RU2565390C2 - Method for determining gravity pressure and coefficients of general lateral pressure and general relative lateral distortion of soil and peat ground - Google Patents

Abstract

FIELD: physics.

SUBSTANCE: invention refers to physics of material contact interaction of a both natural, and damaged ponderable medium in mass and at a crest of slopes. The parameters of an angle of internal friction φ_str and a specific cohesion с_str of the sampled medium taken at a depth h of the ponderable material mass are determined in the laboratory environment. The dependences φ_d=arcsin[2sinφ_str/(1+sin²φ_str)]- φ_str, c_d=c_str[2-tgφ_d/tgφ_str] are used to derive the parameters of an angle of internal friction and a specific cohesion of the structurally damaged medium at a survey depth respectively, wherein p_n=(γ_strh-c_str)ctgφ_str is a natural pressure at the depth h. A tangential natural pressure at the depth h is defined as τ_xy=p_x=p_y=γ_strh·cos²φ_str. The dependence derived by the author is used to determine the parameters of a coefficient of general lateral pressure of the medium at rest $${\zeta }_0^{str}=\mathrm{0,5}\sin 2{\phi }_{str},$$

at damaged natural mass structure $${\zeta }_0^d=\mathrm{0,5}\sin 2{\phi }_d,$$

in open pit walls $${\zeta }_{0atm}^{str}={\gamma }^{str}h\cdot \cos {\phi }^{str}/\left[\left({\gamma }^{str}h-c^{str}\right)ctg{\phi }^{str}+p_{atm}\right]=\frac{c^{str}{\cos }^2{\phi }^{str}\left(1+\sin {\phi }^{str}\right)}{c^{str}\cos {\phi }^{str}\left(1-\sin {\phi }^{str}\right)+p_{atm}\left(1+{\sin }^2{\phi }^{str}\right)}$$

and in open pit walls with damaged structure $${\zeta }_{0atm}^d={\gamma }^{d}h\cdot {\cos }^2{\phi }^d/\left[\left({\gamma }^{d}h-c^d\right)ctg{\phi }^d+p_{atm}\right]=\frac{c^d{\cos }^2{\phi }^d\left(1+\sin {\phi }^d\right)}{c^d\cos {\phi }^d\left(1-\sin {\phi }^d\right)+p_{atm}\left(1+{\sin }^2{\phi }^d\right)}.$$

Coefficients of general relative lateral distortion of the medium mass are determined according to the dependence derived by the author $${\nu }_0^{str}=\sin 2{\phi }^{str}/\left(2+\sin 2{\phi }^{str}\right),$$

$${\nu }_0^d=\sin 2{\phi }^d/\left(2+\sin 2{\phi }^d\right)$$

respectively, $$\begin{array}{l}{\nu }_{0atm}^{str}={\gamma }^{str}h\cdot \cos {\phi }^{str}/\left[\left({\gamma }^{str}h-c^{str}\right)ctg{\phi }^{str}+{\gamma }^{str}h\cdot {\cos }^2{\phi }^{str}+p_{atm}\right]=\\ =\frac{c^{str}{\cos }^2{\phi }^{str}\left(1+\sin {\phi }^{str}\right)}{c^{str}\cos {\phi }^{str}\left(1-\sin {\phi }^{str}\right)+c^{str}{\cos }^2{\phi }^{str}\left(1+\sin {\phi }^{str}\right)+p_{atm}\left(1+{\sin }^2{\phi }^{str}\right)}\end{array}$$

in side walls of an open pit, $$\begin{array}{l}{\nu }_{0atm}^d={\gamma }^{d}h\cdot \cos {\phi }^d/\left[\left({\gamma }^{d}h-c^d\right)ctg{\phi }^d+{\gamma }^{d}h\cdot {\cos }^2{\phi }^d+p_{atm}\right]=\\ =\frac{c^d{\cos }^2{\phi }^d\left(1+\sin {\phi }^d\right)}{c^d\cos {\phi }^d\left(1-\sin {\phi }^d\right)+c^d{\cos }^2{\phi }^d\left(1+\sin {\phi }^d\right)+p_{atm}\left(1+{\sin }^2{\phi }^d\right)},\end{array}$$

wherein p_atm=1.033 kg/cm² is a normal atmospheric pressure on the material medium, $${\gamma }_d=\frac{p_{n}tg{\phi }_d+c_d}{h}$$

is a specific gravity of the damaged medium.

