A method for preparing and dynamically testing frozen gravel samples in combination with DIC technology

By preparing and testing surface dyed homogeneous frozen gravel samples, combined with DIC technology and Hopkinson press rod testing system, the problem of difficulty in detecting stress and strain fields of geological materials in the existing technology in high-altitude mountainous areas has been solved, and the frozen gravel has been achieved Efficient detection and dynamic mechanical testing of samples.

CN118758695BActive Publication Date: 2025-02-11TIANJIN UNIV
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Patent Information

Application Number
CN202410961450.0
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2024-07-17
Publication Date
2025-02-11
Estimated Expiration
2044-07-17

AI Technical Summary

Technical Problem

The prior art is difficult to effectively detect stress and strain fields on artificial samples of water, ice and gravel mixed in alpine mountains, which leads to hindering the study of the mechanical properties of geological materials in alpine mountains.

Method used

Using a frozen gravel sample preparation and dynamic testing method that can be combined with DIC technology, the surface dyed homogeneous frozen gravel sample is prepared and clamped into the Hopkinson press rod test system with an ambient cryogenic box. The incident rod is used to apply the injection wave and perform data recording to realize the dynamic mechanical test of the sample.

Benefits of technology

Effective detection of the stress and strain field of frozen gravel samples is achieved, and a laboratory sample preparation method is provided that more accurately simulates the freezing process of rock materials in high-altitude mountainous areas is supported, which is an in-depth analysis and study of the mechanical properties of geological materials in high-altitude mountainous areas.

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Abstract

The present invention discloses a frozen gravel sample preparation and dynamic testing method that can be combined with DIC technology, and relates to the field of rock material preparation, processing and detection technology. The method includes: preparing a homogeneous frozen gravel sample with surface dyeing; clamping the sample between the incident rod and the transmission rod of a Hopkinson pressure bar test system with an environmental low temperature box; applying an incident wave to the incident rod and recording data. The present invention can perform dynamic mechanical testing on special rock and soil bodies existing in simulated high-cold mountainous areas in the laboratory.
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Description

Technical Field

[0001] The invention relates to the technical field of rock material preparation, processing and detection, and in particular to a frozen gravel sample preparation and dynamic testing method that can be combined with DIC technology. Background Art

[0002] With the development of computer, optics and other disciplines, material measurement methods have made new progress. Digital image correlation (DIC) has been widely used and developed as a non-contact measurement method for measuring material stress and strain fields, especially in the measurement of relevant mechanical properties of rock-like materials.

[0003] Alpine mountainous areas are widely distributed in my country, and engineering construction in these areas has ushered in a new round of climax. In order to better support local engineering construction, in-depth research on local geological materials is needed.

[0004] At present, the dynamic research on rock-like samples mostly uses the Hopkinson pressure bar and the corresponding modified equipment to simulate the corresponding engineering geological environment to dynamically load the samples. The stress and strain detection in the dynamic loading of the samples are mostly strain gauges, acoustic emission, DIC and other technologies. However, DIC technology requires the use of the before and after changes of the speckle image as the basic analysis data. The traditional speckle paper cannot be well pasted on samples such as ice, especially artificial samples of water, ice and gravel mixtures that simulate the real geological conditions of high-cold mountainous areas. The lack of corresponding stress and strain field detection technology during the experiment will hinder the corresponding theoretical research, and then affect the economic construction and social development of high-cold mountainous areas.

[0005] Therefore, it is an urgent problem for those skilled in the art to propose a frozen gravel sample preparation and dynamic testing method that can be combined with DIC technology to solve the difficulties existing in the prior art. Summary of the invention

[0006] In view of this, the present invention provides a frozen gravel sample preparation and dynamic testing method that can be combined with the DIC technology. It is a speckle preparation method that can apply the DIC technology on frozen rock and soil. Combined with the internationally used Hopkinson pressure bar test system, dynamic mechanical tests are further carried out in the laboratory on special rock and soil bodies that simulate the high-altitude mountainous areas.

