RU2521116C1 - Determination of rock specimen mechanical properties - Google Patents

Abstract

FIELD: mining.

SUBSTANCE: specimen is loaded by two spherical indenters directed in opposition till its cracking. Destructive force is registered to define cracking surface area in destructed specimen that extends through loading axis, geometrical parameters of destructed zones in areas of contact with spherical indenters, specimen rupture stretching stress and mean compressive stress at the boundary of the larger of destructed zones are calculated. Breaking point and shear resistance are defined as mechanical properties of the specimen. Debris of crushed specimen are used to compose a composite specimen for determination of geometrical parameters of crushed zones at the ends of said composite specimen. Diameter of residual marks of indenters and indent hole length along fracture surface are defined. Surface area of larger destructed zone at contact with indenters, breaking point at uniform stretching, maximum shear resistance and Poisson factor are defined by the formulas.

EFFECT: simplified tests, higher precision of determination of mechanical properties.

5 tbl, 2 dwg

Description

The invention relates to mechanical testing of rocks and materials having a brittle nature of destruction, and can be used in engineering-geological surveys.

A known method for determining the stress state of rocks in the massif (USSR author's certificate No. 1259005, class E21C 39/00, 1986), including pressing a load element in the rock (bottom hole) in the form of a stamp until the rock breaks with the formation of puncture holes and determining the depths indentation of the stamp equal to the depths of the puncture holes.

The disadvantages of the method are the low accuracy of the relative determination of the stress state of the rock without taking into account the absolute values of the ultimate volumetric strength and existing stresses, as well as the complexity and complexity of the tests due to the phased drilling of the well and repeated indentation of the stamp.

A known method for determining contact dynamic strength (USSR author's certificate No. 1346785, class E21C 39/00, 1987), including the shock introduction of the load element (measuring rod tip) into the rock, determination of stresses in the load element and the geometric parameters of the fracture well (depth of the fracture well and its diameter).

The disadvantages of the method are the complexity of the test and recording equipment to determine the maximum stresses in the load element and the complexity of the tests associated with repeated impact of the load element and the need to clean it from the products of destruction.

There is a method of determining the coefficient of internal friction of rocks (USSR author's certificate No. 970197, class G01N 19/02, 1982), which includes applying to the sample a spherical shape of a cleaving force and determining in the plane passing through the loading axis geometrical parameters (base radius and height ) zones of destroyed rock in contact with loading surfaces.

The disadvantages of the method are the complexity of the preparation for testing associated with the manufacture of a specimen of a special spherical shape and the low accuracy of determining the strength indicator due to the difficulty of measuring the dimensions of the zones of the destroyed rock in the plane passing through the loading axis on uneven surfaces of the fragments of the crushed sample.

There is a method of determining the strength characteristics of rocks (USSR author's certificate No. 473930, class G01N 3/12, E21C 39/00, 1975), which includes the introduction of a load element (punch) into the rock sample before destruction with the formation of a through hole and a hole punch on the opposite the free surface of the sample and the determination of the geometric parameters of the puncture hole (diameter and depth of the hole).

The disadvantages of the method are the low accuracy of determining the ultimate strength characteristics using generalized integral indicators for correlation dependencies and the complexity of the tests due to the need to additionally determine one of the strength characteristics (tensile, compressive or shear strengths).

A known method for determining the mechanical properties of rock samples (article: Korshunov V.A. Determination of volumetric strength indicators of rock samples when loaded with spherical indenters. Mining geomechanics and surveying: Collection of scientific papers. - SPb .: VNIMI, 1999. - M- in fuel and energy of the Russian Federation, RAS, - p. 70-75), taken as a prototype and consisting in the fact that the sample is loaded with two counter-directed spherical indenters before it splits, the destructive force is fixed, the area is determined in the destroyed sample the tensile crack surface passing through the loading axis, and the geometric parameters of the fractured zones in the contact areas with both spherical indenters (the depth and maximum width of the zones on the fracture crack surface), the tensile stress of the fracture of the sample and the average compressive stress at the boundary of the largest of the fractured zones are calculated and determined as mechanical properties of the specimen, ultimate strength (ultimate strength under uniaxial compression) and shear resistance (ultimate shear resistance is adhesion).

The disadvantage of this method is the complexity and low accuracy of determining the mechanical properties due to the considerable complexity and insufficient accuracy of determining the geometric parameters of the fractured zones on the surface of the separation crack of a split sample, which usually has a complicated relief shape, inconvenient for measurements. Another disadvantage of this method is its low information content. The capabilities of the method are limited by the determination of strength properties in the area of the "strength certificate" adjacent to the state of "pure shear" and corresponding to failure from separation under the action of tensile and compressive stresses and fracture by shear under the action of uneven compressive low stress levels.