EFFECT: more informative and reliable determination is achieved.

3 cl, 3 ex, 2 dwg

Description

The invention relates to the field of “Physics of material contact interaction”, and specifically to a method for determining the coefficients of the total lateral pressure ζ ₀ and the total relative transverse deformation ν ₀ (similar to the Poisson's ratio for an elastic medium) of a coherent elastic-viscous plastic isotropic soil and elastically elastic peat anisotropic medium.

A known method for determining the coefficient of total lateral pressure ζ ₀ structurally stable soil material array, which consists in the fact that at a given depth h of the array determine the value of the active vertical pressure p _z from the own weight of the overlying layers of the medium and the value of the tangential stress τ corresponding to the lateral pressure p _x = p _y , for example, using catchable flat pressure sensors (mass doses), the coefficient of the total lateral pressure of the medium is determined through the expression ζ ₀ = p _x / p _z = p _y / p _z and statistics are collected on the value of the coefficient ζ ₀ for various types of material medium, and the coefficient of the total relative transverse deformation of the medium at depth h is determined by the dependence v 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 using trapped pressure sensors (pressure sensors) in the vertical and horizontal direction 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 direction due to violations of the natural state of the array when pressure sensors are crushed and when drilling, if necessary, the well being tested.

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 -

, где р_б - вертикальное гравитационное (бытовое) давление, при этом коэффициент общего бокового давления среды определяют как отношение горизонтального к вертикальному давлению ζ₀=р_х/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_х/ε_z=ε_y/ε_z=ζ₀/(1+ζ₀), где ε_х=ε_y и ε_z - относительные деформации среды в точке массива в горизонтальном и вертикальном направлении [3].There is a method of determining the mechanical parameters of a structurally stable soil material medium in an 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 array of medium, the undisturbed structure determines the angle parameter φ _{p of} its internal friction and specific adhesion with _p , characterized in that the value of the coefficient of total lateral pressure is determined by the dependence of Y. Yaki

for sandy soil environments with specific adhesion with _p ≈ 0 and according to G.A. Spalving for cohesive clay soil media -

, where p _b is the vertical gravitational (household) pressure, and the coefficient of the total lateral pressure of the medium is defined 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 coefficient value 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 point of the array in horizontal and vertical direction [3].

The disadvantage of this method of determining the coefficient ζ ₀ is the limited application of the dependencies J. Yaki and G.A. 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.

, а плотность грунтовой среды рассчитывают как

, при удельном весе

, где g - ускорение свободного падения тела в условиях гравитации (см/с²), а величину гравитационного давления в массиве упругоэластичной анизотропной торфяной среды определяют по зависимости

, а плотность торфяной среды рассчитывают как

, при удельном весе

.Closest to the technical nature of the proposed is a method for determining the gravitational pressure of the material medium in the array and its natural density, which consists in the fact that the closest in technical essence to the proposed method is to determine the gravitational pressure of the material medium in the array and its natural density, which consists in that a predetermined depth h (cm) of the array material medium field methods of engineering studies angle φ _p define internal friction and specific adhesion to the _article medium undisturbed under gravity (domestic) pressure p _B, wherein the magnitude of the gravitational pressure of the array uprugovyazkoplastichnoy soil environment is determined depending on

and the density of the soil medium is calculated as

, with specific gravity

, where g is the acceleration of gravity of the body under gravity (cm / s ² ), and the magnitude of the gravitational pressure in the array of an elastically elastic anisotropic peat medium is determined by the dependence

and the density of the peat medium is calculated as

, with specific gravity

.

,A disadvantage of the known invention is that p_{b, d} and p_{b, T} correspond to the principal vertical stress σ_I in an array of dirt and peat medium and the main horizontal shear stress

,

, при необходимости знания величины активного гравитационного давления p_z при соответствующем тангенциальном напряжении на потенциальных линиях сдвига τ_x,y.