[0007] In order to achieve the above object, the present invention adopts the following technical solution:

[0008] A frozen gravel sample preparation and dynamic testing method that can be combined with DIC technology includes the following steps:

[0009] S1. Prepare a homogenous frozen gravel sample with surface dyeing;

[0010] S2, clamp the sample between the incident bar and the transmission bar of the Hopkinson pressure bar test system with an environmental low temperature box;

[0011] S3. The incident rod applies the incident wave and records the data.

[0012] In the above method, optionally, S1 prepares a homogeneous frozen gravel sample with surface dyeing, and the specific steps are as follows:

[0013] S101. Determine the relevant dimensions of the frozen gravel sample: Use a cutting machine to cut the original rock sample and drill the core, select fine-grained granite with an overall grayish white color and a particle size of 0.2 to 1 mm as the basic material of the gravel in the sample, and select gravel particles with a particle size of 0 mm to 3 mm and 3 mm to 5 mm respectively;

[0014] S102, crushing gravel and screening debris: crushing fine-grained granite with a crusher, screening particles, selecting debris with a particle size of 0 mm-3 mm and 3 mm-5 mm, and focusing on selecting rock debris with a particle size aspect ratio close to 1:1 as the basic material of the frozen gravel sample;

[0015] S103. Preparation of saturated frozen gravel sample: prepare a silicone mold with a hole on the top according to the preset overall size of the sample, pour in one-third of the height of the debris with the same particle size range, inject pure water to the same height, stir, repeat three times, and finally make the height of the debris particles flush with the height of the mold; place the silicone mold on a vibration table and vibrate for 60 seconds, let it stand for 48 hours, and then freeze the sample in different low temperature environments for 24 hours to obtain a saturated frozen gravel sample;

[0016] S104, preparation of a porous film: prepare a porous film with an adhesive tape in advance, and punch holes in the film using a program set by a computer;

[0017] S105. Surface melting and refreezing of saturated frozen gravel sample: The saturated frozen gravel sample prepared in step S103 is placed in a silicone mold with holes on the top, and the low temperature environment temperature is adjusted to between zero and one degree, and the surface is melted to a certain extent for several minutes, so that the surface frozen gravel is exposed, and the mold is turned upside down to allow the melted water to flow out through the perforated cover of the mold, and then the low temperature environment is reset to the original temperature to freeze the sample again;

[0018] The melting rate of ice on the sample surface is related to the gravel content, ice content, sample surface area, heat transfer coefficient, and ambient temperature, and can be empirically estimated using the following formula:

[0019]

[0020] Where V is the melting rate of ice, in m / s; K1 is the empirical coefficient; J1 is the proportionality coefficient; S1 is the surface area occupied by gravel, in m 2 ; J2 is the proportionality coefficient; S2 is the surface area occupied by ice, in m 2 ; T0 is the initial sample freezing temperature, in °C; T n is the current ambient temperature, in °C; q is the proportionality coefficient; M is the total mass of the sample, in kg; S is the total surface area of ​​the sample, in m 2 ;

[0021] S106. Pasting of porous film: Put the porous film tightly on the side of the sample in a low temperature environment, and paste the two end surfaces of the film with adhesive tape;

[0022] S107, sample surface dyeing: Use dark acrylic paint to color the film. The dye will dye the gravel surface at the corresponding position at the small hole, forming a speckle image that can be used for DIC technology on the sample surface. After dyeing, continue to cover the film on the sample surface for 24 hours. During this period, use paper that can absorb dye to absorb excess dye, and perform additional dyeing on the areas where the dye is not obvious;

[0023] S108. Resaturated freezing of gravel samples: remove the film on the outside of the sample after stable staining, place it in the original silicone mold with holes on the top, add pure water to fill the surface cracks, freeze the sample in the original low temperature environment for 24 hours, and then grind the end face of the sample in this low temperature environment to ensure that the contact surface with the loading end is not pure ice, and finally obtain a homogeneous frozen gravel sample with surface staining that meets ISRM specifications and can be combined with the DIC method.

