Method for calculating thickness of roller compacted concrete layer surface and analyzing deformation of dam body based on equivalent elastic model

Abstract

This invention relates to the field of mechanical properties and microscopic parameter testing technology of building materials, and provides a method for calculating the thickness of the layer band in roller-compacted concrete and analyzing dam deformation based on an equivalent elastic model. The method for calculating the layer band thickness includes: Step 1: Obtaining relevant parameters of the roller-compacted concrete unit containing the layer band to be measured; Step 2: Decomposing the roller-compacted concrete unit containing the layer band into upper concrete, layer band, and lower concrete, so as to establish an equivalent elastic model of the roller-compacted concrete unit based on the principle of series and parallel connection of composite materials, specifically including: establishing a series equivalent elastic model in the direction perpendicular to the layer band and establishing a parallel equivalent elastic model in the direction parallel to the layer band; Step 3: Combining the relevant parameters of the roller-compacted concrete unit and the series equivalent elastic model and the parallel equivalent elastic model to calculate the thickness of the layer band to be measured.

Description

Technical Field

[0001] This invention relates to the field of mechanical properties and micro-parameter testing technology of building materials, and in particular to a method for calculating the thickness of roller-compacted concrete surface bands and analyzing dam deformation based on an equivalent elastic model. Background Technology

[0002] The unique construction process of roller-compacted concrete (RCC) involves layer-by-layer compaction, leading to the formation of weak layers that affect its properties, such as compressive strength, tensile strength, modulus of elasticity, ultimate tensile strength, shear strength, and impermeability. Studies have found that RCC with layers exhibits worse performance compared to monolithic RCC. Statistical analysis of relevant data revealed that the compressive strength ratio of RCC with layers is 0.77–0.97; the tensile strength ratio is 0.51–0.98; the modulus of elasticity ratio is 0.86–0.99; the ultimate tensile strength ratio is 0.61–0.98; the shear strength ratio is 0.71–0.98; and the impermeability coefficient ratio is 2.35–24.1. Due to the layered structure of RCC, the dam material exhibits transverse isotropic characteristics, displaying bidirectional heterotropic elastic modulus. The properties of the layered concrete differ significantly from those of the monolithic concrete, and the thickness of the layered concrete affects the modulus of elasticity of the RCC unit, thus influencing the overall dam deformation. Therefore, it is necessary to conduct theoretical research on the thickness of the layer.

[0003] Existing technologies for studying roller-compacted concrete (RCC) layer zones have the following shortcomings: some methods treat the layer as a structural surface without thickness, ignoring the actual thickness of the layer zone, leading to significant errors in dam deformation calculations; although some studies have recognized the thickness characteristics of the layer zone, no unified analytical calculation formula that can be directly applied in engineering has been proposed, and most rely on numerical simulation or experimental fitting, which is inefficient and has limited applicability; existing layer-by-layer algorithms and floating mesh methods are mainly used for temperature field calculations, without considering the coupling effect of layer zone thickness on elastic modulus and dam deformation. Summary of the Invention

[0004] To address the aforementioned issues, this invention proposes a method for calculating the thickness of roller-compacted concrete surface layer based on equivalent elastic modulus. The surface layer thickness is derived through a series and parallel elastic equivalent model, thereby achieving quantification of the surface layer thickness.

[0005] In a first aspect, the present invention provides a method for calculating the thickness of a roller-compacted concrete layer based on the equivalent elastic modulus, comprising:

[0006] Step 1: Obtain relevant parameters of the roller-compacted concrete unit containing the layer to be tested, including: the ratio of the elastic modulus of the concrete containing the layer to the elastic modulus of the main body concrete, the ratio of the elastic modulus in the direction perpendicular to the layer to the elastic modulus in the direction parallel to the layer, the ratio of the elastic modulus of the lower body concrete to the elastic modulus of the upper body concrete, and the thickness of the roller-compacted concrete unit.

[0007] Step 2: Decompose the roller-compacted concrete unit containing the layered strip into upper concrete, layered strip and lower concrete, so as to establish the equivalent elastic model of the roller-compacted concrete unit based on the series and parallel principle of composite materials. Specifically, this includes: establishing a series equivalent elastic model in the direction perpendicular to the layered strip and establishing a parallel equivalent elastic model in the direction parallel to the layered strip.

[0008] Step 3: Calculate the thickness of the layer to be measured by combining the relevant parameters of the roller-compacted concrete unit with the series equivalent elastic model and the parallel equivalent elastic model.

[0009] Furthermore, in step 2, the formula for the series equivalent elasticity model is as follows:

[0010]

[0011] in, This represents the equivalent elastic modulus perpendicular to the direction of the layer band. This represents the ratio of the elastic modulus of the lower concrete to the elastic modulus of the upper concrete. Indicates the thickness of the roller-compacted concrete unit. This represents the elastic modulus of the upper concrete. This represents the elastic modulus of the layer. Indicates the length of the upper concrete structure. The layer indicates the thickness.

[0012] Furthermore, in step 2, the formula for the parallel equivalent elasticity model is as follows:

[0013]

[0014] in, It represents the equivalent elastic modulus parallel to the direction of the layer band.