The technical result of the invention is to simplify testing and improve the accuracy of determining the mechanical properties of samples by simplifying the determination of the geometric parameters of the destroyed zones at the ends of the samples in the contact areas with indenters and increasing the information content of tests by additionally determining the strength characteristics of the "strength certificate" in the areas of tensile and compressive high level of stresses (ultimate tensile strength in all-round tension and maximum shear resistance), and that same Poisson's ratio.

The technical result is achieved by the fact that in the method for determining the mechanical properties of rock samples and materials, including loading the sample with two counter-directed spherical indenters before it splits, fixing the destructive force, determining in the destroyed sample the surface area of the separation crack passing through the loading axis, and geometric parameters destroyed zones in the contact areas with both spherical indenters, calculation of tensile tensile stress of the specimen and the average compressive stresses at the boundary of the largest of the destroyed zones and determining, as the mechanical properties of the sample, the ultimate strength and shear resistance, according to the invention, a composite sample is collected from the fragments of the destroyed sample, at the ends of which the geometric parameters of the destroyed zones are determined - the diameter of the residual fingerprints from the indenters and the length of the puncture holes along the surface of the separation crack, determine the surface area of the larger destroyed zone at the contact with the indenters by the formula:

F = π · D _otp · L _l ,

where F is the surface area of the larger destroyed zone;

D _OT - the diameter of the residual imprint from the indenter;

L _l - the length of the hole puncture along the surface of the separation gap;

π = 3.14,

, максимальное сопротивление срезу $${\tau }_{\max }^{к}$$

и коэффициент Пуассона µ_σ по формулам:and as the mechanical properties of the specimen, the ultimate tensile strength is determined $${\sigma }_{\mathrm{at}R}^{\mathrm{to}}$$

maximum shear resistance $${\tau }_{\max }^{\mathrm{to}}$$

and Poisson's ratio µ _σ by the formulas:

; $${\sigma }_{\mathrm{at}R}^{\mathrm{to}}=2\cdot {\sigma }_t$$

;

; $${\tau }_{\max }^{\mathrm{to}}=\frac{3}{2}\cdot \sqrt{p\cdot {\sigma }_t}+\frac{p}{{\sigma }_t}\cdot \frac{\left(p-3\cdot {\sigma }_t\right)}{\mathrm{four}}$$

;

; $${\mu }_{\sigma }=2\cdot \frac{{\sigma }_t}{p}\cdot \frac{\left(2+\sqrt{p/{\sigma }_t}\right)}{\left(\mathrm{one}+\sqrt{p/{\sigma }_t}\right)}$$

;

where σ _t is the tensile stress of the rupture of the sample;

p is the average compressive stress at the boundary of the largest of the destroyed zones.

The method is illustrated in FIG. 1, which shows a diagram of a loading device for implementing the method, and FIG. 2, which shows a diagram for determining in a composite destroyed sample the geometric parameters of the destroyed zone in the contact area with a spherical indenter, where 1 is the device’s body, 2 are rods , 3 — inserts, 4 — spherical indenters, 5 — specimen, 6 — detachment crack, 7 and 8 — fragments of the destroyed specimen, 9 — puncture hole, 10 — residual imprint from the indenter.

The loading device must ensure that a compressive force is applied to the sample by two coaxial counter directional spherical indenters. The housing 1 of the device is a rigid frame, inside of which on the axis of loading 00 there is a movable pair of rods 2 with inserts 3 containing steel spherical indenters 4 to transfer the load to the sample 5.

The method is as follows.

The sample is installed between spherical indenters and uniformly loaded with registration of the compressive force P. Testing of samples of arbitrary, including irregular, shape with untreated surfaces is allowed.

With an increase in the load in the sample, in the contact areas with spherical indenters, the destroyed zones of crushed, compacted by compression material develop. The zones are in the form of truncated ellipsoids. The zone develops more intensively in the weakest region of the sample. When the ultimate stress state is reached, at the boundary of the largest of the destroyed zones, a separation crack 6 appears, which, merging with the second zone, breaks the sample into fragments 7 and 8.

The maximum (destructive) force P is recorded. After that, the characteristic linear dimensions of the surface of the separation crack are measured (for example, with a caliper) in the debris of the sample, from which its area S.

Then, a composite sample is collected from the debris of the sample. To do this, the debris is applied to each other, providing tight contact along the separation gap. In the composite sample, the geometric parameters of the destroyed zones are determined — the diameter of the residual fingerprints from the indenters _Dsp and the length of the puncture holes along the surface of the separation crack L _L. In this case, the boundaries of the puncture hole are distinguished by the wider opening of the crack edges within the puncture, and the diameter of the residual fingerprint is preferable to measure in the direction perpendicular to the separation crack. To simplify and improve the accuracy of measurements, the geometric parameters of the destroyed zones are recommended to be determined by photographing the sample together with the measuring ruler and subsequent processing of the image enlarged on the computer monitor.

The surface area of the destroyed zones at the contact with both indenters F ₁ and F _{2 is} calculated as body surfaces in the form of an ellipsoid, according to the formula:

F = π · D _sap · L _l .