[0024] In the above method, optionally, in S104, the film itself is impermeable to dye and cannot be dyed.

[0025] The above method is optional. In S2, the sample is clamped between the incident rod and the transmission rod of the Hopkinson pressure bar test system with an environmental low temperature box. Specifically, lubricant is applied to both end surfaces of the sample, the center axis of the sample is aligned with the center axis of the incident rod and the transmission rod, so that the incident rod, the sample, and the transmission rod are on the same axis, and a camera is set up to prepare to shoot the sample.

[0026] Specifically, during the test, the sample is located in an environmental low-temperature box throughout the entire process, and the incident rod and the transmission rod are inserted into the box from both sides of the box to load the sample; the incident rod and the transmission rod are made of the same material and have the same manufacturing process. Both rods are pasted with strain gauges and connected to a data processing system. A transmitting device is provided in front of the incident rod, and a shaper is provided on the front end surface of the incident rod.

[0027] The above method is optional, in S3, the incident rod applies an incident wave and records the data, specifically: the experimenter starts the transmitting device after a safety warning, the experimenter records the first incident strain pulse received by the strain gauge of the incident rod and the reflected strain pulse after the stress wave is reflected, records the transmitted strain pulse received by the strain gauge on the transmission rod, the camera records the image data, and imports it into the corresponding processing software for data processing.

[0028] Through the above technical solutions, it can be known that compared with the prior art, the present invention provides a frozen gravel sample preparation and dynamic testing method that can be combined with the DIC technology, which has the following beneficial effects: the surface staining method of the present invention can provide a speckle preparation method for frozen gravel and other low-temperature artificial samples; the sample preparation method of the present invention can provide an empirical estimation formula for estimating the melting rate of the surface ice layer for frozen gravel and other low-temperature artificial samples; the sample preparation method of the present invention provides a method for preparing low-temperature artificial samples such as frozen gravel with different particle gradings; the low-temperature preparation process of the present invention can prepare a laboratory sample preparation method that more accurately simulates the freezing process of rock materials in high-cold mountainous areas; the dynamic testing method of the present invention can obtain an experimental method that can use the DIC technology to detect the stress and strain field of low-temperature artificial samples, and further realize the analysis and research of the mechanical properties of geological materials in the real environment of high-cold mountainous areas. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.

[0030] Figure 1 A flow chart of a frozen gravel sample preparation and dynamic testing method that can be combined with DIC technology provided by the present invention;

[0031] Figure 2 A flow chart for preparing a homogeneous frozen gravel sample with surface dyeing provided by the present invention;

[0032] Figure 3 A schematic diagram of a frozen gravel sample before dyeing provided by the present invention;

[0033] Figure 4 A schematic diagram of a porous film provided by the present invention;

[0034] Figure 5 A schematic diagram of a frozen gravel sample after dyeing provided by the present invention;

[0035] Figure 6A schematic diagram of a combination of a frozen gravel sample and a Hopkinson pressure bar test system with an environmental low temperature box provided by the present invention;

[0036] Description of reference numerals:

[0037] 1 is a gravel particle; 2 is pure water; 3 is ice; 4 is a frozen gravel sample; 5 is a dyeing point; 6 is a film; 7 is a film hole; 8 is an adhesive tape; 9 is an incident rod; and 10 is a transmission rod. DETAILED DESCRIPTION

[0038] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0039] In this application, relational terms such as first and second, etc. are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. The terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of more restrictions, the elements defined by the sentence "comprise one..." do not exclude the existence of other identical elements in the process, method, article or device including the elements.

[0040] Reference Figure 1-6 As shown, the present invention discloses a frozen gravel sample preparation and dynamic testing method that can be combined with DIC technology, comprising the following steps:

[0041] S1. preparing a homogenous frozen gravel sample 4 with surface dyeing;

[0042] S2, clamping the sample between the incident rod 9 and the transmission rod 10 of the Hopkinson pressure bar test system with an environmental low temperature box;

[0043] S3. The incident rod 9 applies an incident wave and records data.