[0015] Further, step 3 specifically includes: when the upper concrete and the lower concrete use the same material, establishing two equivalent elastic modulus relationships containing the layered zone based on the series equivalent elastic model and the parallel equivalent elastic model, and calculating the layered zone thickness based on the two equivalent elastic modulus relationships containing the layered zone.

[0016] When the upper and lower concrete are made of different materials, based on the series equivalent elastic model and the parallel equivalent elastic model, first establish two equivalent elastic modulus relationships without the layer zone, then establish two equivalent elastic modulus relationships with the layer zone, and calculate the layer zone thickness based on the four equivalent elastic modulus relationships.

[0017] Furthermore, when the upper and lower concrete layers are made of the same materials, the formula for calculating the thickness of the layer is as follows:

[0018]

[0019] in, This represents the ratio of the elastic modulus of the concrete including the surface layer to the elastic modulus of the bulk concrete. This represents the ratio of the elastic modulus in the direction perpendicular to the plane to the elastic modulus in the direction parallel to the plane. Indicates the thickness of the roller-compacted concrete unit. The layer indicates the thickness.

[0020] Furthermore, when the upper and lower concrete layers are made of materials with different properties, the formula for calculating the thickness of the layer is as follows:

[0021]

[0022] in, This represents the ratio of the elastic modulus of the lower concrete to the elastic modulus of the upper concrete.

[0023] Furthermore, the method also includes:

[0024] Step 4: Based on the principle of minimum potential energy and the principle of minimum residual energy, calculate the maximum and minimum values ​​of the layer thickness to obtain the extreme value range, and verify whether the layer thickness calculated in Step 3 is within the extreme value range.

[0025] Furthermore, the extreme range of the thickness of the layer is as follows:

[0026]

[0027] in, This represents the ratio of the elastic modulus of the lower concrete to the elastic modulus of the upper concrete. This represents the equivalent elastic modulus perpendicular to the direction of the layer band. This represents the elastic modulus of the upper concrete. This represents the elastic modulus of the layer. Indicates the thickness of the roller-compacted concrete unit. The layer indicates the thickness.

[0028] Secondly, the deformation analysis methods for dams containing bedding zones include:

[0029] The dam body to be analyzed is divided into material zones, and multiple roller-compacted concrete units are established based on the material zone results. The layer thickness of each roller-compacted concrete unit is calculated according to the method described in the first aspect, thereby obtaining the layer data of the dam body to be analyzed.

[0030] Based on finite element analysis, nonlinear analysis was performed on the data of each layer of the dam body to be analyzed, and the horizontal displacement cloud map and vertical displacement cloud map of the dam body were obtained.

[0031] The beneficial effects of this invention are as follows:

[0032] This invention proposes a unified analytical formula for the thickness of the layer band, covering both the same type of concrete and concrete of different properties. The parameters are clearly defined, the calculation is simple, and it can be directly applied in engineering. Furthermore, this invention provides a calculation method for the extreme value range of the layer band. By constraining the calculation results through the extreme value range, its rationality is ensured, and calculation distortion caused by deviations in parameter values ​​is avoided.

[0033] The results calculated by the layer thickness calculation method of this invention can accurately reflect the influence of the layer on the elastic modulus of the dam body. After being substituted into the finite element model, the calculation accuracy of the dam body deformation can be significantly improved. Moreover, this method does not require complex numerical simulation, and only requires input of basic mechanical parameters to complete the calculation, thereby improving the efficiency of engineering design and reducing the design cost. Attached Figure Description

[0034] Figure 1 A structural diagram of a roller-compacted concrete unit containing layers, provided for an embodiment of the present invention;

[0035] Figure 2 The diagram shows the series and parallel connection structure of springs provided in the embodiments of the present invention;

[0036] Figure 3 A flowchart illustrating a method for calculating the thickness of a roller-compacted soil surface zone based on an equivalent elastic model, provided in an embodiment of the present invention;

[0037] Figure 4 This is a diagram illustrating the series and parallel structures of concrete provided in an embodiment of the present invention;

[0038] Figure 5 An equivalent structural diagram of a roller-compacted concrete unit containing a layered surface, provided in an embodiment of the present invention;

[0039] Figure 6 This is a schematic diagram illustrating the calculation of the working condition when the ratio of the elastic modulus of the upper and lower concrete layers is 1, as provided in an embodiment of the present invention.

[0040] Figure 7 This is a schematic diagram illustrating the calculation of working conditions when the ratio of the elastic modulus of the upper and lower concrete layers is not 1, as provided in an embodiment of the present invention.

