Method for obtaining ice-rock interface tensile strength

Abstract

The application discloses an ice-rock interface tensile strength acquisition method and belongs to the technical field of freeze-thaw rock measurement. The acquisition method comprises the following steps: acquiring the rough interface width between ice-rock interfaces, the rough interface height and the freezing temperature; obtaining the micro-unit tensile stress generated by the ice-rock interface bonding effect according to the freezing temperature; and calculating the ice-rock interface tensile strength according to the rough interface width between the ice-rock interfaces, the rough interface height and the micro-unit tensile stress. The application solves the problem of difficulty in obtaining the ice-rock interface tensile strength on site.

Description

Technical Field

[0001] This application relates to the field of freeze-thaw rock measurement technology, specifically to a method for obtaining the tensile strength of the ice-rock interface. Background Technology

[0002] The ice-rock interface refers to the interface between ice and rock. The tensile strength of the ice-rock interface is an important geotechnical parameter in cold regions. Measuring the tensile strength of the ice-rock interface is of great significance for engineering projects in cold regions, especially for preventing rock slope collapses, tunnel frost heave cracking, and bridge foundation frost heave cracking in high-altitude and cold areas.

[0003] Currently, parameters related to the tensile strength of the ice-rock interface are extremely scarce. Obtaining ice-rock interface samples in the field is extremely difficult; even under field conditions, the interface may melt or break due to limitations in the environment and sampling equipment, making it virtually impossible to obtain tensile strength parameters for the ice-rock interface in the field. Furthermore, laboratory testing of the tensile strength of the ice-rock interface is subject to strict limitations on sample preparation, loading season temperature, experimental equipment, and operation, making it equally challenging to obtain the required tensile strength. Summary of the Invention

[0004] This application provides a method for obtaining the tensile strength of the ice-rock interface, which can solve the problem of difficulty in obtaining the tensile strength of the ice-rock interface in the prior art.

[0005] In a first aspect, embodiments of this application provide a method for obtaining the tensile strength of an ice-rock interface, the method comprising:

[0006] Obtain the width, height, and freezing temperature of the rough interface between the ice and rock.

[0007] The micro-unit tensile stress generated by the bonding effect at the ice-rock interface is obtained based on the freezing temperature.

[0008] The tensile strength of the ice-rock interface is calculated based on the width and height of the rough interface between the ice and rock interfaces and the tensile stress of the micro-units.

[0009] In one embodiment, the width of the rough interface, the height of the rough interface, and the freezing temperature between the ice and rock interfaces are all obtained based on actual on-site measurements.

[0010] In one embodiment, the micro-unit tensile stress τ adh for:

[0011]

[0012] Where B is a constant, τ adh0 θ represents the initial tensile stress at the ice-rock interface, and θ is the temperature difference between the freezing temperature and zero degrees Celsius.

[0013] In one embodiment, the initial tensile stress τ at the ice-rock interface adh0 for:

[0014]

[0015] Where, α ice T is a temperature-related parameter. freeze T is the solidification temperature. ref As the reference temperature, γ LV For surface tension, δ ice θ is the molecular distance between ice and rock. c-RMS f(h) is the surface contact angle. RMS ) represents the proportion of ice in contact with the matrix, and T represents the freezing temperature.

[0016] In one implementation, the tensile stress τ of the micro-unit is determined based on experimental data. adh Simplified to:

[0017]

[0018] In one embodiment, the tensile strength σ of the ice-rock interface t for:

[0019]

[0020] Where S is the rough interface area of ​​the ice-rock interface, and A is the projected area of ​​the ice-rock interface.

[0021] In one embodiment, the rough interface area S of the ice-rock interface is derived through cylindrical specimen testing, including:

[0022] The cylindrical sample was cut into a cross-section to form multiple protrusions, serving as a rough interface between ice and rock. The highest point of the middle protrusion was located in the plane of the diameter, and the protrusions were symmetrically arranged on both sides of the diameter. Using an approximation method, the inclined surface of each protrusion was approximated as a trapezoid. The rough interface area S of the ice-rock interface was: S = 2(S1 + S2 + ... + S...). i ), where i represents the label of the trapezoid from the diameter to the circumference.

