Method for measuring layered density of aeolian sand

Abstract

The invention discloses a method for measuring layered density of aeolian sand. The method comprises the following steps: a water tank with an open top is arranged in advance, the bottom of the water tank is communicated with a plurality of connecting pipes, each connecting pipe is vertically provided with a pressure measuring pipe, a floating plate floating on the water surface is arranged in the water tank, and a sand containing box is fixed on the floating plate; when the whole floating plate and the sand containing box float stably and the height of the water column in the pressure measuring pipe is stable, the initial height of the water column in the pressure measuring pipe is recorded; aeolian sand layers with the thickness of d are added into the sand containing box in batches, the change value of the height delta h of a water column in the pressure measuring pipe is recorded, and the mass, the volume and the density of aeolian sand of the layer under the height change of delta h are calculated; the steps are repeated, it is assumed that the number of the aeolian sand layers is n, and when the total thickness of the aeolian sand layers reaches D, the sand layer final mass mtotal and the total density rho total of the total thickness D of the aeolian sand layers are calculated; and finally carrying out recursive calculation to obtain the layering density of each aeolian sand. The invention aims to provide a layered density measurement method capable of measuring each layer of aeolian sand.

Description

Technical Field

[0001] The invention relates to the technical field of aeolian sand measurement, and in particular to a method for measuring the layered density of aeolian sand. Background Art

[0002] Aeolian sand is a layer of sand that is blown and deposited by the wind. In permafrost areas, a large amount of aeolian sand caused by desertification covers and accumulates on the surface. The accumulation thickness of aeolian sand can reach several meters, which changes the surface environment and seriously affects the occurrence of frozen soil. However, the impact of aeolian sand on frozen soil is still unclear. When the thickness of aeolian sand accumulation is different, there are large differences in the processes such as heat conduction and water transfer of the sand layer, and the impact on the underlying frozen soil is also different, which is related to the change in density after the aeolian sand is accumulated. Aeolian sand is piled up together. Due to pressure and other effects, the density of the bottom, middle, top and each layer of the sand layer is different, resulting in different water, heat and other properties of each layer. At present, there is a lack of a method for measuring the density of layers after the accumulation of aeolian sand. Therefore, there is an urgent need for a method for measuring the density of each layer of aeolian sand. Summary of the invention

[0003] The purpose of the present invention is to overcome the above-mentioned deficiencies in the prior art and to provide a method for measuring the layered density of each layer of aeolian sand.

[0004] To achieve the above object, the present invention is implemented through the following technical solutions:

[0005] A method for measuring the density of aeolian sand layers, the steps are as follows:

[0006] (1) A water tank with an open top is pre-arranged, and a plurality of connecting pipes are connected to the bottom of the water tank. A pressure measuring tube is vertically arranged on each connecting pipe. A floating board floating on the water surface is provided in the water tank, and a sand box is fixed on the floating board;

[0007] (2) When the floating plate and the sand box float stably as a whole and the height of the water column in the pressure measuring tube is stable, record the initial height of the water column in the pressure measuring tube;

[0008] (3) Add a layer of aeolian sand with a thickness of d to the sand container in batches, record the change in the height Δh of the water column in the pressure measuring tube, and calculate the mass, volume, and density of the aeolian sand layer under the change in height Δh;

[0009] (4) Repeat step (3), assuming that there are n layers of aeolian sand. When the total thickness of the aeolian sand layer reaches D, calculate the final mass m of the sand layer with a total thickness of D. total , total density ρ total ;

[0010] (5) Finally, the density of each aeolian sand layer is obtained by recursive calculation.