[0041] Figure 8 The layer thickness provided in the embodiments of the present invention A diagram illustrating the relationship between the value and the β value;

[0042] Figure 9 The layer thickness provided in the embodiments of the present invention The relationship between the value and the value of n (n 1) Schematic diagram;

[0043] Figure 10 A mechanical model diagram of a transversely isotropic body provided in an embodiment of the present invention;

[0044] Figure 11 Different embodiments of the present invention The variation diagram of the extreme values ​​of the thickness of the layer zone with respect to the value of β;

[0045] Figure 12 This is a cross-sectional and material zoning diagram of the dam body provided in an embodiment of the present invention;

[0046] Figure 13 A material partitioning diagram considering the influence of the layer band is provided for an embodiment of the present invention;

[0047] Figure 14 This is a calculation model diagram of a roller-compacted concrete unit provided in an embodiment of the present invention;

[0048] Figure 15 Finite element model diagram provided for embodiments of the present invention;

[0049] Figure 16 Vertical displacement cloud diagram of the dam body provided in the embodiment of the present invention;

[0050] Figure 17 A point distribution location map provided for embodiments of the present invention;

[0051] Figure 18 This is a schematic diagram illustrating the relationship between dam displacement and dam height, provided for an embodiment of the present invention. Detailed Implementation

[0052] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of the embodiments of this invention will be clearly described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0053] To facilitate understanding of this invention, the constitutive relationship of roller-compacted concrete containing layered zones and the equivalent elastic modulus of springs are first introduced:

[0054] (1) Constitutive relation of roller-compacted concrete including bedding zones:

[0055] The layer is created by the thin-layer construction of roller-compacted concrete. In reality, the layer is not a surface, but rather a layer band of a certain thickness. The layer connects the upper and lower concrete layers, forming a roller-compacted layer unit, such as... Figure 1 As shown in the figure For the thickness of the layer; The thickness of the compacted layer is generally taken as 30cm.

[0056] The construction process of roller-compacted concrete (RCC) involves layer-by-layer compaction, which forms a layered structure in the RCC, resulting in a dam material exhibiting transverse isotropic characteristics. A transversely isotropic body is a special case of an orthotropic body, where the number of independent elastic parameters is reduced from 21 to 5. According to Hooke's theorem, the relationship between strain and stress is shown in formula (1).

[0057] (1)

[0058] In the formula, , and These are the elastic modulus, shear modulus, and Poisson's ratio perpendicular to the plane, respectively. , and The elastic modulus, shear modulus, and Poisson's ratio are parallel to the plane.

[0059] (2) Equivalent elastic modulus of the spring:

[0060] The equivalent elastic modulus is typically calculated using the decomposition stiffness method. This method breaks down a complex structure into several substructures, where the total stiffness of the structure is composed of the stiffness of each substructure, forming an equivalent structure. The equivalent structure must maintain the same total thickness and stiffness as the original structure. The equivalent stiffness is calculated using the parallel and series connection methods for springs. Series and parallel connection models of springs are shown below. Figure 2 As shown.

[0061] Spring stiffness refers to the force required for a spring to produce a unit elongation. , These refer to the stiffness of spring 1 and spring 2, respectively. When the two springs are connected in series, the equivalent stiffness of the series structure is assumed to be... Two springs under force Under the action, the total deformation is The equivalent stiffness of the springs connected in series can be obtained. formula:

[0062] (2)

[0063] When two springs are connected in parallel, the two springs exert force on each other. Under the action, the same deformation is produced. Assuming the equivalent stiffness in parallel connection is Then, the equivalent stiffness formula for parallel springs can be obtained:

[0064] (3)

[0065] like Figure 3 As shown in the figure, an embodiment of the present invention provides a method for calculating the thickness of roller-compacted concrete surface bands based on an equivalent elastic model, comprising:

[0066] S101: Obtain relevant parameters of the roller-compacted concrete unit containing the surface zone to be tested, including: the ratio of the elastic modulus of the concrete containing the surface zone to the elastic modulus of the bulk concrete. The ratio of the elastic modulus in the vertical direction to the elastic modulus in the horizontal direction The ratio of the elastic modulus of the lower concrete to the elastic modulus of the upper concrete. and the thickness of the roller-compacted concrete unit .

[0067] in, The value range is set to 0.5~0.8. The value ranges from 0.86 to 0.99. Its value is related to the concrete surface treatment measures and treatment effects. The worse the construction quality, the smaller the coefficient.

[0068] S102: Decompose the roller-compacted concrete unit containing the layered zone into upper concrete, layered zone and lower concrete, so as to establish an equivalent elastic model of the roller-compacted concrete unit based on the principle of series and parallel connection of composite materials. Specifically, this includes: establishing a series equivalent elastic model in the direction perpendicular to the layered zone and establishing a parallel equivalent elastic model in the direction parallel to the layered zone.

[0069] S103: Calculate the thickness of the layer to be measured by combining the relevant parameters of the roller-compacted concrete unit with the series equivalent elastic model and the parallel equivalent elastic model.

[0070] The method for calculating the thickness of the layer in roller-compacted soil provided in this embodiment of the invention uses an elastic model to obtain the calculation formula for the layer, thereby calculating the thickness of the layer in the roller-compacted concrete unit model.

[0071] As one possible implementation method, this invention provides detailed steps for establishing an equivalent elastic model of a roller-compacted concrete unit based on the principle of series and parallel connection of composite materials.