The larger of the two values of F ₁ and F ₂ -F is selected.

The tensile tensile stress of the specimen σ _t and the average compressive stress p at the boundary of the largest of the destroyed zones are calculated by the formulas:

; $${\sigma }_t=\frac{P}{S}$$

;

$$p=\frac{P}{F}$$ .

, максимальное сопротивление срезу $${\tau }_{\max }^{к}$$

и коэффициент Пуассона µ_σ по формулам:Comprehensive tensile strength $${\sigma }_{\mathrm{at}R}^{\mathrm{to}}$$

maximum shear resistance $${\tau }_{\max }^{\mathrm{to}}$$

and Poisson's ratio µ _σ by the formulas:

; $${\sigma }_{\mathrm{at}R}^{\mathrm{to}}=2\cdot {\sigma }_t$$

;

; $${\tau }_{\max }^{\mathrm{to}}=\frac{3}{2}\cdot \sqrt{p\cdot {\sigma }_t}+\frac{p}{{\sigma }_t}\cdot \frac{\left(p-3\cdot {\sigma }_t\right)}{\mathrm{four}}$$

;

$${\mu }_{\sigma }=2\cdot \frac{{\sigma }_t}{p}\cdot \frac{\left(2+\sqrt{p/{\sigma }_t}\right)}{\left(\mathrm{one}+\sqrt{p/{\sigma }_t}\right)}$$

The experimental justification for determining the surface area of the destroyed zone at the contact with the indenter is the results of comparing the values of the surface area of the destroyed zone determined by the proposed method and in accordance with the prototype method (through the values of the maximum width D and depth h of the zone on the surface of the separation crack according to the formula: F = π · D · h) for various rocks and brittle materials.

The similarity of the shape and size of the fracture zone on the surface of the separation crack and on the end of the sample at the contact with the indenter in the split sample is established. In this case, the geometrical parameters of the fractured zone at the end of the sample (the length of the puncture hole along the surface of the separation crack L _L and the diameter of the residual indent from the indenter D _sp ) differ insignificantly from the similar parameters of the zone on the surface of the separation crack (maximum width D and depth h of the zone, respectively).

Table 1 presents examples of the determination by comparative methods of the geometric parameters of the destroyed zones and the values of their surface area in samples of 22 samples of rocks and brittle materials. The deviation of the results of the determinations by the compared methods ranged from -8 to 11%, averaged 6% and was associated with the difficulty of measuring the fuzzy boundaries of the zones on the relief surfaces of the fracture cracks in split samples using the prototype method. The proposed method, the definition of the parameters of the destroyed zones on a more even external surface of the sample greatly simplifies the measurement and, accordingly, increases the accuracy of the determination. The positive effect is even more significant when indenters are pressed into a pre-prepared surface (into the polished flat surface of disk samples or the side surface of core fragments).

служат результаты анализа с использованием построения паспорта прочности горных пород (огибающей предельных кругов Мора) в области действия растягивающих напряжений.Theoretical basis for determining the tensile strength in all-round tension $${\sigma }_{\mathrm{at}R}^{\mathrm{to}}$$

The results of the analysis are used using the construction of a rock strength certificate (envelope of the Mora limit circles) in the field of tensile stress.

(статья: Коршунов В.А. Определение показателей объемной прочности образцов горных пород при их нагружении сферическими инденторами. Горная геомеханика и маркшейдерское дело: Сборник научных трудов. - СПб.: ВНИМИ, 1999. - М-во топлива и энергетики РФ, РАН. - с.70-75). Известно также, что этому предельному напряженному состоянию на «паспорте прочности» соответствует перелом огибающей кривой на два качественно различных участка. При этом огибающая предельных кругов Мора в области разрушения от отрыва при совместном действии растягивающих и сжимающих напряжений может быть приближенно принята прямолинейной, что не противоречит опытным данным по испытанию хрупких материалов (монография: Евдокимов П.Д., Сапегин Д.Д. Прочность, сопротивляемость сдвигу и деформируемость оснований сооружений на скальных породах. Изд-во «Энергия», М. - Л., 1964, 174 с.). При нагружении образца сферическими инденторами этот прямолинейный участок «паспорта прочности», соответствующий величине предельного сопротивления срезу (сцепления) $${\tau }_0=\sqrt{{\sigma }_t\cdot p}$$

, будет характеризоваться наклоном на «паспорте прочности», равным углу внутреннего трения $${\varphi }_0=arctg\left(\frac{p-{\sigma }_t}{2\cdot \sqrt{p\cdot {\sigma }_t}}\right)$$

. Тогда величина максимально возможного (по абсолютной величине) растягивающего напряжения, соответствующего пределу прочности на отрыв, может быть вычислена как максимальный диаметр предельного круга растягивающих напряжений Мора - круга Мора с центром в точке -σ_t на оси нормальных напряжений и радиусом, равным σ_t. Таким образом, определяемая согласно предлагаемому способу величина прочности при всестороннем растяжении $${\sigma }_{вр}^{к}$$