[0023] In one embodiment, the area of ​​each trapezoid is:

[0024]

[0025] Where D is the diameter of the cylinder; a is the width of the bottom edge of each of the protrusions, i.e., the width of the rough interface; and c is the height of each of the protrusions, i.e., the height of the rough interface.

[0026] In one embodiment, the rough interface area S of the ice-rock interface is:

[0027]

[0028] In one embodiment, the tensile strength σ of the ice-rock interface t Specifically:

[0029]

[0030] The beneficial effects of the technical solutions provided in this application include at least the following:

[0031] By obtaining the rough interface width, rough interface height, and freezing temperature between the ice and rock interfaces, the tensile strength of the ice-rock interface can be calculated. Since the rough interface width, rough interface height, and freezing temperature can be measured on-site and the required parameters are few, it is not necessary to obtain ice-rock interface samples on-site. The subsequent calculation process can be performed off-site, thus solving the problem of obtaining the tensile strength of the ice-rock interface on-site.

[0032] Since the calculated parameters are actual measurements taken on-site, a comparison between the theoretical calculation results and the experimental data revealed that the error between the theoretical calculation results and the experimental data is very small, and they can be used as the basis for theoretical calculations. Attached Figure Description

[0033] Figure 1 This is a schematic flowchart illustrating an embodiment of the method for obtaining the tensile strength of the ice-rock interface according to this application.

[0034] Figure 2 This is a schematic top view of the circular rough surface in an embodiment of this application;

[0035] Figure 3 This is a schematic diagram of the protrusion structure in an embodiment of this application;

[0036] Figure 4 This is a schematic diagram comparing the theory and experiment when c takes different values ​​in this application;

[0037] Figure 5 This is a schematic diagram comparing theoretical and experimental results at different freezing temperatures in this application. Detailed Implementation

[0038] To enable those skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present application, and not all embodiments. Based on the embodiments of the present application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present application.

[0039] The terms "comprising" and "having," and any variations thereof, in the specification, claims, and accompanying drawings of this application are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or apparatus that includes a series of steps or units is not limited to the steps or units listed, but may optionally include steps or units not listed, or may optionally include other steps or units inherent to such process, method, product, or apparatus.

[0040] To make the objectives, technical solutions, and advantages of this application clearer, the embodiments of this application will be described in further detail below with reference to the accompanying drawings.

[0041] In a first aspect, embodiments of this application provide a method for obtaining the tensile strength of the ice-rock interface, solving the problem in the prior art that it is difficult to obtain the tensile strength of the ice-rock interface in the field.

[0042] Reference Figure 1 This is a flowchart illustrating an embodiment of the method for obtaining the tensile strength of the ice-rock interface according to this application. The ice-rock interface refers to the interface between ice and rock, which is a rough interface. The aforementioned method includes the following steps:

[0043] S1. Obtain the width, height, and freezing temperature of the rough interface between the ice and rock.

[0044] S2. Based on the above freezing temperature, the micro-unit tensile stress generated by the bonding effect at the ice-rock interface is obtained.

[0045] S3. Calculate the tensile strength of the ice-rock interface based on the obtained width and height of the rough interface and the tensile stress of the micro-units.

[0046] In step S1 above, the width of the rough interface, the height of the rough interface, and the freezing temperature between the ice and rock can all be obtained based on actual on-site measurements.

[0047] In step S2 above, a micro-unit refers to dividing the ice-rock interface into countless small units using calculus. Each small unit is called a micro-unit, and each micro-unit contains bonding forces between ice and rock particles. The bonding force between these ice and rock particles is called the micro-unit tensile stress. According to Vyalow's research, the micro-unit tensile stress τ... adh It can be represented as:

[0048]

[0049] Where B is a constant, τ adh0 θ represents the initial tensile stress at the ice-rock interface, and θ is the temperature difference between the freezing temperature and zero degrees Celsius.

[0050] The above-mentioned initial tensile stress τ adh0 The derivation can be simplified to:

[0051]

[0052] Where, α ice T is a temperature-related parameter. freeze T is the solidification temperature. ref As the reference temperature, γ LV For surface tension, δ ice θ is the molecular distance between ice and rock. c-RMS f(h) is the surface contact angle. RMS ) represents the proportion of ice in contact with the matrix, and T represents the freezing temperature.