[0072] The method for calculating the equivalent stiffness of a spring is also applicable to calculating the equivalent elastic modulus of concrete. Assume two concrete blocks have the same thickness and width, and the thickness... ,width The lengths of the two concrete blocks are respectively , The unit deformation length is When two concrete blocks are connected in series, such as Figure 4 As shown in (a).

[0073] stiffness of the two concrete blocks , and equivalent stiffness is :

[0074] , , (4)

[0075] In the formula, and These are the elastic moduli of concrete block 1 and block 2, respectively; and These are the lengths of concrete block 1 and block 2, respectively; This is the equivalent elastic modulus of the series structure.

[0076] From equations (2) and (4), the formula for the equivalent elastic modulus of a series concrete structure can be obtained:

[0077] (5)

[0078] When two concrete blocks are connected in parallel, such as Figure 4 As shown in (b), the equivalent stiffness of the two concrete blocks is... :

[0079] (6)

[0080] In the formula: It represents the equivalent elastic modulus of the parallel structure.

[0081] From equations (3) and (6), the formula for the equivalent elastic modulus of concrete structures in parallel configuration can be obtained:

[0082] (7)

[0083] The layered structure of roller-compacted concrete (RCC) gives the dam body transverse isotropic properties. The difference in elastic modulus between the parallel and perpendicular plane zones affects the strength and stability of the RCC. Based on the method for calculating the equivalent elastic modulus of concrete, the equivalent elastic modulus of the RCC unit containing the layered zones is calculated. Its equivalent structure is as follows: Figure 5 As shown. A roller-compacted concrete unit consists of three parts: upper concrete, lower concrete, and a layer strip. The elastic moduli of these three parts are as follows: , and The thickness of the roller-compacted concrete layer is The length of the layer is The upper and lower concrete sections have the same length. .

[0084] Assume the equivalent elastic modulus perpendicular to the direction of the layer is The equivalent structure in this direction is in series, which can be obtained from formula (5):

[0085] (8)

[0086] make Substituting into formula (8), we can obtain the series equivalent elastic model perpendicular to the direction of the layer band:

[0087] (9)

[0088] In the formula, This represents the equivalent elastic modulus perpendicular to the direction of the layer band. This represents the ratio of the elastic modulus of the lower concrete to the elastic modulus of the upper concrete. Indicates the thickness of the roller-compacted concrete unit. This represents the elastic modulus of the upper concrete. This represents the elastic modulus of the layer. Indicates the length of the upper concrete structure. The layer indicates the thickness.

[0089] Assume the equivalent elastic modulus parallel to the direction of the layer is The equivalent structure in this direction is in parallel form, which can be obtained from formula (7):

[0090] (10)

[0091] make Substituting into formula (10), we can obtain the parallel equivalent elastic model perpendicular to the direction of the layer:

[0092] (11)

[0093] In the formula, It represents the equivalent elastic modulus parallel to the direction of the layer band.

[0094] The elastic modulus of the layer can be obtained from formulas (9) and (11). formula:

[0095] (12)

[0096] As one possible implementation method, the present invention provides specific steps S3:

[0097] When the upper and lower concrete are made of the same material, the equivalent elastic modulus relationship of the two layers is established based on the series equivalent elastic model and the parallel equivalent elastic model. The thickness of the layer is calculated based on the equivalent elastic modulus relationship of the two layers.

[0098] Specifically, for roller-compacted concrete materials within the same zone, where the upper and lower concrete bodies are of the same type, assuming the elastic modulus of the main roller-compacted concrete is... The elastic modulus of the upper and lower concrete is... This working condition =1, the calculation model is as follows Figure 6 As shown.

[0099] Assume that the ratio of the elastic modulus of roller-compacted concrete to that of the vertical and parallel layers is constant. ,but

[0100] (13)

[0101] The rapid construction process of roller-compacted concrete (RCC) involves layer-by-layer compaction, forming a layered structure that gives the dam material transverse isotropic characteristics and bidirectional anisotropic elastic modulus. In the Longtan RCC dam in my country, the elastic modulus in the vertical direction is 0.8 times that in the parallel direction. Therefore, the parameters of this invention's embodiments... The value range is set to 0.5~0.8.

[0102] The layered zone is a weak zone in concrete, and roller-compacted concrete containing the layered zone has poor performance. Assuming the ratio of the elastic modulus of the roller-compacted concrete containing the layered zone to the elastic modulus of the bulk concrete is... ,but

[0103] (14)

[0104] In the formula: The elastic modulus of roller-compacted concrete containing layered zones; The elastic modulus of the compacted concrete is the bulk material.

[0105] Statistical studies have found a constant The value ranges from 0.86 to 0.99. Its value is related to the concrete surface treatment measures and treatment effects. The worse the construction quality, the smaller the coefficient.