[0011] Furthermore, in step (3), the floating plate is subjected to the gravity of the aeolian sand and squeezes the water downward into the connecting pipe and then into the pressure measuring pipe. The pressure F generated by the aeolian sand squeezing the water water Equivalent to the weight of water entering the piezometer:

[0012] F water =ρ water ·g·A·Δh (1)

[0013] Where Δh is the height difference of the water in the piezometer, A is the cross-sectional area of ​​the piezometer, and ρ water is the density of water, g is the acceleration due to gravity. Each time a layer of wind-blown sand with a thickness of d is added, the water column in the pressure tube rises by Δh i Corresponding to the additional pressure F water,i , we can get the mass m of the newly added aeolian sand for the i-th time i for:

[0014] m i =ρ water ·A·Δh i (2)

[0015] Among them, m t is the mass of newly added aeolian sand in the i-th layer, Δh i is the change in the height of the water column in the piezometer after the i-th layer of aeolian sand is added. After the i-th new addition of aeolian sand, the total mass of the i-th layer of aeolian sand in the sandbox is:

[0016]

[0017] Among them, m k is the mass of the kth layer of aeolian sand, and the volume of each layer of newly added aeolian sand is V i The newly added thickness d of the layer and the bottom area S of the sandbox yield:

[0018] V i =S·d i (4)

[0019] Accumulated to the i-th layer, the total volume is V total,i for:

[0020]

[0021] Among them, d k is the thickness of the kth layer of aeolian sand, and the density is calculated as Substituting formula (3) and formula (5) into the density calculation formula, we can get the initial density ρ of the i-th layer of aeolian sand: i,init for:

[0022]

[0023] Furthermore, in step (4), when the aeolian sand is added n times to reach the final total thickness D, the final mass of the aeolian sand at this thickness is M total for:

[0024]

[0025] Total density of sand layer ρ total The density formula and formula (7) can be used to calculate:

[0026]

[0027] Furthermore, in step (5), assuming that when the aeolian sand reaches the final total thickness D, the density of each layer in the sand layer increases with the compaction of the upper sand layer. At this time, a recursive formula is defined to calculate the final compaction density of each layer from top to bottom, and the density of the top layer remains unchanged, that is, ρ n,final =ρ n,init , recursively from the top to the bottom, for each layer i below the top, according to the cumulative pressure P of the upper layer i Inversely deduce its final compaction density, assuming that the compaction relationship is:

[0028] ρ i,final =ρ i,init ·(1+α·P i ) (9)

[0029] Among them, P i is the cumulative pressure on the i-th layer, α is the compaction coefficient of aeolian sand. After the compaction coefficient α is obtained by a suitable method, the sand layer pressure of the i-th layer is calculated from the mass and gravity of the upper sand layer:

[0030]

[0031] Starting from the top nth layer, the final density of all i layers can be obtained as:

[0032]

[0033] Furthermore, the compaction coefficient α can be obtained through compaction experiments. When conducting compaction experiments, a container is prepared and filled with aeolian sand. The volume change of aeolian sand is measured under different pressure conditions. When no external pressure is applied, the initial volume of aeolian sand is V0. The external pressure is gradually increased, and the volume V of aeolian sand is measured at each pressure level. P , until the applied pressure no longer produces a significant change in volume, which is considered to have reached the maximum pressure. At this time, the compaction coefficient can be obtained by two fitting methods:

[0034] The first one, the empirical exponent n, is more adaptable to the nonlinear behavior that occurs during the compaction process:

[0035]

[0036] Where P is the applied external pressure, which can be logarithmically transformed for ease of fitting:

[0037]

[0038] The second method is to fit the simple compression coefficient α, which shows that there is a roughly linear relationship between the density increment and the pressure change. The curve fitting method is used to fit the compression coefficient α:

[0039] Δρ=ρ init ·α·P (14)

[0040] Among them, Δρ is the density increment caused by the applied pressure P, that is, the density change of aeolian sand, ρ init is the initial density of aeolian sand before pressure is applied.

[0041] Compared with the prior art, the present invention has the following beneficial effects:

[0042] The present invention solves the technical problem of measuring the stratification of aeolian sand on the surface of permafrost areas, and can obtain the stratified density of each layer of aeolian sand. Based on the change in the height of the water column in the pressure measuring tube, the degree of pressure of the aeolian sand on the water in the sand box can be obtained, and then the mass of the sand can be inferred. The experimental difficulty is relatively low. At the same time, it will not be affected by the volume and accumulation state of the sand. In actual experiments, if you want to accurately obtain the stratified density of each layer, the head pressure is the simplest and most reliable means. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 It is a schematic diagram of the structure of the pressure measuring tube and the water tank in the present invention;

[0044] Figure 2 for Figure 1 Top view of the .

