Method for calculating dynamic ice pressure of earth and rockfill dam under action of wave and wind load

Abstract

The invention discloses a method for calculating the dynamic ice pressure of an earth and rockfill dam under the action of waves and wind loads. The method comprises the steps that local ice calculation parameters at the average temperature for many years in winter are obtained through a test; arranging wave measuring equipment in a water area in front of the earth and rockfill dam, and collecting winter wave parameters of the water area; calculating the limit wave height of ice layer cracking according to the ice calculation parameters and the water area winter wave parameters; comparing the limit wave height of ice layer cracking with the measured maximum wave height of the water area, and determining whether the ice layer generates cracks or not; and calculating the critical ice thickness when the ice layer is bent and damaged under the condition that the crack exists or does not exist, comparing the critical ice thickness with the measured actual ice thickness in front of the dam, determining the types of the ice layers, dividing the ice layers into single-layer ice and overlapped ice, and substituting the ice layers into different formulas to calculate the dynamic ice pressure generated by the wave and wind load effects on the dam slope of the earth and rockfill dam. The method for calculating the dynamic ice pressure of the earth and rockfill dam under the action of the waves and the wind loads, provided by the invention, better conforms to the actual condition of the dam slope of the earth and rockfill dam, and has the advantages of high applicability and high calculation precision.

Description

Technical Field

[0001] The invention relates to a method for calculating the dynamic ice pressure of an earth-rock dam, and in particular to a method for calculating the dynamic ice pressure of an earth-rock dam under the action of wave and wind loads. Background Art

[0002] Under the action of waves and wind loads, large areas of ice move as a whole, generating dynamic ice pressure on the earth-rock dam slope that hinders the relative movement of the ice layer. This process is accompanied by ice cracking and the generation of overlapping ice. When designing hydraulic structures, in order to ensure the safety of the earth-rock dam slope structure and avoid damage to the structure caused by dynamic ice pressure, it is necessary to calculate the dynamic ice pressure to determine the strength of the structure. Currently, the dynamic ice pressure calculation formula in the "Load Design Code for Hydraulic Structures" (SL744-2016) is generally used for dynamic ice pressure calculation. There are the following problems: (1) Single-layer ice and overlapping ice are not distinguished during calculation, resulting in low calculation accuracy; (2) Poor applicability, and the object of action is limited to the vertical dam surface or other wide and long buildings. Summary of the invention

[0003] Purpose of the invention: The purpose of the invention is to provide a method for calculating the dynamic ice pressure of earth-rock dams under wave and wind loads with strong applicability and high calculation accuracy.

[0004] Technical solution: The method for calculating the dynamic ice pressure of an earth-rock dam under the action of wave and wind loads of the present invention comprises: determining the type of ice layer, wherein the type of ice layer comprises single-layer ice and overlapping ice;

[0005] When the ice layer is a single layer of ice, the calculation formula for the dynamic ice pressure F is:

[0006] F=mλ(0.18b 0.5 h 1.2 σ c +γδvA1sinθ11+0.015βwA2sinθ2)

[0007] Where m is the dam slope shape coefficient; λ is the dam slope coefficient; b is the ice layer width, m; h is the ice layer thickness, m; σ c is the uniaxial compressive strength of ice, kPa; γ is a coefficient related to the surface roughness under the ice layer, and 1 kN˙s / m is used for a single layer of ice. 3 ; δ is the viscosity coefficient of ice; v is the velocity of water under the ice layer, m / s; A1 is the surface area under the ice layer, m 2 ; θ1 is the horizontal angle between the water flow direction and the dam slope, °; β is the contact coefficient, ranging from 0.4 to 0.7; w is the standard wind pressure of the reservoir, kN / m 2 ; A2 is the upper surface area of ​​the ice layer, m 2 ; θ2 is the horizontal angle between the wind speed direction and the dam slope, °;

[0008] When the ice layer is overlapping ice, the calculation formula of dynamic ice pressure F is:

[0009] F=mλ(0.2b 0.5 h 1.1 σ c +γδvA1sinθ1+0.015βwA2sinθ2)

[0010] Where γ is a coefficient related to the surface roughness under the ice layer, and 1.2 kN˙s / m is used for overlapping ice. 3 .