[0106] The equivalent elastic modulus of the vertical layer of roller-compacted concrete can be obtained from equations (8) and (9). Equivalent elastic modulus at parallel levels :

[0107] (15)

[0108] The equivalent elastic modulus of the roller-compacted concrete unit containing the layered zone is calculated according to the series relationship. The elastic modulus of the layered zone can be obtained from formulas (8) and (14). :

[0109] (16)

[0110] Then, the equivalent elastic modulus of the roller-compacted concrete unit containing the surface zone is calculated according to the parallel relationship. Formula (17) can be obtained from formula (10) and formula (16):

[0111] (17)

[0112] The thickness of the layer can be obtained from formulas (16) and (17). The analytical formula is:

[0113] (18)

[0114] In the formula, This represents the ratio of the elastic modulus of the concrete including the surface layer to the elastic modulus of the bulk concrete. This represents the ratio of the elastic modulus in the direction perpendicular to the plane to the elastic modulus in the direction parallel to the plane. Indicates the thickness of the roller-compacted concrete unit. The layer indicates the thickness.

[0115] When the upper and lower concrete are made of different materials, based on the series equivalent elastic model and the parallel equivalent elastic model, first establish two equivalent elastic modulus relationships without the layer zone, then establish two equivalent elastic modulus relationships with the layer zone, and calculate the layer zone thickness based on the four equivalent elastic modulus relationships.

[0116] Specifically, for roller-compacted concrete materials in the transition zones within different zones, the upper and lower concrete bodies are of different properties. Assuming the elastic modulus of the upper part of the roller-compacted concrete body is... The lower body part is ,make and E2 E1, this operating condition 1. The calculation model is as follows: Figure 7 As shown.

[0117] Equivalent structures excluding layered bands, such as Figure 7 As shown in (a), the equivalent elastic modulus is calculated according to the series and parallel structures, as follows:

[0118] (19)

[0119] (20)

[0120] In the formula, For vertical values ​​without layered zones Towards the elastic modulus; Horizontal direction without bedding zone Towards the elastic modulus.

[0121] achievable towards and Towards elastic modulus ratio formula:

[0122] (twenty one)

[0123] like Figure 7 As shown in (b), for a roller-compacted concrete unit containing a layered strip, the elastic modulus is calculated according to the series equivalent structure, and the elastic modulus of the layered strip in the equivalent structure can be obtained. :

[0124] (twenty two)

[0125] like =1, then formula (22) is formula (18).

[0126] Then, the equivalent elastic modulus is calculated according to the parallel structure. From formula (10) and formula (22), we can obtain:

[0127] (twenty three)

[0128] Substituting equations (19) and (22) into equation (23), we obtain the result containing only parameters. The quadratic equation of :

[0129] (twenty four)

[0130] Solving the quadratic equation in one variable yields the thickness of the layer. The analytical formula is:

[0131] (25)

[0132] In the formula, This represents the ratio of the elastic modulus of the lower concrete to the elastic modulus of the upper concrete.

[0133] In summary, the thickness of the layer can be obtained from equations (18) and (25). The overall analytical formula is as follows:

[0134] (26)

[0135] (1) =1 case

[0136] when When =1, Value and and The value is related to the concrete modulus of elasticity, but not to the concrete modulus of elasticity. Value and and The value relationships are shown in Table 1.

[0137] Table 1 When =1, layer thickness Values ​​and β Value Relationship

[0138]

[0139] As shown in Table 1, when When ∈ (0.52, 0.76), and The larger the value, the thicker the layer. The smaller the value, the closer the performance of roller-compacted concrete is to that of bulk concrete, which aligns with engineering practices. When When =1, the layer thickness is... Value and Value relationships such as Figure 8 As shown.

[0140] Depend on Figure 8 It can be seen that the layer has thickness. Value with The value increases and then decreases. The larger the value The smaller the value; as The value decreases, and the thickness of the layer increases. The rate of increase in the value slowed down; and The larger the value, the thicker the layer. The smaller the value, the more consistent it is with the actual situation.

[0141] (2) 1. Situation

[0142] when At time 1, the layer thickness Value and , Related to value. With Changes, layer thickness Value and Value change relationship, such as Figure 9 As shown.

[0143] Depend on Figure 9 It can be seen that when The closer the value is to 1, the greater the thickness of the layer. The greater the value, the more pronounced the decrease in layer thickness. When the value approaches infinity, the elastic modulus of the upper and lower concretes differs too much, resulting in one being soft and the other hard, which will cause deformation coordination problems. The thickness of the layer is close to 0, the layer cannot be formed, and the upper and lower parts cannot be bonded.

[0144] As one possible implementation, the method further includes:

[0145] Step 4: Based on the principle of minimum potential energy and the principle of minimum residual energy, calculate the maximum and minimum values ​​of the layer thickness to obtain the extreme value range, and verify whether the layer thickness calculated in Step 3 is within the extreme value range.

[0146] Specifically, to facilitate the study of the extreme value problem of bedding zone thickness, a compacted element of a transversely isotropic body with a length of 1m, a width of 1m, and a height of B is used as the calculation model. The bedding zone element model is as follows: Figure 10 As shown.

[0147] Assuming that allowable stress is applied to the unit body, and allowable strain is generated under the conditions of deformation continuity and displacement boundary, and assuming that the shear stress is zero, the stress and strain relationship of the transversely isotropic body is shown in Equation (27).