, равная 2·σ_t, по своему физическому смыслу соответствует максимальной возможной абсолютной величине прочности на разрыв хрупкого тела, обусловленной величиной главного растягивающего напряжения для конкретных условий нагружения образца сферическими инденторами.It is known that at the moment of specimen split, tangential stresses equal to the value of ultimate shear resistance (adhesion) act on the surface of the separation crack at the boundary of the destroyed zone $${\tau }_0=\sqrt{{\sigma }_t\cdot p}$$

(article: VA Korshunov. Determination of volumetric strength indicators of rock samples when loaded with spherical indenters. Mining geomechanics and surveying: Collection of scientific papers. - St. Petersburg: VNIMI, 1999. - M-fuel and energy of the Russian Federation, RAS. - p. 70-75). It is also known that this extreme stress state on the "strength certificate" corresponds to a fracture of the envelope curve into two qualitatively different sections. In this case, the envelope of the Mora limit circles in the region of fracture from separation under the combined action of tensile and compressive stresses can be approximately assumed to be linear, which does not contradict the experimental data on the testing of brittle materials (monograph: Evdokimov PD, Sapegin DD Strength, resistance the shift and deformability of the foundations of structures on rocks. Publishing house "Energy", M. - L., 1964, 174 pp.). When loading a sample with spherical indenters, this straight-line section of the "strength certificate", corresponding to the value of the ultimate shear resistance (adhesion) $${\tau }_0=\sqrt{{\sigma }_t\cdot p}$$

, will be characterized by a slope on the "strength certificate" equal to the angle of internal friction $${\varphi }_0=arctg\left(\frac{p-{\sigma }_t}{2\cdot \sqrt{p\cdot {\sigma }_t}}\right)$$

. Then the value of the maximum possible (in absolute value) tensile stress corresponding to the tensile strength can be calculated as the maximum diameter of the limit circle of tensile stresses of Mohr - the Mohr circle centered at the point -σ _t on the axis of normal stresses and a radius equal to σ _t . Thus, determined according to the proposed method, the value of the tensile strength $${\sigma }_{\mathrm{at}R}^{\mathrm{to}}$$

, equal to 2 · σ _t , in its physical meaning corresponds to the maximum possible absolute value of the tensile strength of a brittle body, due to the magnitude of the main tensile stress for specific conditions of loading the sample with spherical indenters.

служат результаты сопоставления значений предела прочности $${\sigma }_{вр}^{к}$$

и σ_о, определенных предлагаемым способом и стандартным расчетным методом построения паспорта прочности по данным определения пределов прочности при одноосном сжатии и растяжении (ГОСТ 21153.8-88 «Породы горные. Метод определения предела прочности при объемном сжатии. Приложение 2 обязательное. Методы построения паспорта прочности»). При этом в качестве исходных данных для расчетного метода были использованы значения предела прочности при одноосном сжатии, определенные в соответствии со способом-прототипом, и предела прочности при растяжении, вычисленные с использованием способа по патенту РФ №2435955, кл. E21C 39/00, G01N 3/08, 2011:Experimental justification for determining the tensile strength in all-round tension $${\sigma }_{\mathrm{at}R}^{\mathrm{to}}$$

results of comparison of values of ultimate strength $${\sigma }_{\mathrm{at}R}^{\mathrm{to}}$$

and σ _о determined by the proposed method and standard calculation method for constructing a strength certificate based on the determination of tensile strengths under uniaxial compression and tension (GOST 21153.8-88 "Mountain rocks. Method for determining the tensile strength under volume compression. Appendix 2 is mandatory. Methods for constructing a strength certificate" ) In this case, as the initial data for the calculation method, the values of the uniaxial compression tensile strength determined in accordance with the prototype method and the tensile strength calculated using the method according to the RF patent No. 2435955, cl. E21C 39/00, G01N 3/08, 2011:

; $${\sigma }_c=p+\sqrt{p\cdot {\sigma }_t}$$

;

. $${\sigma }_p^{\mathrm{to}}=2\cdot \frac{{\sigma }_t\cdot p}{{\sigma }_t+p}$$

.

и σ_o (в долях от σ_t) для горных пород или хрупких материалов, характеризуемых показателем хрупкости K_xp (отношением пределов прочности при одноосном сжатии и растяжении σ_c/σ_p) в широком диапазоне от 5 до 20, соответствующем реальным горным породам. Отклонение результатов определений сравниваемыми способами уменьшалось от 9 до 3% с увеличением показателя хрупкости и, в среднем, составило 5%, что соизмеримо с точностью методов.Table 2 presents dimensionless strength values $${\sigma }_{\mathrm{at}R}^{\mathrm{to}}$$

and σ _o (in fractions of σ _t ) for rocks or brittle materials characterized by the fragility index K _xp (ratio of tensile strengths under uniaxial compression and tension σ _c / σ _p ) in a wide range from 5 to 20, corresponding to real rocks. The deviation of the results of the determinations by the compared methods decreased from 9 to 3% with an increase in the fragility index and, on average, amounted to 5%, which is comparable with the accuracy of the methods.