[0044] Further, see Figure 2 As shown, S1 prepares a surface-dyed homogenized frozen gravel sample 4, and the specific steps are as follows:

[0045] S101. Determine the relevant dimensions of the frozen gravel sample 4: Use a cutting machine to cut the original rock sample and drill the core, select fine-grained granite with an overall grayish white color and a particle size of 0.2 to 1 mm as the basic material of the gravel in the sample, and according to the method recommended by the International Society for Rock Mechanics and Engineering (ISRM), when using a 50 mm diameter SHPB for impact testing, the gravel size should be less than 5 mm, so the rock debris particle sizes selected are 0 mm-3 mm and 3 mm-5 mm respectively. Gravel particles 1;

[0046] S102, crushing gravel and screening debris: refer to Figure 3 As shown, fine-grained granite is crushed by a crusher, the particles are screened, gravel particles 1 with a particle size of 0mm-3mm and 3mm-5mm are selected, and rock fragments with a particle size aspect ratio close to 1:1 are concentratedly selected as the basic material of the frozen gravel sample;

[0047] S103. Preparation of saturated frozen gravel samples: prepare a silicone mold with a hole on the top according to the preset overall size of the sample, pour in one-third of the height of debris of the same particle size range, inject pure water 2 to the same height, stir, repeat three times, and finally make the height of the debris particles flush with the height of the mold; considering the volume growth of water in the process of freezing into ice 3, the water surface height should be lower than the mold height by a certain distance, so that the pure water 2 and the gravel particles 1 can be fully in contact; place the silicone mold on a vibration table and vibrate for 60 seconds, let it stand for 48 hours, and then freeze the sample in different low temperature environments for 24 hours to obtain a saturated frozen gravel sample 4; in order to meet the ISRM requirements for flatness and verticality, it is necessary to grind the end face of the sample in a low temperature environment, and ensure that the contact surface with the loading end is not pure ice. Through the above steps, a uniform sample that meets the ISRM requirements and conforms to the assumption of continuous medium mechanics can be obtained;

[0048] S104, Preparation of porous film: refer to Figure 4 As shown, in order to realize the arrangement of speckles on the sample surface in combination with the DIC technology, a film 6 with an adhesive tape 8 needs to be prepared in advance, and the film is punched using a computer-set program. The film holes 7 are of uniform size and have a high surface coverage rate. Each dot occupies 5-10 pixels.

[0049] S105. Surface melting and refreezing of saturated frozen gravel sample: The saturated frozen gravel sample 4 prepared in step S103 is placed in a silicone mold with holes on the top, and the low temperature environment temperature is adjusted to between zero and one degree, and the surface is melted to a certain extent for several minutes, so that the surface frozen gravel is exposed, and the mold is turned upside down to allow the melted water to flow out through the perforated cover of the mold, and then the low temperature environment is reset to the original temperature to freeze the sample again; this step is to make the ice layer that may cover the surface of the sample disappear, expose the surface of the particles, so that all dyes can be dyed on the gravel surface during dyeing;

[0050] The melting rate of ice on the sample surface is related to the gravel content, ice content, sample surface area, heat transfer coefficient, and ambient temperature, and can be empirically estimated using the following formula:

[0051]

[0052] In the formula: the relevant parameters can be obtained through a series of experiments, V is the ice melting rate, the unit is m / s; K1 is the empirical coefficient; J1 is the proportionality coefficient; S1 is the surface area occupied by gravel, the unit is m 2 ; J2 is the proportionality coefficient; S2 is the surface area occupied by ice, in m 2 ; T0 is the initial sample freezing temperature, in °C; T n is the current ambient temperature, in °C; q is the proportionality coefficient; M is the total mass of the sample, in kg; S is the total surface area of ​​the sample, in m 2 ;

[0053] S106, pasting the porous film: tightly cover the porous film on the side of the sample in a low temperature environment, and paste the two end surfaces of the film 6 with adhesive tape 8;