, if necessary, knowledge of the magnitude of the active gravitational pressure p _z at the corresponding tangential stress on potential shear lines τ _{x, y} .

и соответствующей главному напряжению σ₁, в исследуемой точке массива, а величину главного касательного напряжения определяют как

, достигается тем, что для массива грунта определяют тангенциальное напряжение на потенциальных потенциальных линиях сдвига как

, величину активного вертикального гравитационного давления в точке массива определяют как

, где

- давление связности грунта, коэффициент общего бокового давления грунта определяют как

, коэффициент общей относительной поперечной деформации - как

, а для массива торфа тангенциальное напряжение на потенциальных потенциальных линиях сдвига определяют как

при активном гравитационном давлении в точке массива торфа

, величину коэффициента общего бокового давления торфа определяют как

, а коэффициент общей относительной поперечной деформации в массиве - как

, при этом для боковых стенок открытой вертикальной выработки в массиве структурированной грунтовой среды коэффициент общего бокового давления после замера атмосферного давления р_атм или принятия его нормальным по величине р_атм=1,033 кГ/см² определяют какThe technical result by the method of determining gravitational pressure and the coefficients of the total lateral pressure and the total relative lateral deformation of the soil and peat environment, which consists in determining at a given depth h of the array the physical parameters of the strength of the medium of the undisturbed structure - angle φ _{p of} internal friction and specific adhesion - s _p, common side medium pressure coefficient is determined from the dependence of ζ ₀ = p _{x / p z = p y / p} z, where p _x = p _y - measured lateral horizontal pressure when given by the vertically pressure p _z at a depth h, coefficient total relative shear deformation 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 - the measured relative deformations of the medium under pressure p _z at the point of the array in the horizontal and vertical directions, at a given depth h of the array of visco-elastic structured soil, take the value of gravitational (household) pressure as

and corresponding to the principal stress σ ₁ , at the studied point of the array, and the magnitude of the principal tangential stress is determined as

, is achieved by the fact that for a soil mass, the tangential stress on the potential potential shear lines is determined as

, the value of the active vertical gravitational pressure at the point of the array is determined as

where

- soil connectivity pressure, the coefficient of the total lateral pressure of the soil is determined as

, the coefficient of total relative transverse deformation - as

, and for a peat mass, the tangential stress on potential potential shear lines is defined as

with active gravitational pressure at the point of the peat massif

, the value of the coefficient of the total lateral pressure of peat is defined as

, and the coefficient of total relative transverse deformation in the array - as

, while for the side walls of open vertical excavation in an array of structured soil environment, the coefficient of total lateral pressure after measuring atmospheric pressure p _atm or accepting it as normal in value p _atm = 1,033 kg / cm ² is determined as

, а коэффициент ее общей относительной поперечной деформации - как

, and the coefficient of its total relative transverse deformation - as

, причем в стенках открытой вертикальной выработки в массиве грунтовой среды с нарушенной от внешнего воздействия структурой при доступе атмосферного давления Р_атм=1,033 кГ/см² коэффициент общего бокового давления определяют как

, где

,

- соответственно угол внутреннего трения и удельное сцепление среды с нарушенной структурой, ее коэффициент общего бокового давления - как

, удельный вес грунта - как

, а коэффициент общей относительной поперечной деформации грунта - как

.

moreover, in the walls of open vertical excavation in an array of soil with a structure disturbed by external influences when atmospheric pressure is available P _atm = 1.033 kg / cm ^{2, the} coefficient of total lateral pressure is determined as

where

,

- respectively, the angle of internal friction and the specific adhesion of the medium with the disturbed structure, its coefficient of total lateral pressure - as

, specific gravity of soil - as

, and the coefficient of the total relative transverse deformation of the soil - as

.

The present invention is based on the provision “Physics of material contact interaction”, 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 in a broken state”.

The invention is illustrated by graphic materials, where in FIG. 1 is a graph p = f (τ) of the limiting state of a cohesive elastoplastic soil material medium — soil, FIG. 2 is a graph of p = f (τ) of the limiting state of a connected anisotropic elastically elastic peat medium.