[0011] Furthermore, the method for determining the ice layer type includes:

[0012] The calculation parameters of ice under the local winter multi-year average temperature are obtained through experiments, including ice density ρ, uniaxial compression strength σ c , bending strength σ f , elastic modulus E, Poisson's ratio v; arrange wave measurement equipment in the waters in front of the earth-rock dam to collect winter wave parameters in the waters, including wave height H, wave period T, and wave speed c;

[0013] The limit wave height of ice cracking is calculated based on the calculation parameters of ice and the winter wave parameters of the water area; the elastic thin plate bending theory is introduced, and the limit wave height is the wave height corresponding to the internal stress of the ice layer being the bending strength of the ice; by comparing the limit wave height of ice cracking with the measured maximum wave height of the water area, it is determined whether the ice layer has cracks due to wave fluctuations;

[0014] The critical ice thickness for bending failure of the ice layer with or without cracks is calculated and compared with the actual ice thickness measured in front of the dam to determine the ice layer type.

[0015] Furthermore, if the measured maximum wave height of the water area is ≤ the limit wave height, then no cracks will occur in the ice layer; if the measured maximum wave height of the water area is > the limit wave height, then cracks will occur in the ice layer.

[0016] Furthermore, if the actual ice thickness is ≤ the critical ice thickness, it is single-layer ice; if the actual ice thickness is > the critical ice thickness, it is overlapping ice.

[0017] Furthermore, the critical wave height H for ice breaking max The calculation formula is:

[0018]

[0019] Where L is the length of the ice layer, m.

[0020] Furthermore, in the presence of cracks, the critical ice thickness h for the bending failure of the ice layer is 1max The calculation formula is:

[0021]

[0022] Among them, ε is a coefficient related to the salinity and porosity of ice, which is 0.4 to 0.6; g is the acceleration of gravity, which is 9.8 m / s 2 .

[0023] Furthermore, in the absence of cracks, the critical ice thickness h for bending failure of the ice layer is 2max The calculation formula is:

[0024]

[0025] Among them, ε is a coefficient related to the salinity and porosity of ice, which is 0.4 to 0.6; g is the acceleration of gravity, which is 9.8 m / s 2 .

[0026] Furthermore, the dam slope shape coefficient m is 1 for a rectangle and 0.9 for a polygon or a circle.

[0027] Furthermore, the dam slope coefficient λ is 1 when the dam slope inclination angle is 0° to 15°, and is 0.8 when the dam slope inclination angle is 15° to 45°.

[0028] Furthermore, the viscosity coefficient δ of ice is 1 below -10°C, 0.95 between -10°C and 0°C, and 0.9 above 0°C.

[0029] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages:

[0030] (1) The ice layer types were refined, and different formulas were used to calculate the dynamic ice pressure of single-layer ice and overlapping ice, which improved the calculation accuracy of the dynamic ice pressure of earth-rock dam slope protection.

[0031] (2) The dynamic ice pressure calculation formula takes into account the dam slope parameters, such as the dam slope shape coefficient and the slope coefficient, which is more in line with the actual situation of earth-rock dams and can be used to calculate the dynamic ice pressure of earth-rock dams with different slope ratios and shapes. It solves the limitation problem of the object of dynamic ice pressure in the "Code for Load Design of Hydraulic Structures" (SL744-2016) and has stronger applicability.

[0032] (3) The dynamic ice pressure calculation formula in the Code for Load Design of Hydraulic Structures (SL744-2016) was split and optimized, and the problem of inconsistent units on the left and right sides of the formula was solved. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 It is a flowchart of a method for calculating dynamic ice pressure of an earth-rock dam under the action of wave and wind loads provided by an embodiment of the present invention;

[0034] Figure 2 is a schematic diagram of deformation of an ice layer due to wave fluctuations in an embodiment of the present invention;

[0035] Figure 3 It is a schematic diagram of dynamic ice pressure generated by different types of ice layers on the slope of an earth-rock dam in an embodiment of the present invention. DETAILED DESCRIPTION

[0036] The present invention will be further described below in conjunction with the accompanying drawings.

[0037] like Figure 1 As shown, an embodiment of the present invention provides a method for calculating dynamic ice pressure of an earth-rock dam under wave and wind loads, which specifically includes the following steps:

[0038] (1) The calculation parameters of ice under the local winter multi-year average temperature are obtained through experiments, including ice density ρ, uniaxial compression strength σ c , bending strength σ f , elastic modulus E, Poisson's ratio ν. Wave measurement equipment is arranged in the waters in front of the earth-rock dam to collect winter wave parameters in the waters, including wave height H, wave period T, and wave speed c.