[0054] S107, sample surface dyeing: Use low-temperature-resistant, wear-resistant, and water-resistant dark acrylic paint to paint the film 6. Since the film 6 itself is impermeable to dye and cannot be dyed, the dye will dye the gravel surface at the corresponding position at the small hole, thereby forming a speckle image that can be used for DIC technology on the sample surface; in order to ensure that the dye is stably dyed and does not diffuse randomly, it is necessary to continue to cover the film on the sample surface for 24 hours after dyeing. During this period, it is necessary to use dye-absorbent paper to absorb excess dye, and perform additional dyeing on the areas where the dye is not obvious;

[0055] S108, gravel sample resaturation freezing: refer to Figure 5As shown, the film on the outside of the sample after stable staining at staining point 5 is removed, and placed in the original silicone mold with holes on the top, pure water 2 is added to fill the surface cracks, and the sample is frozen in the original low temperature environment for 24 hours. After that, the end face of the sample is polished in this low temperature environment to ensure that the contact surface with the loading end is not pure ice, and finally a homogeneous frozen gravel sample that meets ISRM specifications and can be combined with DIC method for surface staining is obtained.

[0056] Furthermore, in S104, the film 6 itself is impermeable to dye and cannot be dyed.

[0057] Further, see Figure 6 As shown, in S2, the sample is clamped between the incident rod 9 and the transmission rod 10 of the Hopkinson pressure bar test system with an environmental low temperature box. Specifically, a proper amount of lubricant is applied to both end surfaces of the sample to reduce the friction effect caused by the sample and the end surfaces of the test rod, the center axis of the sample is aligned with the center axis of the incident rod 9 and the transmission rod 10, so that the incident rod 9, the sample, and the transmission rod 10 are on the same axis, and a camera is set up to prepare to shoot the sample.

[0058] Furthermore, during the test, the sample is located in the ambient low temperature box throughout the test, and the incident rod 9 and the transmission rod 10 penetrate into the box from both sides of the box and load the sample;

[0059] Furthermore, the incident rod 9 and the transmission rod 10 are made of the same material and have the same manufacturing process. Both rods are attached with strain gauges and connected to a data processing system to detect the strain pulses of the incident rod 9 and the transmission rod 10, and further calculate the strain. A launching device is provided in front of the incident rod 9, so that a bullet can be used to apply a stress wave to the incident rod and transmit it to the sample. In addition, a shaper is provided on the front end face of the incident rod 9 for waveform shaping.

[0060] Furthermore, in S3, the incident rod 9 applies an incident wave and records data, specifically: the experimenter starts the transmitting device after a safety warning, and records the first incident strain pulse received by the strain gauge of the incident rod 9 and the reflected strain pulse after the stress wave is reflected, and records the transmitted strain pulse received by the strain gauge on the transmission rod 10. The camera records the image data, which is imported into the corresponding processing software for data processing, and the experiment ends here.

[0061] Each embodiment in this specification is described in a progressive manner, and the same or similar parts between the embodiments can refer to each other, and each embodiment focuses on the differences from other embodiments. In particular, for the system or system embodiment, since it is basically similar to the method embodiment, the description is relatively simple, and the relevant parts can refer to the partial description of the method embodiment. The system and system embodiments described above are merely schematic, wherein the units described as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, they may be located in one place, or they may be distributed on multiple network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the scheme of this embodiment. Ordinary technicians in this field can understand and implement it without creative work.