, величина которого равна радиусу р_б,_Г=r_Г круга Мора предельного состояния среды при растяжении, давление связности среды равно

и противодействует растяжению среды за краями точки. При

радиус

.Considering the graph p = f (τ) of the limit state of S. Coulomb cohesive elastic-viscoplastic soil medium (Fig. 1) in a natural stress-strain state, we determine the vertical gravitational (household) pressure at a point at a depth h of the soil mass as

whose value is equal to the radius r _b , _G = r _G of the Mohr circle of the limiting state of the medium under tension, the pressure of the medium is connected

and counteracts the stretching of the medium beyond the edges of the point. At

radius

.

, а соответствующее ему касательное тангенциальное напряжение

при тангенциальном давлении на потенциальных линиях сдвига

. Коэффициент общего бокового давления упругопластичной грунтовой среды определяется какThe active natural vertical pressure at a point at depth h will be

, and the corresponding tangential tangential stress

at tangential pressure on potential shear lines

. The coefficient of the total lateral pressure of an elastoplastic soil medium is defined as

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

.

при соответствующем тангенциальном напряжении в точке на этой же глубине

.Considering the graph (FIG. 2) p = f (τ) of a limiting condition of a connected elastic peaty medium, such as peat undrained deposits with a high degree of anisotropy _AE = _E / E _g = 0.4 compressibility in the vertical and the horizontal direction define a vertical pressure at depth h like

with the corresponding tangential stress at a point at the same depth

.

, тогда активное вертикальное давление в точке на глубине h будет равно

. Коэффициент общего бокового давления упругоэластичной торфяной среды определяется как

Peat Connectivity Pressure

then the active vertical pressure at a point at depth h will be

. The coefficient of the total lateral pressure of an elastically elastic peat medium is defined as

.and the coefficient

.

Example 1 of the implementation of the method.

, а коэффициент общей относительной поперечной деформации суглинка определяем по зависимости

. Статистические справочные данные имеют значения ζ₀=0,11…0,82, ν₀=0,20…0,25 для тугопластичных суглинков [1].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 _p h ₁ -c _p) ctgφ _p = (0,02 · 90-0,2) ctg23 ° = -0,0471 kg / cm ² , p _b2 = (γ _p h ₂ -s _p ) ctgφ _p = (0.02 · 280-0.2) ctg23 ° = 0.8481 kg / cm ² . The coefficient of total lateral 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 = 0.20 ... 0.25 for stiff plastic loams [1].

. Коэффициент общего бокового давления становится равным

, а коэффициент общей относительной поперечной деформации среды

2) In 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 = arcsin [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 [2-tgφ ⁿ / tgφ ^p ] = 0.2 [2-tg19.6843 ° / tg23 °] = 0.2314 kg / cm ² ,

. The coefficient of total lateral pressure becomes equal

, and the coefficient of the total relative transverse deformation of the medium

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 vertical drop> 30 cm at a distance l = 10 ... 15 m from the edge of the cliff. At the same time, on the lateral surface of the cliff coastline, closed cracks are observed to a depth of h≈0.5 ... 0.1 m from the horizontal surface and the soil is repelled by 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 stretches to a horizontal surface is h _p = s ^p / γ ^p = 0.2 / 0.0025 = 89 cm for a specific adhesion of the medium with ^pp = 0.2 kg / cm ² .

, τ_Г=γ^cтрh=0,0027·89=0,2403 кГ/см² иThe angle of internal friction of the soil environment of the coastal slopes is approximately φ _φ = arctan (h _0l / l) = arctan (8 ... 10/15) = 28 ° ... 33.7 ° ≈31 °, then the coefficient of total relative deformation will be ν _{0 89} ^p = sin2φ / [2 (1 + sin2φ ^p)] = 0.2345 - at depths of h _p = 89 cm and h = 10 m, and the total lateral pressure coefficient, respectively, will be equal to ζ _0,89 = ζ ₁₀ = sin62 ° / (2 + sin62 °) = 0.3063 - respectively at