[0045] Reference numerals:

[0046] 1-pressure measuring tube, 2-connecting pipe, 3-water tank, 4-sand box, 5-floating board. DETAILED DESCRIPTION

[0047] The present invention will be described in detail below with reference to the accompanying drawings and in conjunction with embodiments.

[0048] like Figure 1 and Figure 2 As shown, a method for measuring the density of aeolian sand layers, the steps are as follows:

[0049] (1) A water tank 3 with an open top is pre-arranged, and a plurality of connecting pipes 2 are connected to the bottom of the water tank 3. A piezometer 1 is vertically arranged on each connecting pipe 2. A floating board 5 floating on the water surface is provided in the water tank 3, and a sand box 4 is fixed on the floating board 5. This method can obtain the density of each layer by adding aeolian sand layer by layer and measuring the change in the head pressure of the piezometer 1. When aeolian sand is loaded into the sand box 4 and placed in water, the aeolian sand in the sand box 4 will exert pressure on the water, causing the water to be squeezed and flow to the piezometer 1. By measuring the change in the height of the water column in the piezometer 1, the degree of pressure exerted by the aeolian sand in the sand box 4 on the water can be understood, and then the mass of the sand can be inferred, and the volume can be obtained by the increased sand layer thickness and the bottom area of ​​the sand box 4, and finally the layered density of the sand layer can be obtained.

[0050] (2) When the floating plate 5 and the sand box 4 float stably as a whole and the height of the water column in the pressure measuring tube 1 is stable, the initial height of the water column in the pressure measuring tube 1 is recorded.

[0051] (3) Add a layer of aeolian sand with a thickness of d to the sand container 4 in batches, record the change in the height Δh of the water column in the pressure measuring tube 1, and calculate the mass, volume, and density of the aeolian sand layer under the height change of Δh. The specific method is:

[0052] The floating plate 5 is subjected to the gravity of the aeolian sand and squeezes the water downward to the connecting pipe 2 and then enters the pressure measuring pipe 1. The pressure F generated by the aeolian sand squeezing the water water Equivalent to the weight of water entering the piezometric tube 1:

[0053] F water =ρ water ·g·A·Δh (1)

[0054] Where Δh is the height difference of water in the pressure measuring tube 1, A is the cross-sectional area of ​​the pressure measuring tube 1, and ρ water is the density of water, g is the acceleration due to gravity. Each time a layer of wind-blown sand with a thickness of d is added, the water column in the pressure measuring tube 1 rises by Δh i Corresponding to the additional pressure F water,i , we can get the mass m of the newly added aeolian sand for the i-th time i for:

[0055] m i =ρ water ·A·Δh i (2)

[0056] Among them, m i is the mass of newly added aeolian sand in the i-th layer, Δh i is the change in the height of the water column in the pressure measuring tube 1 after the i-th layer of aeolian sand is added. After the i-th new addition of aeolian sand, the total mass of the i-th layer of aeolian sand in the sand box 4 is:

[0057]

[0058] Among them, m k is the mass of the kth layer of aeolian sand, and the volume of each layer of newly added aeolian sand is V i The newly added thickness d of the layer and the bottom area S of the sandbox 4 yield:

[0059] V i =S·d i (4)

[0060] Accumulated to the i-th layer, the total volume is V total,i for:

[0061]

[0062] Among them, d k is the thickness of the kth layer of aeolian sand, and the density is calculated as Substituting formula (3) and formula (5) into the density calculation formula, we can get the initial density ρ of the i-th layer of aeolian sand: i,init for:

[0063]