[0053] Since most of the parameters in the above theoretical calculations are micro-parameters, it is difficult to obtain all of them through experiments. Based on the experimental data in the literature (Vyalov SS. Rheological Properties and Bearing Capacitypf Permafrost [in Russian], Izd.Akad.Nauk SSSR, Moscow.1950.) referring to formula (2), the following empirical formula (3) is used to obtain the tensile stress τ of the micro-element. adh .

[0054]

[0055] In step S3 above, the tensile strength σ of the ice-rock interface is calculated. t The formula can be derived based on ice-rock interface experiments. The basic formula is as follows:

[0056]

[0057] Where S is the rough interface area of ​​the ice-rock interface, and A is the projected area of ​​the ice-rock interface.

[0058] In some embodiments, the rough interface area S is derived through a cylindrical specimen experiment. This experiment includes: preparing a specimen by wire-cutting the cross-section of a cylindrical specimen into a wavy shape to form multiple protrusions, representing the rough interface between ice and rock. (See reference...) Figure 2 The diameter of the circular cross-section is D. The entire circle is divided into segments D / a. The highest point of a central protrusion is located in the plane containing diameter D, and protrusions are symmetrically arranged on both sides of this diameter. (Refer to...) Figure 3 'a' represents the width of the bottom edge of each protrusion, i.e., the width of the rough interface; 'c' represents the height of each protrusion, i.e., the height of the rough interface.

[0059] Since the interior of the convex wavy surface is an inclined plane while the edge is curved, it is difficult to represent using the surface equation. Therefore, an approximation method is used, that is, the curve of the circumference is represented as a straight line, and the curved trapezoid is modified into a trapezoid. The calculation process is relatively convenient. It is equivalent to two trapezoids forming a convexity. As the line cut is farther away from the center of the circle and closer to the circumference, the upper and lower bases of each trapezoid change. The approximate area of ​​the entire surface is derived as follows:

[0060] Starting from the diameter and moving to one side, the area of ​​the first trapezoid is:

[0061]

[0062] The area of ​​the second trapezoid is:

[0063]

[0064] The area of ​​the third trapezoid is:

[0065]

[0066] The area of ​​the i-th trapezoid is:

[0067]

[0068] Since the entire surface is symmetrical from left to right, the rough interface area S of the ice-rock interface is:

[0069] S = 2(S1 + S2 + ... + S) i (9)

[0070] Furthermore, the rough interface area S of the ice-rock interface is:

[0071]

[0072] Substituting into the above formula (4), the tensile strength σ of the ice-rock interface t for:

[0073]

[0074] Combining this with the above formula (2), the tensile strength σ of the ice-rock interface t for:

[0075]

[0076] Finally, substituting into the empirical formula (3), we get:

[0077]

[0078] As can be seen from formula (12), the tensile strength of the ice-rock interface is related to the freezing temperature, which mainly affects the electrostatic constant α between the compensating water and ice.ice Furthermore, it was found that freezing temperature was also related to the "bumps" on the rock surface, among which... It can be expressed as a functional relationship related to the roughness JRC of the ice-rock rough interface.

[0079] Based on current literature, roughness joint profiles are categorized into three types: straight, wavy, and sawtooth, and functional relationships are established accordingly.

[0080] Straight (0≤JRC≤8)

[0081] JRC=12.862R+10.316arctan(100R a -4.017 R 2 =0.908 (14)

[0082] Wavy (8≤JRC≤16)

[0083] JRC = 2.719R + 0.585arctan(100R) a ) 2 +6.169 R 2 =0.924 (15)

[0084] Serrated (16≤JRC≤20)

[0085] JRC=10.544R+0.327arctan(100R a ) 2 +10.377 R 2 =0.908 (16)

[0086] In this application, Li Zhong implements the following, and the expressions for each parameter are as follows:

[0087]

[0088]

[0089] In tensile strength This can be represented using JRC piecewise functions as follows:

[0090] Straight (0≤JRC≤8)

[0091]

[0092] Wavy (8≤JRC≤16)

[0093]

[0094] Serrated (16≤JRC≤20)

[0095]

[0096] Based on the experimental conditions, the values ​​of c were 0, 2, 3, 4, and 5 mm, and the values ​​of freezing temperature θ were -10, -20, -30, -40, and -50℃, respectively. The relationship between the value of c (related to roughness) and the tensile strength curve, as well as the relationship between freezing temperature and tensile strength curve, were obtained through theoretical calculations and compared with the experimental data.