[0148] (27)

[0149] In the formula, the stiffness matrix D, ; ; ; . and These are the elastic modulus and Poisson's ratio perpendicular to the plane, respectively; and The elastic modulus and Poisson's ratio are parallel to the plane.

[0150] The variational method in elasticity uses the energy principle to derive energy equations and solve functional extremum problems, yielding approximate solutions. The principle of minimum potential energy states that under a given external force, all possible displacements satisfying equilibrium conditions minimize the total potential energy of the elastic system. The principle of minimum complementary energy states that under external forces, the stresses satisfying deformation compatibility conditions minimize the total complementary energy of the elastic system. This section applies the principles of minimum potential energy and minimum complementary energy to determine the extremum range of the layer thickness.

[0151] Specifically, the maximum thickness of the layer zone is calculated as follows:

[0152] Assuming the upper concrete, lower concrete, and layered concrete in the layered unit are isotropic, the thickness of the compacted unit is... , The elastic modulus of the roller-compacted concrete. The thickness of the upper and lower sections of the roller-compacted concrete; The elastic modulus of the roller-compacted concrete substructure. The thickness of the roller-compacted concrete layer; The compacted surface has an elastic modulus; ; Equivalent elastic modulus. Assuming the allowable strain field of a layered element with zero shear stress is:

[0153] (28)

[0154] Then let , , , ,Depend on Equation (29) can be obtained:

[0155] (29)

[0156] In the formula, , , The coefficients are undetermined, and the subscripts 1, 2 and 3 represent the upper concrete, lower concrete and layer concrete, respectively.

[0157] Strain energy of layered unit for:

[0158] (30)

[0159] In the formula: , and These represent the volumes of the upper concrete, lower concrete, and layer concrete, respectively.

[0160] From equation (27), the stress expression is derived as follows:

[0161] (31)

[0162] From equations (30) and (31), we can obtain equation (32):

[0163] (32)

[0164] make , , Through functional extrema , The undetermined coefficients are obtained. , .

[0165] (33)

[0166] (34)

[0167] Bundle Obtaining extreme values and Substituting the values ​​into equation (33), the extreme values ​​of strain energy can be obtained. for:

[0168] (35)

[0169] In the formula, ,in , and It is a constant.

[0170] Overall research and analysis show that the strain energy under real-world conditions is:

[0171] (36)

[0172] By the law of least potential energy, we have:

[0173] (37)

[0174] Substituting equations (35) and (36) into equation (37), we get:

[0175] (38)

[0176] From equation (38), we can see that, And because ,at this time Get the maximum value .

[0177] When the upper concrete, lower concrete, and layer concrete are connected in series, the equivalent elastic modulus calculation formula is Equation (9):

[0178] when hour, Substituting into equation (9), we obtain the maximum value of the layer thickness:

[0179] (39)

[0180] Specifically, the minimum thickness of the bedding zone is calculated as follows:

[0181] Assuming the allowable stress field of the layered unit is a uniaxial pure stress state:

[0182] (40)

[0183] Residual energy corresponding to allowable stress field for:

[0184] (41)

[0185] Complementary energy corresponding to the actual stress field for:

[0186] (42)

[0187] According to the principle of minimum potential energy:

[0188] (43)

[0189] Substituting equations (44) and (42) into equation (43), we get:

[0190] (44)

[0191] From formula (44), we know that when the equality is taken, we obtain the minimum value of the layer thickness:

[0192] (45)

[0193] From equations (39) and (45), the formula for the extreme range of the thickness of the layer zone is derived:

[0194] (46)

[0195] in, This represents the ratio of the elastic modulus of the lower concrete to the elastic modulus of the upper concrete. This represents the equivalent elastic modulus perpendicular to the direction of the layer band. This represents the elastic modulus of the upper concrete. This represents the elastic modulus of the layer. Indicates the thickness of the roller-compacted concrete unit. The layer indicates the thickness.

[0196] Furthermore, this embodiment discusses the range of thickness values ​​for the layer. =1, =30cm, body concrete elastic modulus =10 GPa, Layer with elastic modulus If GPa, then substituting into formula (46), we get:

[0197] , (47)

[0198] The reduction factor of the elastic modulus of the layer relative to the matrix concrete is discussed. and For values ​​between 0.10 and 0.99, the extreme values ​​of the layer thickness are as follows: Figure 11 As shown. The reasonable range for the thickness of the layer band requires that the elastic modulus of the layer band be no less than 0.5 times the elastic modulus of the bulk material. As the layer band is a weak point, excessively low strength is detrimental to the safety of the engineering structure, and the minimum... Value less than / 3, then the reasonable range of layer thickness values ​​is shown in Table 6.

[0199] Table 6 Differences and Thickness at value The range of values

[0200]

[0201] Table 6 shows the appropriate layer thickness values. The value is 0.85-0.99. The larger the value, the thicker the layer, and the closer the layer strength band is to the bulk strength. When and When the value is close to 1, the layer thickness is close to 10cm, which is similar to the bulk properties.