[0064] (4) Repeat step (3), assuming that there are n layers of aeolian sand. When the total thickness of the aeolian sand layer reaches D, calculate the final mass m of the sand layer with a total thickness of D. total , total density ρ total The specific method is:

[0065] When the aeolian sand is added n times to reach the final total thickness D, the final mass of the aeolian sand at this thickness is M total for:

[0066]

[0067] Total density of sand layer ρ total The density formula and formula (7) can be used to calculate:

[0068]

[0069] (5) Finally, the density of each aeolian sand layer is obtained by recursive calculation. The specific method is:

[0070] Assuming that when the aeolian sand reaches the final total thickness D, the density of each layer in the sand layer increases with the compaction of the sand layer above. At this time, a recursive formula is defined to calculate the final compaction density of each layer from top to bottom, and the density of the top layer remains unchanged, that is, ρ n,final =ρ n,init , recursively from the top to the bottom, for each layer i below the top, according to the cumulative pressure P of the upper layer i Inversely deduce its final compaction density, assuming that the compaction relationship is:

[0071] ρ i,final =ρ i,init ·(1+α·P i ) (9)

[0072] Among them, P i is the cumulative pressure on the i-th layer, and α is the compaction coefficient of the aeolian sand. The compaction coefficient α reflects the degree of compression of the aeolian sand when it is subjected to the pressure of the upper layer. The compaction coefficient α can be obtained through the compaction experiment. When conducting the compaction experiment, a container is prepared, filled with aeolian sand, and the volume change of the aeolian sand is measured under different pressure conditions. When no external pressure is applied, the initial volume of the aeolian sand is V0, and the external pressure is gradually increased, and the volume V of the aeolian sand is measured at each pressure level. P , until the applied pressure no longer produces a significant change in volume, which is considered to have reached the maximum pressure. At this time, the compaction coefficient can be obtained by two fitting methods:

[0073] The first one, the empirical exponent n, is more adaptable to the nonlinear behavior that occurs during the compaction process:

[0074]

[0075] Where P is the applied external pressure, which can be logarithmically transformed for ease of fitting:

[0076]

[0077] The empirical exponent n can fit the actual experimental data more accurately, especially under high pressure, and has stronger adaptability.

[0078] The second method is to fit the simple compression coefficient α, which shows that there is a roughly linear relationship between the density increment and the pressure change. Through the experimental data, the compression coefficient α is obtained by using the curve fitting method:

[0079] Δρ=ρ init ·α·P (14)

[0080] Among them, Δρ is the density increment caused by the applied pressure P, that is, the density change of aeolian sand, ρ init is the initial density of aeolian sand before pressure is applied.

[0081] The simple compaction coefficient fitting calculation and operation are simpler and more convenient, and are suitable for situations where the density changes are small.

[0082] After obtaining the compaction coefficient using a suitable method, the pressure of the sand layer in the i-th layer is calculated from the mass and gravity of the upper sand layer:

[0083]

[0084] Starting from the top nth layer, the final density of all i layers can be obtained as:

[0085]

[0086] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for measuring the density of aeolian sand layers, characterized in that: Here are the steps: (1) a water tank (3) with an open top is arranged in advance, a plurality of connecting pipes (2) are connected to the bottom of the water tank (3), a pressure measuring tube (1) is vertically arranged on each connecting pipe (2), a floating board (5) floating on the water surface is provided in the water tank (3), and a sand container (4) is fixed on the floating board (5); (2) When the floating plate (5) and the sand box (4) float stably as a whole and the height of the water column in the pressure measuring tube (1) is stable, the initial height of the water column in the pressure measuring tube (1) is recorded; (3) adding a layer of aeolian sand with a thickness of d into the sand container (4) in batches, recording the change in the height Δh of the water column in the pressure measuring tube (1), and calculating the mass, volume and density of the aeolian sand layer under the height change of Δh; (4) Repeat step (3), assuming that there are n layers of aeolian sand. When the total thickness of the aeolian sand layer reaches D, calculate the final mass m of the sand layer with a total thickness of D. total , total density ρ total ; (5) Finally, the density of each aeolian sand layer is obtained by recursive calculation.