[0039] (2) Based on the calculation parameters of ice and the winter wave parameters of the water area, calculate the limit wave height for ice cracking. Figure 2 As shown in the figure, when the waves in the water area propagate from the upstream to the earth-rock dam, the wave energy generated enters the ice layer from the edge of the ice layer, causing the ice layer to bend and deform. Therefore, the elastic thin plate bending theory is introduced to calculate the bending stress caused by the deformation of the ice layer caused by waves of different wave heights. When the internal stress of the ice layer is the bending strength of the ice, the corresponding wave height is the limit wave height that causes the ice layer to crack.

[0040] The critical wave height H for ice breaking max The calculation formula is:

[0041]

[0042] Among them, H max is the critical wave height for ice layer cracks, m; σ f is the bending strength of ice, kPa; ν is the Poisson's ratio of ice; E is the elastic modulus of ice, kPa; h is the thickness of the ice layer, m; L is the length of the ice layer, m; c is the wave speed, m / s; T is the wave period, s.

[0043] Further, by comparing the extreme wave height of ice cracking with the measured maximum wave height of the water area, it is determined whether the ice layer has cracks due to wave fluctuations. Specifically, if the measured maximum wave height of the water area is ≤ the extreme wave height, the ice layer will not have cracks; if the measured maximum wave height of the water area is > the extreme wave height, the ice layer will have cracks.

[0044] (3) Based on the fact that the internal stress accumulated by the ice layer due to the change of its motion state may cause the ice layer to bend and break, resulting in overlapping ice, the critical ice thickness for bending and breaking of the ice layer with or without cracks is calculated on the basis of whether the ice layer has cracks in step (2) and compared with the actual ice thickness measured in front of the dam to determine the type of ice layer. Specifically, if the actual ice thickness is ≤ the critical ice thickness, it is single-layer ice; if the actual ice thickness is > the critical ice thickness, it is overlapping ice.

[0045] In the presence of cracks, the critical ice thickness h for the bending failure of the ice layer 1max The calculation formula is:

[0046]

[0047] Among them, h 1max is the critical ice thickness for bending failure when there are cracks in the ice layer, m; σ c is the uniaxial compressive strength of ice, kPa; ν is the Poisson's ratio of ice; ε is a coefficient related to the salinity and porosity of ice, generally ranging from 0.4 to 0.6; ρ is the density of ice, kg / m 3 ; g is the acceleration due to gravity, which is 9.8m / s 2 ; E is the elastic modulus of ice, kPa.

[0048] In the absence of cracks, the critical ice thickness h for bending failure of the ice layer is 2max The calculation formula is:

[0049]

[0050] Among them, h 2max is the critical ice thickness for bending failure when there are no cracks in the ice layer, m.

[0051] (4) Calculate the dynamic ice pressure exerted by the ice layer on the slope of the earth-rock dam due to wave and wind loads.

[0052] like Figure 3 As shown in the figure, the dynamic ice pressure generated by the ice layer on the slope of the earth-rock dam due to the action of waves and wind loads includes the squeezing force T1 of the wave on the cross section of the ice layer, the friction force T2 of the wave on the lower surface of the ice layer, and the friction force T3 of the wind load on the upper surface of the ice layer.

[0053] Determining the type of ice layer as single layer ice or overlapping ice according to steps (1) to (3);

[0054] When the ice layer is a single layer of ice, the calculation formula for the dynamic ice pressure F is:

[0055] F=mλ(0.18b 0.5 h 1.2 σ c+γδvA1sinθ1+0.015βwA2sinθ2) (4)

[0056] Wherein, m is the dam slope shape coefficient, which is 1 for a rectangle and 0.9 for a polygon or circle; λ is the dam slope coefficient, which is 1 when the dam slope angle is 0° to 15° and 0.8 when the dam slope angle is 15° to 45°; b is the ice layer width, m; h is the ice layer thickness, m; σ c is the uniaxial compressive strength of ice, kPa; γ is a coefficient related to the surface roughness under the ice layer, and 1 kN˙s / m is used for a single layer of ice. 3 ; δ is the viscosity coefficient of ice, which is 1 below -10℃, 0.95 between -10℃ and 0℃, and 0.9 above 0℃; v is the velocity of water under the ice layer, m / s; A1 is the surface area under the ice layer, m 2 ; θ1 is the horizontal angle between the water flow direction and the dam slope, °; β is the contact coefficient, ranging from 0.4 to 0.7; w is the standard wind pressure of the reservoir, kN / m 2 ; A2 is the upper surface area of ​​the ice layer, m 2 ; θ2 is the horizontal angle between the wind speed direction and the dam slope, °;

