0,2403 [2-tg23,5004 ° / tg31 °] = 0.3067 kg / cm ² , $${\gamma }_n=\frac{p_{b}tg{\phi }_n+{\mathrm{from}}_n}{h}=\frac{-0.1037\cdot tg\mathrm{23,5004}°+0.3067}{89}=0.003{\text{kg / cm}}^{\text{3}}$$

where the gravitational (household) pressure p _b = (γ _ctp h-s _pg ) ctgφ _pg = (0.002 · 89-0.2403) ctg31 ° = -0.1037 kg / cm ² . The coefficient of total lateral pressure becomes equal $$\begin{array}{l}{\zeta }_{01\mathrm{but}tm}^n={\gamma }_{n}h\cdot tg{\phi }_n/({\gamma }_{n}h+p_{\mathrm{but}tm}tg{\phi }_n-{\mathrm{from}}_n)=\\ =0.003\cdot 89\cdot tg23°\mathrm{,\; 5004}/(0.003\cdot 89+\mathrm{1,033}\cdot tg23°\mathrm{,\; 5004}-0.3067)=\mathrm{0.2836,}\end{array}$$

and the coefficient of total relative transverse deformation $$\begin{array}{l}{\nu }_{01\mathrm{but}tm}^n={\gamma }_{n}h\cdot tg{\phi }_n/\left[{\gamma }_{n}h(\mathrm{one}+tg{\phi }_n)+p_{\mathrm{but}tm}tg{\phi }_n-{\mathrm{from}}_n\right]=\\ =0.003\cdot 89\cdot tg23°\mathrm{,\; 5004}/[0.003\cdot 89(\mathrm{one}+tg23°\mathrm{,\; 5004})+\mathrm{1,033}\cdot tg23°\mathrm{,\; 5004}-0.3067]=\mathrm{0.2209.}\end{array}$$

. По предлагаемой зависимости $${\zeta }_{10}^{cтp}=tg{\phi }_{cтp}=tg36°=\mathrm{0,7265}$$

, что соответствует расчетным показателям.Example 3 implementation of the method. An undried peat deposit with a thickness of 3 m as an elastic material medium at a depth of h = 200 cm has the following parameters: φ _p = 36 °, s _p = 0.22 kg / cm ² and γ _p = 0.0022 kg / cm ² . Gravity pressure at a depth of h = 2 m is p _b = (γ _ctp h-s _pg ) ctgφ _pg = (0.0022 · 200-0.22) ctg36 ° = 0.3028 kg / cm ² at horizontal household pressure p _x = _y = γ p _pg h = 0,0022 · 200 = 0.44 kg / cm ² and the pressure p _in the connected peat = -c _pg ctgφ _p = -0,22 · ctg36 ° = -0,3028 kg / cm ² . Then the coefficient of total lateral pressure at depth h will be equal to $${\zeta }_0=\frac{p_x=p_y}{p_b-p_{\mathrm{at}}}=\frac{0.44}{0.3028+0.3028}=0.7265$$

. According to the proposed dependency $${\zeta }_{10}^{ctp}=tg{\phi }_{ctp}=tg36°=0.7265$$

, which corresponds to the calculated indicators.

The coefficient of the total relative transverse deformation of peat at depth h is ν = ζ ₀ / (1 + ζ ₀ ) = 0.7265 / 1.7265 = 0.4208.

The present invention for the first time through the physical parameters of the specific adhesion and the angle of internal friction allows to obtain the calculated parameters ζ ₀ and ν ₀ with a high degree of reliability, determined by the accuracy of establishing the strength parameters of the medium under study - φ _page, with _page and φ _n , with _n , and also determine the parameter specific gravity of the disturbed structure γ _n

Information sources

1. Tsitovich N.A. Soil mechanics (short course): Textbook for high schools. - 3rd ed., Ext. - M.: Higher School, 1979. - S. 34-37, 168.

2. Golly A.V. Methodology for measuring stress and strain in soils: a Training manual. - L .: LISI, 1984. - S. 50-53.

3. Glotov N.M., Leontiev A.I. and other Foundations and foundations of transport facilities: Textbook for universities. - M .: Transport, 1995 .-- S. 160-161.

Claims (2)

1. The method for determining the mechanical parameters of the material medium, which consists in determining physical parameters of the medium strength of the undisturbed structure at a given depth h of the array — the angle φ _{p of} internal friction and the specific adhesion with _p , the coefficient of the total lateral pressure of the medium is determined by the dependence ζ ₀ = p _x / p _z = p _y / p _z , where p _z is the vertical pressure at depth h, the coefficient of relative transverse deformation of the medium is determined by the dependence ν ₀ = ε _x / ε _z = ε _y / ε _z = ζ ₀ / (1 + ζ ₀ ), where ε _x = ε _y and ε _z is the relative deformation of the medium at the point array in the horizontal and vertical direction, characterized in that at a given depth h of the material array, the specific gravity γ _{p of the} structured medium is determined and its lateral horizontal gravitational pressure is calculated as p _x = p _y = γ _p h, the coefficient of the total lateral pressure of the structured medium is determined according to

at p _z = p _b + c _p ctgφ _p , where gravitational household pressure p _b = (γ _p h-s _p ) ctgφ _p , and for an array of a material medium with a disturbed structure, the specific gravity of the disturbed structure medium is determined from dynamic or static effects

, lateral pressure - p _x = p _y = γ _n h, and the coefficient of total lateral pressure is determined by the dependence

, where φ _n = arcsin [2sinφ _p / (1 + sin ² φ _p )] - φ _p , s _n = s _p [2-tgφ _n / tgφ _p ] - respectively, the angle of internal friction and the specific adhesion of the medium with the broken structure at vertical pressure p _z = p _b + c _n ctgφ _n , while the atmospheric pressure p _atm is measured or it is taken to be normal in value p _atm = 1,033 kg / cm ² and the total lateral pressure coefficient is determined in the walls of the open vertical output in the array of structured medium addictions

, and in the walls of open vertical excavation in an array of medium with a disturbed structure, the coefficient of total lateral pressure is determined by the dependence

. 2. The method according to p. 1, characterized in that they determine the specific gravity of the structured medium γ _p , and the coefficient of the total relative transverse deformation of the structured medium in the array is calculated by the dependence

, the coefficient of the total relative transverse deformation of a material environment with a broken structure is calculated according to

, on the open side surface of the mine in the array of structured medium, determine its specific gravity γ _p and calculate the coefficient of its total relative transverse deformation according to

, and in the walls of the open vertical excavation in an array with a disturbed structure, the coefficient of the total relative transverse deformation is determined by the dependence

.

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