предложенным способом служит экспериментально установленная связь минимального главного нормального напряжения $${\sigma }_3^{М}$$

, соответствующего достижению максимального сопротивления срезу $${\tau }_{\max }^{к}$$

, с величинами предельного сопротивления срезу (сцепления) τ₀ и параметрами предельного напряжения состояния, соответствующего минимальному главному нормальному напряжению, равному пределу прочности при одноосном сжатии σ_с.The theoretical justification for determining the maximum shear resistance $${\tau }_{\max }^{\mathrm{to}}$$

the proposed method is the experimentally established relationship of the minimum main normal voltage $${\sigma }_3^M$$

corresponding to achieving maximum shear resistance $${\tau }_{\max }^{\mathrm{to}}$$

, with the values of the ultimate shear resistance (adhesion) τ ₀ and the parameters of the ultimate state stress corresponding to the minimum principal normal stress equal to the ultimate strength under uniaxial compression σ _s .

If we take the envelope of the Mora limit circles in the region of fracture by shear under the action of uneven compressive low-level stresses as straightforward, which does not contradict the experimental data on the testing of brittle rocks and materials, the established relationship can be expressed as follows:

, $${\sigma }_3^M=\frac{{\sigma }_{\mathrm{one}}-{\sigma }_c}{2}-2\cdot {\tau }_0$$

,

where (σ ₁ -σ _c ) / 2 is the radius of the limit Mohr circle corresponding to the minimum principal normal stress equal to σ _c .

было выражено через величины σ_c и $${\sigma }_{вр}^{к}$$

и отношение p/σ_t компонент предельного напряженного состояния на границе разрушенной зоны, соответствующего расколу образца:After algebraic transformations $${\sigma }_3^M$$

was expressed in terms of σ _c and $${\sigma }_{\mathrm{at}R}^{\mathrm{to}}$$

and the ratio p / σ _{t of the} components of the ultimate stress state at the boundary of the destroyed zone corresponding to the split of the sample:

. $${\sigma }_3^M=\sqrt{p/{\sigma }_t}\cdot \left(\frac{{\sigma }_c}{2}-{\sigma }_{\mathrm{at}R}^{\mathrm{to}}\right)$$

.

вычислялась путем решения системы двух уравнений. Одним из которых является линейное уравнение τ=С+tφ·σ_n, описывающее прямолинейный участок «паспорта прочности» в области всестороннего неравномерного сжатия, характеризуемой величинами условного сцепления C и соответствуещего угла внутреннего трения φ. При этом $$C=\frac{\sqrt[4]{{\sigma }_t\cdot p}\cdot \left(\sqrt{{\sigma }_t}+\sqrt{p}\right)}{2}$$

и $$tg\varphi =\frac{\sqrt{p}-\sqrt{{\sigma }_t}}{2\cdot \sqrt[4]{{\sigma }_t\cdot p}}$$

.Value $${\tau }_{\max }^{\mathrm{to}}$$

calculated by solving a system of two equations. One of which is the linear equation τ = С + tφ · σ _n , which describes the straight-line section of the “strength certificate” in the area of comprehensive non-uniform compression, characterized by the values of conditional adhesion C and the corresponding angle of internal friction φ. Wherein $$C=\frac{\sqrt[\mathrm{four}]{{\sigma }_t\cdot p}\cdot \left(\sqrt{{\sigma }_t}+\sqrt{p}\right)}{2}$$

and $$tg\varphi =\frac{\sqrt{p}-\sqrt{{\sigma }_t}}{2\cdot \sqrt[\mathrm{four}]{{\sigma }_t\cdot p}}$$

.

и касающегося предельной огибающей.The second equation was the expression for the limit circle of Mohr crossing the abscissa axis of the "strength certificate" at $${\sigma }_3^M$$

and concerning the ultimate envelope.