, Τ _r = γ ^Page h = 0,0027 · 89 = 0.2403 kg / cm ² and

,

,

τ = γ ^p h = 0,0027 · 1000 = 2.7 kg / cm ² and τ _xy = τ ² _r cos φ _p = cos 2.7 ^{February 31} ° = 1,9838 kg / cm ^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

or

2) In the event of an earthquake, the natural soil structure of the cliff of the coastline will be disturbed to its values at a depth of 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 ^pg [2-tgφ ⁿ / tgφ ^pg ] = 0.2 [2-tg23.5004 ° / tg31 °] = 0.2553 kg / cm ² ,

,

where the gravitational (household) pressure p _b = (γ ^sth h-s ^p ) ctgφ ^p = (0.00236 · 89-0.2) ctg31 ° = 0.0167 kg / cm ² .

The coefficient of total lateral pressure becomes equal

.and the coefficient of total relative transverse deformation

.

и

. Гравитационное давление на глубине h=2 м составляет величину

при горизонтальном тангенциальном напряжении

и давлении связности торфа

. Коэффициент общего бокового давления торфа на глубине h будет равен

.Example 3 implementation of the method. Undehydrated peat deposit with a thickness of 3 m as an elastic anisotropic elastic material medium at a depth of h = 200 cm has the following indicators:

and

. Gravity pressure at a depth of h = 2 m is

at horizontal tangential stress

and peat connectivity pressure

. The coefficient of the total lateral pressure of peat at a depth h will be equal to

.

, что соответствует расчетным показателям.According to

, which corresponds to the calculated indicators.

The coefficient of the total relative transverse deformation of peat at depth h is ν = ζ _{0, T} (1 + ζ _{0, T} ) = 0.4755 / 1.4755 = 0.3223.

The present invention for the first time through the physical parameters of 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 investigated medium - φ _page , with _page and φ _n , with _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.

4. RF patent No. 2549533 “A method for determining the gravitational pressure of a material medium in an array and its natural density” / Khrustalev E.N., B.I. No. 12 dated 04/27/2015 (prototype).

Claims (3)

1. A method for determining gravitational pressure and total lateral pressure coefficient and the total relative transverse strain dirt and the peat medium, comprising the steps of determining at a predetermined depth h of the array physical strength parameters undisturbed environment - _page angle φ 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 measured lateral horizontal pressure at a given vertical pressure p _z at a depth h, k the coefficient of the total relative transverse deformation of the medium is determined by the dependence v ₀ = ε _x / ε _z = ε _y / ε _z = ζ ₀ / (1 + ζ ₀ ), where ε _x = ε _y and ε _z are the measured relative deformations of the medium under pressure p _z at the point of the array in the horizontal and vertical direction, at a given depth h of the array of the visco-elastic structured soil medium, take the value of gravitational (household) pressure as

and corresponding to the main stress σ ₁ at the studied point of the array, and the value of the main tangential stress is determined as

, characterized in that for the soil mass determine the tangential stress on potential shear lines as

, the value of the active vertical gravitational pressure at the point of the array is determined as

where

- soil connectivity pressure, the coefficient of the total lateral pressure of the soil is determined as

, the coefficient of total relative transverse deformation - as

, and for a peat mass, the tangential stress on potential shear lines is determined as

with active gravitational pressure at the point of the peat massif

, the value of the coefficient of the total lateral pressure of peat is defined as

, and the coefficient of total relative transverse deformation in the array - as

. 2. The method according to p. 1, characterized in that for the side walls of an open vertical excavation in an array of structured soil medium, the coefficient of total lateral pressure after measuring atmospheric pressure p _atm or accepting it at a normal value of p _atm = 1,033 kg / cm ² is determined as

,
and the coefficient of its total relative transverse deformation - as

3. The method according to p. 1, characterized in that in the walls of an open vertical excavation in an array of soil with a structure disturbed by external influences with atmospheric pressure access p _atm = 1.033 kg / cm ^2, the total lateral pressure coefficient is determined as

,
Where

,

- respectively, the angle of internal friction and the specific adhesion of the medium with a disturbed structure,
its total lateral pressure coefficient is how

,
specific gravity of soil - how

,
and the coefficient of the total relative transverse deformation of the soil - as

.

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