[0202] This invention also provides a method for analyzing the deformation of a dam containing bedding zones, including:

[0203] S201: Divide the dam body to be analyzed into material zones, establish multiple roller-compacted concrete units based on the material zone results, and calculate the layer thickness of each roller-compacted concrete unit according to the roller-compacted concrete layer thickness calculation method based on the equivalent elastic model described in the above embodiment, thereby obtaining the layer data of the dam body to be analyzed.

[0204] Specifically, in this embodiment, a typical section of a roller-compacted concrete dam is a roller-compacted concrete gravity dam with a crest width of 15 m, a crest elevation of 630 m, a maximum dam height of 215 m, and a total crest length of 990 m, comprising 39 dam sections. This embodiment uses a typical dam section for finite element analysis, and its dam cross-section and material zoning are as follows. Figure 12 As shown.

[0205] The parameters of the dam body materials, cushion layer and bedrock of each zone are shown in Table 2.

[0206] Table 2 Material Parameters

[0207]

[0208] Among them, zones 1, 2, and 3 of the roller-compacted concrete dam body are roller-compacted zones, employing a layer-by-layer compaction construction process. Considering the influence of the layer, each roller-compacted zone consists of numerous compaction units. Due to the different properties of the upper and lower concrete layers, a transition zone is formed between the concrete layers with different properties. Therefore, the material zoning considering the influence of the layer zone is as follows: Figure 13 As shown.

[0209] The height of each compaction unit is the height of the compaction layer. It is assumed that the bedding zone forms at the exact center of the compaction unit, and the transition zone is considered as one compaction unit. The thickness of the compacted layer in this embodiment is... =30 cm, the calculation model of the compaction unit including the bedding zone is as follows Figure 14 As shown.

[0210] The bidirectional elastic modulus of transversely isotropic roller-compacted concrete is calculated based on the equivalent elastic modulus theory, specifically the elastic modulus parallel to and perpendicular to the compaction layers. Each compaction zone consists of countless identical compaction elements, and the bidirectional elastic modulus of each compaction zone is equal to the bidirectional elastic modulus of the compaction element. The influence of the layer bands is considered using the constitutive relation of transversely isotropic bodies, thus ignoring layer modeling and improving computational efficiency. This embodiment includes the ratio of the elastic modulus of the layer concrete to the elastic modulus of the concrete bulk. Take 0.9; the elastic modulus ratio of roller-compacted concrete to that in the parallel and perpendicular directions. Taking 0.6, the calculated layer thickness and bidirectional elastic modulus are shown in Table 3.

[0211] Table 3. Layer thickness and bidirectional elastic modulus

[0212]

[0213] When n=1, the thickness of the layer band The value is independent of the elastic modulus (or simply elastic modulus); At that time, the layer has thickness value to elastic modulus ratio related( Considering the influence of the layer zone, the dam material is treated as a transversely isotropic material. The change in the elastic modulus of the vertical layer is more significant, and the elastic modulus of the concrete in the layer zone is lower than that of the bulk concrete.

[0214] S202: Based on finite element calculation, nonlinear analysis is performed on the data of each layer of the dam body to be analyzed to obtain the horizontal displacement cloud map and the vertical displacement cloud map of the dam body.

[0215] Specifically, in the finite element method (FEM) calculation, the dam material is analyzed nonlinearly using the DP model. Due to the consideration of the influence of the bedding plane, the transition zone mesh is very dense, resulting in a long calculation time for the 3D model and requiring a large amount of computing memory, which places high demands on the computer. Given that the typical dam section thickness is 25 meters, it is reasonable to treat the dam body as a plane strain problem for FEM calculation. The FEM model is as follows: Figure 15 As shown, there are 241,451 nodes and 240,026 cells.

[0216] Considering the influence of the strata, the displacement and stress changes of the dam body with and without the influence of the strata are compared. The working conditions and loads of the finite element calculation are shown in Table 4.

[0217] Table 4 Calculation conditions and loads

[0218]

[0219] The finite element method yields the horizontal and vertical displacement contour maps of the dam body under two working conditions: with and without consideration of the influence of the layer zone. Figure 16 As shown, it can be seen that the horizontal and vertical displacements of the dam body after considering the layers both increase. The maximum horizontal displacement occurs at the top of the dam, increasing from 5.92 cm to 7.41 cm; the maximum vertical displacement occurs at the downstream face, increasing from 7.39 cm to 9.33 cm.

[0220] Six points were selected on the downstream side, from the bottom to the top of the dam, and their locations are shown below. Figure 15 As shown in Table 5, with the height at the dam base as 0 m, the displacement of the downstream face of the dam body as the dam height increases is analyzed. The relationship between dam displacement and dam height is as follows: Figure 17 As shown.

[0221] Table 5 Calculation results of displacement of roller-compacted concrete dam body

[0222]

[0223] Depend on Figure 18 It can be seen that, considering the layer thickness, in the displacement analysis of six points along the downstream face of the dam, both horizontal and vertical displacements increase with the rise of the dam's position. The maximum horizontal displacement occurs at point 6 on the dam crest, increasing from 5.93 cm to 7.41 cm, a 1.25-fold increase. The maximum vertical displacement occurs at point 4 in the upper middle section of the dam, increasing from 7.03 cm to 8.97 cm, a 1.26-fold increase. Therefore, for the structural safety of the dam, the influence of the layer thickness should be considered.