приняло вид:After algebraic transformations, the expression is relatively $${\tau }_{\max }^{\mathrm{to}}$$

took the form:

$${\tau }_{\max }^{\mathrm{to}}=\frac{3}{2}\cdot \sqrt{p\cdot {\sigma }_t}+\frac{p}{{\sigma }_t}\cdot \frac{\left(p-3\cdot {\sigma }_t\right)}{\mathrm{four}}$$

служат результаты сопоставления значений τ_max, определенных предлагаемым способом и стандартным расчетным методом построения паспорта прочности по данным определения пределов прочности при одноосном сжатии и растяжении (ГОСТ 21153.8-88 «Породы горные. Метод определения предела прочности при объемном сжатии. Приложение 2 обязательное. Методы построения паспорта прочности»). При этом в качестве исходных данных для расчетного метода были использованы значения пределов прочности σ_с и σ_р, определенные в соответствии со способом-прототипом и с использованием способа по патенту РФ №2435955, кл. E21C 39/00, G01N 3/08, 2011.Experimental justification for determining the maximum shear resistance $${\tau }_{\max }^{\mathrm{to}}$$

the results of comparing the values of τ _max determined by the proposed method and the standard calculation method for constructing a strength certificate according to the determination of tensile strengths under uniaxial compression and tension (GOST 21153.8-88 "Mountain rocks. Method for determining the tensile strength during bulk compression) are used. Appendix 2 is mandatory. Construction methods strength certificates ”). Moreover, as the initial data for the calculation method, we used the values of tensile strengths σ _s and σ _p determined in accordance with the prototype method and using the method according to the RF patent No. 2435955, class. E21C 39/00, G01N 3/08, 2011.

Table 3 shows the dimensionless values of the maximum shear resistance τ _max (in fractions of σ _t ) for rocks or brittle materials characterized by the fragility index K _xp (ratio σ _c / σ _p ) in the range from 5 to 20. The deviation of the determination results varied in in the range from -6 to + 6% with an increase in the fragility index and amounted, on average, to less than 3.5%, which is comparable with the accuracy of the methods.

, и диапазона сжимающих минимальных главных нормальных напряжений, равного предельному сопротивлению срезу (сцеплению) τ₀. Диапазону разрушения путем сдвига на паспорте прочности соответствует диапазон максимальных касательных напряжений с минимальными главными нормальными напряжениями от предельного сопротивления срезу τ₀ до предела прочности при одноосном сжатии σ_c.The theoretical justification for determining the Poisson's ratio µ _σ is the experimentally established geomechanical similarity of the Poisson's ratio and the ratio of the ranges of ultimate stresses on the “rock strength certificate” corresponding to fracture by rupture and shear. The fracture range by rupture on the strength certificate is the sum of the range of tensile minimum principal normal stresses equal to the ultimate tensile strength under comprehensive tensile stress $${\sigma }_{\mathrm{at}R}^{\mathrm{to}}$$

, and the range of compressive minimum principal normal stresses equal to the ultimate shear resistance (adhesion) τ ₀ . The range of fracture by shear on the strength certificate corresponds to the range of maximum tangential stresses with minimum principal normal stresses from ultimate shear resistance τ ₀ to ultimate strength under uniaxial compression σ _c .

After algebraic transformations, the expression with respect to μ _σ takes the form:

. $${\mu }_{\sigma }=2\cdot \frac{{\sigma }_t}{p}\cdot \frac{\left(2+\sqrt{p/{\sigma }_t}\right)}{\left(\mathrm{one}+\sqrt{p/{\sigma }_t}\right)}$$

.

The experimental justification for determining the Poisson's ratio μ _σ is the results of comparing the values determined by the proposed method with the values of μ ^k determined by a known indirect method (RF patent No. 2447284, class E21C 39/00, G01N 3/08, 2012) and with calculated dimensionless parameters method of constructing a strength certificate according to the determination of tensile strength under uniaxial compression and tension (GOST 21153.8-88 "Mountain rocks. Method for determining the tensile strength in bulk compression. Appendix 2 is mandatory. Methods for constructing a passport and strength ”). In this case, the initial data for the calculation method were used the values of tensile strengths under uniaxial compression σ _c and tension σ _p determined by the method of loading with spherical indenters, and the sum of dimensionless parameters of the calculation method (K ₁ + q ₁ ) was used as an analog of the Poisson coefficient and q ₂ , in the physical sense similar to the Poisson's ratio μ _σ

Table 4 presents the values of the Poisson's ratios µ _σ and µ ^k and the sum of dimensionless parameters (K ₁ + q ₁ ) and q ₂ for rocks or brittle materials characterized by the fragility index K _xp (ratio σ _c / σ _p ) in the range from 5 up to 20. Comparison of the calculated values of the Poisson's ratio indicates a completely acceptable convergence of the results. The deviation of the values of μ _σ determined by the proposed method, as a rule, did not exceed 10% and, on average, amounted to 8% compared to the results of determination by the known indirect method.

As an example of the effectiveness of using the method, table 5 presents the results of comparative mechanical tests to determine the complex of mechanical characteristics of Cambrian clay (Metrostroy, St. Petersburg), performed according to the proposed method, as well as by the calculation method according to GOST 21153.8-88 “Mountain rocks. Method for determining the strength in bulk compression. Appendix 2 is mandatory. Methods for constructing a strength certificate "and by conducting volumetric tests in accordance with GOST 21153.8-88" Mountain rocks. Method for determining the strength in bulk compression. "

The mechanical properties of Cambrian clay calculated by the calculation method were based on experimental data on the uniaxial tensile and compression strength limits determined by the prototype method and amounted to 0.437 and 2.59 MPa, respectively.