[0057] When the ice layer is overlapping ice, the calculation formula of dynamic ice pressure F is:

[0058] F=mλ(0.2b 0.5 h 1.1 σ c +γδvA1sinθ1+0.015βwA2sinθ2) (5)

[0059] Where γ is a coefficient related to the surface roughness under the ice layer, and 1.2 kN˙s / m is used for overlapping ice. 3 .

[0060] In a specific example, the dynamic ice pressure on the slope of an earth-rock dam caused by wave and wind loads is calculated. The test temperature is controlled to be the local average temperature in winter for many years, and the density of ice is measured to be 0.998×10 3 kg / m 3 , uniaxial compressive strength is 2MPa, bending strength is 1.0MPa, elastic modulus is 3GPa, Poisson's ratio is 0.35. The collected wave parameters in the waters in front of the dam show that the average wave speed in the winter waters is 5m / s, the average period is 6s, and the maximum wave height is 1m. The measured thickness of the ice layer in front of the dam is 0.6m, the length is 6m, the width is 10m, and the upper surface area of ​​the ice layer is 92m 2 , the lower surface area is 75m 2 The water flow velocity under the ice layer is 3m / s, and the horizontal angle between the water flow direction and the dam slope is 85°. The basic wind pressure in the area is 1.52kN / m 2, the horizontal angle between the average wind direction and the dam slope is 60°. The slope of the upstream dam of the reservoir is 1:2.5, the slope coefficient is 0.8, the contact surface is rectangular, and the dam slope shape coefficient is 1. The temperature on that day is -5℃, and the viscosity coefficient of ice is 0.95. The upper surface of the ice layer is relatively rough, and the contact coefficient is 0.6. The value of ε is 0.4.

[0061] First, the critical wave height for ice cracks to occur is calculated according to formula (1).

[0062]

[0063] The calculated limit wave height is 0.244m. The maximum wave height in the water area is greater than the limit wave height, and cracks appear in the ice layer.

[0064] Formula (2) is used to calculate the critical ice thickness for bending failure of the ice layer.

[0065]

[0066] The critical ice thickness is calculated to be 0.299 m. At this time, the ice thickness in front of the dam is greater than the critical ice thickness, and the ice layer type is overlapping ice. Formula (5) is used to calculate the dynamic ice pressure generated by the flow of the ice layer on the cold region reservoir dam.

[0067]

[0068] The calculated dynamic ice pressure is 781.874 kN. The dynamic ice pressure calculated using the Code for Load Design of Hydraulic Structures (SL744-2016) is 636.644 kN.

[0069] In another specific example, the ice layer in front of the dam measured on that day was 0.25m thick, 5.5m long, 8m wide, and the upper surface area of ​​the ice layer was 50m 2 , the lower surface area is 45m 2 The remaining parameters are the same as the previous specific example. The calculated limit wave height for ice cracks is 0.76m. The maximum wave height in the water area is greater than the limit wave height, and cracks appear in the ice. Formula (2) is used to calculate the critical ice thickness for bending failure of the ice layer, which is 0.299m. At this time, the ice thickness in front of the dam is less than the critical ice thickness, and the ice layer type is single-layer ice. Formula (4) is used to calculate the dynamic ice pressure generated by the flow of the ice layer on the cold region reservoir dam.

[0070] The calculated dynamic ice pressure is 279.948 kN. According to the Code for Load Design of Hydraulic Structures (SL744-2016), the dynamic ice pressure is 203.332 kN.