[0097] Reference Figure 4 The graph shows a comparison of the theoretical curves and experimental data of tensile strength for different values ​​of c. (Refer to...) Figure 5 This is a comparison graph showing the theoretical curves and experimental data of tensile strength at different freezing temperatures θ. By comparing the experimental results with the theoretically derived calculations, it can be seen that the theoretical curve of tensile strength derived from theory is within the error range of the experimental data.

[0098] In summary, the method for obtaining the tensile strength of the ice-rock interface in this application only requires the width and height of the rough interface between the ice and rock, as well as the freezing temperature, to calculate the tensile strength. Furthermore, a comparison between the theoretical calculation results and experimental data reveals that the errors are very small. This method enables the rapid on-site determination of the ice-rock interface tensile strength parameters based on relevant parameters, serving applications in cold-region engineering. It solves the problem of the difficulty in obtaining the tensile strength of the ice-rock interface on-site.

[0099] It should be noted that the sequence numbers of the embodiments in this application are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments.

[0100] In some processes described in the embodiments of this application, multiple operations or steps are included in a specific order. However, it should be understood that these operations or steps may not be executed in the order they appear in the embodiments of this application, or they may be executed in parallel. The sequence number of the operation is only used to distinguish different operations, and the sequence number itself does not represent any execution order. In addition, these processes may include more or fewer operations, and these operations or steps may be executed sequentially or in parallel, and these operations or steps may be combined.

[0101] The above are merely preferred embodiments of this application and do not limit the patent scope of this application. Any equivalent structural or procedural transformations made using the content of this application's specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of this application.

Claims

1. A method for obtaining the tensile strength of an ice-rock interface, characterized in that, The acquisition method includes: Obtain the width, height, and freezing temperature of the rough interface between the ice and rock. The micro-unit tensile stress generated by the ice-rock interface bonding effect is obtained based on the freezing temperature. , ,in B It is a constant. The initial tensile stress at the ice-rock interface, θ The difference between the freezing temperature and zero degrees Celsius; Calculate the tensile strength of the ice-rock interface based on the width and height of the rough interface and the tensile stress of the micro-unit. , ,in A Let be the projected area of ​​the ice-rock interface. S The rough interface area of ​​the ice-rock interface, the S Derived through cylindrical specimen experiments, including: The cross-section of the cylindrical sample was line-cut to form multiple protrusions, serving as a rough interface between ice and rock. The highest point of the middle protrusion was located in the plane of the diameter, and the protrusions were symmetrically arranged on both sides of the diameter. An approximation method was used to approximate the slope of each protrusion as a trapezoid. The rough interface area of ​​the ice-rock interface... S for: ,in i The designation indicates a trapezoid extending from the diameter towards the circumference.

2. The method for obtaining the tensile strength of the ice-rock interface as described in claim 1, characterized in that, The width, height, and freezing temperature of the rough interface between the ice and rock were all obtained based on actual on-site measurements.

3. The method for obtaining the tensile strength of the ice-rock interface as described in claim 1, characterized in that, The initial tensile stress at the ice-rock interface for: in, For parameters related to temperature, This is the solidification temperature. As the reference temperature, For surface tension, The molecular distance between ice and rock. The surface contact angle, The proportion of ice in contact with the matrix, T This is the freezing temperature.

4. The method for obtaining the tensile strength of the ice-rock interface as described in claim 3, characterized in that, Based on experimental data, the tensile stress of the micro-unit is... Simplified to: 。 5. The method for obtaining the tensile strength of the ice-rock interface as described in claim 1, characterized in that, The area of ​​each trapezoid is: in, D The diameter of the cylinder; a The width of the bottom edge of each of the protrusions, i.e., the width of the rough interface; c The height of each of the protrusions, i.e., the height of the rough interface.

6. The method for obtaining the tensile strength of the ice-rock interface as described in claim 5, characterized in that, The rough interface area of ​​the ice-rock interface S for: 。 7. The method for obtaining the tensile strength of the ice-rock interface as described in claim 6, characterized in that, The tensile strength of the ice-rock interface Specifically: 。

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