[0062] The above description of the disclosed embodiments enables one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for preparing and dynamically testing frozen gravel samples in combination with DIC technology, characterized in that: The following steps are involved: S1. Prepare a homogeneous frozen gravel sample with surface dyeing, the specific steps are as follows: S101. Determine the relevant dimensions of the frozen gravel sample: Use a cutting machine to cut the original rock sample and drill the core, select fine-grained granite with an overall grayish white color and a particle size of 0.2-1 mm as the basic material of the gravel in the sample, and select gravel particles with a particle size of 0 mm-3 mm and 3 mm-5 mm respectively; S102, crushing gravel and screening debris: crushing fine-grained granite with a crusher, screening particles, selecting debris with a particle size of 0 mm-3 mm and 3 mm-5 mm, and focusing on selecting rock debris with a particle size aspect ratio close to 1:1 as the basic material of the frozen gravel sample; S103. Preparation of saturated frozen gravel sample: prepare a silicone mold with a hole on the top according to the preset overall size of the sample, pour in one-third of the height of the debris with the same particle size range, inject pure water to the same height, stir, repeat three times, and finally make the height of the debris particles flush with the height of the mold; place the silicone mold on a vibration table and vibrate for 60 seconds, let it stand for 48 hours, and then freeze the sample in different low temperature environments for 24 hours to obtain a saturated frozen gravel sample; S104, preparation of a porous film: prepare a porous film with an adhesive tape in advance, and punch holes in the film using a program set by a computer; S105. Surface melting and refreezing of saturated frozen gravel sample: The saturated frozen gravel sample prepared in S103 is placed in a silicone mold with holes on the top, and the low temperature environment temperature is adjusted to between zero and one degree, and the surface is melted to a certain extent for several minutes, so that the surface frozen gravel is exposed, and the mold is turned upside down to allow the melted water to flow out through the perforated cover of the mold, and then the low temperature environment is reset to the original temperature to freeze the sample again; S106. Pasting of porous film: Put the porous film tightly on the side of the sample in a low temperature environment, and paste the two end surfaces of the film with adhesive tape; S107, sample surface dyeing: Use dark acrylic paint to color the film. The dye will dye the gravel surface at the corresponding position at the small hole, forming a speckle image for DIC technology on the sample surface. After dyeing, continue to cover the film on the sample surface for 24 hours. During this period, use paper that can absorb dye to absorb excess dye, and perform additional dyeing on the areas where the dye is not obvious; S108, re-saturation freezing of gravel sample: remove the film on the outside of the sample after stable dyeing, place it in the original silicone mold with holes on the top, add pure water to fill the surface cracks, freeze the sample in the original low temperature environment for 24 hours, and then grind the end face of the sample in the low temperature environment to ensure that the contact surface with the loading end is not pure ice, and finally obtain a homogeneous frozen gravel sample that meets ISRM specifications and can be combined with DIC method for surface dyeing; S2, clamp the sample between the incident bar and the transmission bar of the Hopkinson pressure bar test system with an environmental low temperature box; S3. The incident rod applies the incident wave and records the data.

2. A method for preparing and dynamically testing frozen gravel samples in combination with DIC technology according to claim 1, characterized in that: In S104, the film itself is impermeable to the dye and cannot be dyed.

3. A method for preparing and dynamically testing frozen gravel samples in combination with DIC technology according to claim 1, characterized in that: In S2, the sample is clamped between the incident rod and the transmission rod of the Hopkinson pressure bar test system with an environmental low temperature box. Specifically, lubricant is applied to both end surfaces of the sample, the center axis of the sample is aligned with the center axis of the incident rod and the transmission rod, so that the incident rod, the sample, and the transmission rod are on the same axis, and a camera is set up to prepare to shoot the sample.

4. A method for preparing and dynamically testing frozen gravel samples in combination with DIC technology according to claim 3, characterized in that: During the test, the sample is located in the ambient low temperature box throughout the test. The incident rod and the transmission rod penetrate into the box from both sides of the box and load the sample. The incident rod and the transmission rod are made of the same material and have the same manufacturing process. Both rods are pasted with strain gauges and connected to the data processing system. A transmitting device is provided in front of the incident rod, and a shaper is provided on the front end face of the incident rod.

5. A method for preparing and dynamically testing frozen gravel samples in combination with DIC technology according to claim 1, characterized in that: In S3, the incident rod applies an incident wave and records the data. Specifically, the experimenter starts the transmitting device after giving a safety warning. The experimenter records the first incident strain pulse received by the strain gauge of the incident rod and the reflected strain pulse after the stress wave is reflected. The transmission strain pulse received by the strain gauge on the transmission rod is recorded. The camera records the image data and imports it into the corresponding processing software for data processing.

Citation Information

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