Tests for volumetric compression of cylindrical samples of Cambrian clay were carried out in a BV-21 transcendental deformation stabilometer connected to a pump station designed to create a working fluid pressure of up to 60 MPa and mounted on a TsDM-100 hydraulic press, designed to create a compressive force of up to 100 tons . To build a strength certificate, we used the results of determining the tensile strengths σ ₁ for given values of lateral hydrostatic pressure σ ₃ in the range from 0.5 to 6.0 MPa. The value of the maximum shear resistance according to the determination of tensile strengths under volume compression was calculated as the maximum (asymptotic) value of the limiting shear stresses corresponding to the limiting Mohr stress circles.

, определенного предлагаемым способом от аналогичных экспериментальных и расчетных значений составило -2,4 и -5,8%, соответственно. Отклонение значения предела прочности $${\sigma }_{вр}^{к}$$

образцов кембрийской глины при всестороннем растяжении от расчетного значения σ₀ составило 8,3%.Comparison of the calculated values of the mechanical properties of Cambrian clay in various ways indicates a completely acceptable convergence of the results. Value deviation $${\tau }_{\max }^{\mathrm{to}}$$

determined by the proposed method from similar experimental and calculated values was -2.4 and -5.8%, respectively. Tensile Strength Deviation $${\sigma }_{\mathrm{at}R}^{\mathrm{to}}$$

Cambrian clay samples under comprehensive tension from the calculated value of σ ₀ amounted to 8.3%.

The deviation of the value of the Poisson's ratio µ _σ = 0.36, determined by the proposed method, from similar values µ ^k = 0.36 and (K ₁ + q ₁ ) + q ₂ = 0.37, determined by a known indirect method (RF patent No. 2447284, class E21C 39/00, G01N 3/08, 2012) and according to GOST 21153.8-88 “Mountain rocks. Method for determining the tensile strength in bulk compression. Appendix 2 is mandatory. Methods for constructing a strength certificate ”, amounted to -0.9 and -4.5%, respectively.

The implementation of the method allows to significantly simplify testing, increase the accuracy and informativeness of determining the mechanical properties of rocks and materials having a brittle nature of destruction, an affordable and highly productive method of loading samples of arbitrary, including irregular, shape with spherical indenters.

Table 1 The method for determining the mechanical properties of rock samples and materials No. Name of mountain Proposed Prototype method Deviation p / p breed or fragile way % results material L _l D _opt F D h F mm mm cm ² mm mm cm ² one 2 3 four 5 6 7 8 9 one Marl 8 four 1.01 8 3.8 0.96 5.3 2 Crosslinking marl with siltstone 7.5 5 1.18 7 5 1.10 7.1 3 Siltstone-1 9 6 1.70 9 6.5 1.84 -7.7 four Siltstone-2 eleven 4.8 1,66 eleven 4.8 1,66 0 5 Mudstone 9.5 7 2.09 9 7 1.98 5,6 6 Limestone-1 9.5 6.2 1.85 11.5 5.5 1.99 -6.9 7 Limestone-2 7 four 0.88 7 four 0.88 0 8 Marble 6 3,5 0.66 6 3.2 0.60 9,4 9 Sandstone 1 10.5 7 2,31 9.5 7.5 2.24 3.2 10 Sandstone 2 7 3,7 0.81 7 3,5 0.77 5.7 eleven Andesite 8.8 6.8 1.88 8.6 6.6 1.78 5,4 12 Dolerite 6.5 4.1 0.84 6.3 3.9 0.77 8.5 13 Amphibolite 8.5 7.5 2.00 8.5 7 1.87 7.1 fourteen Gneiss gabbro four 3,5 0.44 four 3.3 0.41 6.1 fifteen Granite 12.5 6.5 2,55 eleven 7 2.42 5.5 16 Cambrian clay fourteen 9.5 4.18 13.3 10.5 4.39 -4.8 17 Coal 11.1 4.2 1.46 eleven 3.8 1.31 11.5 eighteen Iron ore 14.2 8 3.57 fourteen 7.7 3.39 5,4 19 Gypsum 11.5 10.5 3.79 eleven 10 3.46 9.8 twenty Rosin 9.5 7 2.09 10.5 6.5 2.14 -2.6 21 Epoxy resin four 3.2 0.40 3.9 3,1 0.38 5.9 22 Equivalent material (sand epoxy) 20.5 19 12.24 twenty 18.5 11.62 5.3

Tab. 2 The method for determining the mechanical properties of rock samples and materials No. Indicator Dimensionless Strength Deviation p / p fragility in full tension % results K _xp = σ _c / σ _p