2. A method for measuring the density of aeolian sand layers according to claim 1, characterized in that: In step (3), the floating plate (5) is subjected to the gravity of the aeolian sand and squeezes the water downward into the connecting pipe (2) and then into the pressure measuring pipe (1). The pressure F generated by the aeolian sand squeezing the water water Equivalent to the weight of water entering the piezometric tube (1): F esyrt =ρ ester ·g·A·Δh (1) Where, Δh is the height difference of water in the pressure tube (1), A is the cross-sectional area of ​​the pressure tube (1), and ρ water is the density of water, g is the acceleration due to gravity, and each time a layer of aeolian sand with a thickness of d is added, the water column in the pressure tube (1) rises by Δh i Corresponding to the additional pressure F water,i , we can get the mass m of the newly added aeolian sand for the i-th time i for: m i =ρ water ·A·Δh i (2) Among them, m i is the mass of newly added aeolian sand in the i-th layer, Δh i is the change in the height of the water column in the piezometer (1) after the i-th layer of aeolian sand is added. After the i-th new addition of aeolian sand, the total mass of the i-th layer of aeolian sand in the sand container (4) is: Among them, m k is the mass of the kth layer of aeolian sand, and the volume of each layer of newly added aeolian sand is V i The newly added thickness d of the layer and the bottom area S of the sandbox (4) yield: V i =S·d i (4) Accumulated to the i-th layer, the total volume V total,i for: Among them, d k is the thickness of the kth layer of aeolian sand, and the density is calculated as Substituting formula (3) and formula (5) into the density calculation formula, we can get the initial density ρ of the i-th layer of aeolian sand: i,init for:

3. A method for measuring the density of aeolian sand layers according to claim 1, characterized in that: In step (4), when the aeolian sand is added n times to reach the final total thickness D, the final mass of the aeolian sand at this thickness is M total for: Total density of sand layer ρ total The density formula and formula (7) can be used to calculate:

4. A method for measuring the density of aeolian sand layers according to claim 1, characterized in that: In step (5), assuming that when the aeolian sand reaches the final total thickness D, the density of each layer in the sand layer increases with the compaction of the upper sand layer. At this time, a recursive formula is defined to calculate the final compaction density of each layer from top to bottom, and the density of the top layer remains unchanged, that is, ρ n,final =ρ n,init , recursively from the top to the bottom, for each layer i below the top, according to the cumulative pressure P of the upper layer i Inversely deduce its final compaction density, assuming that the compaction relationship is: r i,final =ρ i,init ·(1+α·P i ) (9) Among them, P i is the cumulative pressure on the i-th layer, α is the compaction coefficient of aeolian sand. After the compaction coefficient α is obtained by a suitable method, the sand layer pressure of the i-th layer is calculated from the mass and gravity of the upper sand layer: Starting from the top nth layer, the final density of all i layers can be obtained as:

5. A method for measuring the density of aeolian sand layers according to claim 4, characterized in that: The compaction coefficient α can be obtained through compaction experiments. When conducting compaction experiments, a container is prepared and filled with aeolian sand. The volume change of aeolian sand is measured under different pressure conditions. When no external pressure is applied, the initial volume of aeolian sand is V0. The external pressure is gradually increased, and the volume V of aeolian sand is measured at each pressure level. P , until the applied pressure no longer produces a significant change in volume, which is considered to have reached the maximum pressure. At this time, the compaction coefficient can be obtained by two fitting methods: The first one, the empirical exponent n, is more adaptable to the nonlinear behavior that occurs during the compaction process: Where P is the applied external pressure, which can be logarithmically transformed for ease of fitting: The second method is to fit the simple compression coefficient α, which shows that there is a roughly linear relationship between the density increment and the pressure change. The curve fitting method is used to fit the compression coefficient α: Dr=r init ·a·P (14) Where Δρ is the density increment caused by the applied pressure P, i.e. the density change of aeolian sand, and ρ init is the initial density of aeolian sand before pressure is applied.

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