Claims

1. A method for calculating dynamic ice pressure of earth-rock dam under wave and wind loads, characterized in that: include: determining ice layer types, wherein the ice layer types include single layer ice and overlapping ice; When the ice layer is a single layer of ice, the calculation formula for the dynamic ice pressure F is: F=mλ(0.18b 0.5 h 1.2 s c +γδvA1sinθ1+0.015βwA2sinθ2) Where m is the dam slope shape coefficient; λ is the dam slope coefficient; b is the ice layer width, m; h is the ice layer thickness, m; σ c is the uniaxial compressive strength of ice, kPa; γ is a coefficient related to the surface roughness under the ice layer, and 1 kN˙s / m is used for a single layer of ice. 3 ; δ is the viscosity coefficient of ice; v is the velocity of water under the ice layer, m / s; A1 is the surface area under the ice layer, m 2 ; θ1 is the horizontal angle between the water flow direction and the dam slope, °; β is the contact coefficient, ranging from 0.4 to 0.7; w is the standard wind pressure of the reservoir, kN / m 2 ; A2 is the upper surface area of ​​the ice layer, m 2 ; θ2 is the horizontal angle between the wind speed direction and the dam slope, °; When the ice layer is overlapping ice, the calculation formula of dynamic ice pressure F is: F=mλ(0.2b 0.5 h 1.1 s c +γδvA1sinθ1+0.015βwA2sinθ2) Where γ is a coefficient related to the surface roughness under the ice layer, and 1.2 kN˙s / m is used for overlapping ice. 3 .

2. The method for calculating dynamic ice pressure of earth-rock dam under wave and wind loads according to claim 1 is characterized in that: Methods for determining ice type include: The calculation parameters of ice under the local winter multi-year average temperature are obtained through experiments, including ice density ρ, uniaxial compression strength σ c , bending strength σ f , elastic modulus E, Poisson's ratio v; arrange wave measurement equipment in the waters in front of the earth-rock dam to collect winter wave parameters in the waters, including wave height H, wave period T, and wave speed c; The limit wave height of ice cracking is calculated based on the calculation parameters of ice and the winter wave parameters of the water area; the elastic thin plate bending theory is introduced, and the limit wave height is the wave height corresponding to the internal stress of the ice layer being the bending strength of the ice; by comparing the limit wave height of ice cracking with the measured maximum wave height of the water area, it is determined whether the ice layer has cracks due to wave fluctuations; The critical ice thickness for bending failure of the ice layer with or without cracks is calculated and compared with the actual ice thickness measured in front of the dam to determine the ice layer type.

3. The method for calculating dynamic ice pressure of earth-rock dam under wave and wind loads according to claim 2 is characterized in that: If the measured maximum wave height in the water area is ≤ the limit wave height, then no cracks will occur in the ice layer; if the measured maximum wave height in the water area is greater than the limit wave height, then cracks will occur in the ice layer.

4. The method for calculating dynamic ice pressure of earth-rock dam under wave and wind loads according to claim 2 is characterized in that: If the actual ice thickness is ≤ the critical ice thickness, it is single layer ice; if the actual ice thickness is greater than the critical ice thickness, it is overlapping ice.

5. The method for calculating dynamic ice pressure of earth-rock dam under wave and wind loads according to claim 2 is characterized in that: The critical wave height H for ice breaking max The calculation formula is: Where L is the length of the ice layer, m.

6. The method for calculating dynamic ice pressure of earth-rock dam under wave and wind loads according to claim 2 is characterized in that: In the presence of cracks, the critical ice thickness h for bending failure of the ice layer is 1max The calculation formula is: Among them, ε is a coefficient related to the salinity and porosity of ice, which is 0.4 to 0.6; g is the acceleration of gravity, which is 9.8 m / s 2 .

7. The method for calculating dynamic ice pressure of earth-rock dam under wave and wind loads according to claim 2 is characterized in that: In the absence of cracks, the critical ice thickness h for bending failure of the ice layer is 2max The calculation formula is: Among them, ε is a coefficient related to the salinity and porosity of ice, which is 0.4 to 0.6; g is the acceleration of gravity, which is 9.8 m / s 2 .

8. The method for calculating dynamic ice pressure of earth-rock dam under wave and wind loads according to claim 1 is characterized in that: The dam slope shape coefficient m is 1 for a rectangle and 0.9 for a polygon or circle.

9. The method for calculating dynamic ice pressure of earth-rock dam under wave and wind loads according to claim 1 is characterized in that: The dam slope coefficient λ is 1 when the dam slope angle is 0°~15°, and is 0.8 when the dam slope angle is 15°~45°.

10. The method for calculating dynamic ice pressure of earth-rock dam under wave and wind loads according to claim 1, characterized in that: The viscosity coefficient δ of ice is 1 below -10℃, 0.95 between -10℃ and 0℃, and 0.9 above 0℃.

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