(предлагаемый способ) $${\sigma }_{\mathrm{at}R}^{\mathrm{to}}/{\sigma }_t$$

(proposed method) σ _o / σ _t (calculation by
GOST 21153.8-88) one 2 3 four 5 one 5.51 2.00 1.84 8.8 2 6.09 2.00 1.85 7.9 3 6.67 2.00 1.86 7.3 four 8.38 2.00 1.89 5.9 5 10.63 2.00 1.90 5,0 6 12.85 2.00 1.92 4.1 7 15.60 2.00 1.93 3.6 8 18.33 2.00 1.94 3.3 9 21.58 2.00 1.94 3.0

Table 3 No. Indicator Indicator Dimensionless values Deviation p / p the ultimate fragility maximum resistance results intense K _xp = σ _c / σ _p cut τ _max / σ _t % state proposed according to GOST K = p / σ _t way 21153.8-88 one 2 3 four 5 6 one 7 5.51 10.97 11.61 -5.5 2 8 6.09 14.24 14.81 -3.8 3 9 6.67 18.00 18.54 -2.9 four 12 8.38 32,20 32.51 -1.0 5 16 10.63 58.00 57.94 0.1 6 twenty 12.85 91.71 90.49 1.3 7 25 15.60 145.00 140.93 2.9 8 thirty 18.33 210.72 201.72 4,5 9 36 21.58 306.00 289.25 5.8

Table 4 The method for determining the mechanical properties of rock samples of materials No. Indicator Coefficient Coefficient Amount Deviation p / p fragility Poisson's μ _σ Poisson µ ^to parameters results K _xp = σ _c / σ _p (K ₁ + q ₁ ) + q ₂ definitions (proposed (indirect (according to coefficients way) way) GOST Poisson,% 21153.8-88) one 2 3 four 5 6 one 5.51 0.36 0.40 0.42 8.7 2 6.09 0.32 0.34 0.36 7.9 3 6.67 0.28 0.30 0.31 7.4 four 8.38 0.20 0.22 0.22 7.1 5 10.63 0.15 0.16 0.15 7.6 6 12.85 0.12 0.13 0.11 8.4 7 15.60 0.09 0.10 0.09 9.3 8 18.33 0.08 0.09 0,07 10,2 9 21.58 0.06 0,07 0.06 11.2

Table 5 The method for determining the mechanical properties Determination of strength at Estimated method for The proposed method volumetric compression GOST 21153.8-88 GOST 21153.8-88 Side Axial Maxi Limit Maxi Limit Maxi pressure pressure little strength little strength little σ ₃ , MPa σ _1, MPa resist at resist at resist laziness completely laziness completely laziness cut ronnem cut ronnem cut MPa stretching MPa stretching MPa MPa MPa one 2 3 four 5 6 7 0.5 4.47 4.02 1,5 6.91 3.0 9.00 9.62 3.30 0.456 3.42 0.494 3.22 5,0 11.50 10.50 6.0 12.66 11.26

Claims (1)

1. A method for determining the mechanical properties of rock samples and materials, including loading the sample with two counter-directed spherical indenters before it splits, fixing the destructive force, determining in the destroyed sample the surface area of the separation crack passing through the loading axis, and the geometric parameters of the destroyed zones in the contact areas with both spherical indenters, calculation of tensile tensile stress of the specimen and average compressive stress at the boundary of the largest x zones and determination of the tensile strength and shear resistance as the mechanical properties of the sample, characterized in that a composite sample is collected from the fragments of the destroyed sample, at the ends of which the geometric parameters of the destroyed zones are determined - the diameter of the residual fingerprints from the indenters and the length of the puncture holes along the surface of the separation crack, determine the surface area of the larger destroyed zone at the contact with indenters according to the formula:
F = π · D _otp · L _l ,
where F is the surface area of the larger destroyed zone;
D _OT - the diameter of the residual imprint from the indenter;
L _l - the length of the hole puncture along the surface of the separation gap;
π = 3.14,
and as the mechanical properties of the specimen, the ultimate tensile strength is determined $${\sigma }_{\mathrm{at}R}^{\mathrm{to}}$$

maximum shear resistance $${\tau }_{\max }^{\mathrm{to}}$$

and Poisson's ratio µ _σ by the formulas:
$${\sigma }_{\mathrm{at}R}^{\mathrm{to}}=2\cdot {\sigma }_t$$

;
$${\tau }_{\max }^{\mathrm{to}}=\frac{3}{2}\cdot \sqrt{p\cdot {\sigma }_t}+\frac{p}{{\sigma }_t}\cdot \frac{\left(p-3\cdot {\sigma }_t\right)}{\mathrm{four}}$$

;
$${\mu }_{\sigma }=2\cdot \frac{{\sigma }_t}{p}\cdot \frac{\left(2+\sqrt{p/{\sigma }_t}\right)}{\left(\mathrm{one}+\sqrt{p/{\sigma }_t}\right)}$$

where σ _t is the tensile stress of the rupture of the sample;
p is the average compressive stress at the boundary of the largest of the destroyed zones.

Images