[0224] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for calculating the thickness of roller-compacted concrete surface bands based on an equivalent elastic model, characterized in that, include: Step 1: Obtain relevant parameters of the roller-compacted concrete unit containing the layer to be tested, including: the ratio of the elastic modulus of the concrete containing the layer to the elastic modulus of the main body concrete, the ratio of the elastic modulus in the direction perpendicular to the layer to the elastic modulus in the direction parallel to the layer, the ratio of the elastic modulus of the lower body concrete to the elastic modulus of the upper body concrete, and the thickness of the roller-compacted concrete unit. Step 2: Decompose the roller-compacted concrete unit containing the layered strip into upper concrete, layered strip and lower concrete, so as to establish the equivalent elastic model of the roller-compacted concrete unit based on the series and parallel principle of composite materials. Specifically, this includes: establishing a series equivalent elastic model in the direction perpendicular to the layered strip and establishing a parallel equivalent elastic model in the direction parallel to the layered strip. Step 3: Calculate the thickness of the layer to be measured by combining the relevant parameters of the roller-compacted concrete unit with the series equivalent elastic model and the parallel equivalent elastic model.

2. The method for calculating the thickness of roller-compacted concrete surface bands based on an equivalent elastic model according to claim 1, characterized in that, In step 2, the formula for the series equivalent elasticity model is as follows: in, This represents the equivalent elastic modulus perpendicular to the direction of the layer band. This represents the ratio of the elastic modulus of the lower concrete to the elastic modulus of the upper concrete. Indicates the thickness of the roller-compacted concrete unit. This represents the elastic modulus of the upper concrete. This represents the elastic modulus of the layer. Indicates the length of the upper concrete structure. The layer indicates the thickness.

3. The method for calculating the thickness of roller-compacted concrete surface bands based on an equivalent elastic model according to claim 2, characterized in that, In step 2, the formula for the parallel equivalent elasticity model is as follows: in, It represents the equivalent elastic modulus parallel to the direction of the layer band.

4. The method for calculating the thickness of roller-compacted concrete surface bands based on an equivalent elastic model according to claim 1, characterized in that, Step 3 specifically includes: when the upper concrete and the lower concrete use the same material, establish two equivalent elastic modulus relationships containing the layered zone based on the series equivalent elastic model and the parallel equivalent elastic model, and calculate the layered zone thickness based on the two equivalent elastic modulus relationships containing the layered zone. When the upper and lower concrete are made of different materials, based on the series equivalent elastic model and the parallel equivalent elastic model, first establish two equivalent elastic modulus relationships without the layer zone, then establish two equivalent elastic modulus relationships with the layer zone, and calculate the layer zone thickness based on the four equivalent elastic modulus relationships.

5. The method for calculating the thickness of roller-compacted concrete surface bands based on an equivalent elastic model according to claim 4, characterized in that, When the upper and lower concrete layers are made of the same materials, the formula for calculating the thickness of the layer is as follows: in, This represents the ratio of the elastic modulus of the concrete including the surface layer to the elastic modulus of the bulk concrete. This represents the ratio of the elastic modulus in the direction perpendicular to the plane to the elastic modulus in the direction parallel to the plane. Indicates the thickness of the roller-compacted concrete unit. The layer indicates the thickness.

6. The method for calculating the thickness of roller-compacted concrete surface bands based on an equivalent elastic model according to claim 5, characterized in that, When the upper and lower concrete layers are made of different materials, the formula for calculating the thickness of the layer is as follows: in, This represents the ratio of the elastic modulus of the lower concrete to the elastic modulus of the upper concrete.

7. The method for calculating the thickness of roller-compacted concrete surface bands based on an equivalent elastic model according to claim 1, characterized in that, The method also includes: Step 4: Based on the principle of minimum potential energy and the principle of minimum residual energy, calculate the maximum and minimum values ​​of the layer thickness to obtain the extreme value range, and verify whether the layer thickness calculated in Step 3 is within the extreme value range.

8. The method for calculating the thickness of roller-compacted concrete surface bands based on an equivalent elastic model according to claim 7, characterized in that, The extreme range of thickness of the layer is shown below: in, This represents the ratio of the elastic modulus of the lower concrete to the elastic modulus of the upper concrete. This represents the equivalent elastic modulus perpendicular to the direction of the layer band. This represents the elastic modulus of the upper concrete. This represents the elastic modulus of the layer. Indicates the thickness of the roller-compacted concrete unit. The layer indicates the thickness.

9. A method for analyzing the deformation of a dam containing bedding zones, characterized in that, include: The dam body to be analyzed is divided into material zones, and multiple roller-compacted concrete units are established based on the material zone results. The layer thickness of each roller-compacted concrete unit is calculated according to the method described in any one of claims 1 to 8, thereby obtaining the layer data of the dam body to be analyzed. Based on finite element analysis, nonlinear analysis was performed on the data of each layer of the dam body to be analyzed, and the horizontal displacement cloud map and vertical displacement cloud map of the dam body were obtained.

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