A high and steep slope spillway longitudinal slope differentiation design method and spillway structure

Abstract

The present application relates to the technical field of water conservancy and hydropower engineering, and particularly relates to a design method for longitudinal slope differentiation of a spillway of a high and steep slope and a spillway structure. The method comprises formulating an initial first longitudinal slope of a bank slope side spillway hole bottom slope and an initial second longitudinal slope of a river channel side spillway hole bottom slope, then constructing a comprehensive cost function according to the excavation cost of the bank slope side spillway hole and the backfill cost of the river channel side spillway hole, substituting the first longitudinal slope and the second longitudinal slope into the comprehensive cost function, iteratively solving to obtain the minimum value of the comprehensive cost function, and finally determining the bank slope side spillway hole bottom slope longitudinal slope and the river channel side spillway hole bottom slope longitudinal slope corresponding to the minimum value as the optimal bottom slope parameter combination, and designing the target spillway structure according to the bottom slope parameter combination. The present application quantifies the bottom slope design through iterative optimization of the cost function, reduces the earthwork amount, and disperses the water tongues of the two holes longitudinally to avoid concentrated scouring of the bank slope.

Description

Technical Field

[0001] This invention relates to the field of water conservancy and hydropower engineering technology, and in particular to a longitudinal slope differentiation design method and spillway structure for high and steep slope spillways. Background Technology

[0002] As the most important flood discharge structure in water conservancy and hydropower projects, the rationality of the spillway's layout is directly related to flood discharge safety, bank stability, and project economy. In the conventional layout of hydropower station hubs, when there is a natural bend in the river section at the dam site, designers usually adopt the "straightening the bend" approach, placing the spillway on the convex bank of the bend so that the end of the spillway faces the middle of the downstream riverbed. This utilizes the natural topography of the bend to guide the downstream flow away from the bank, reducing the risk of erosion damage to the downstream bank from high-speed water flow and ensuring the long-term stability of the hub and the downstream bank. However, not all dam sites have ideal bend topographic conditions. Constrained by regional geological structures and river geomorphological development patterns, many hydropower project dam sites are located in sections with straight natural riverbeds and steep banks, lacking usable bend convex bank topography. Under such topographic conditions, the layout of spillways cannot follow the traditional bend diversion approach, facing more severe technical challenges.

[0003] For spillway layouts under conditions of steep slopes and straight river channels, existing technologies conventionally employ a multi-hole, uniformly sloped spillway scheme. This means that the bottom slopes of each spillway opening are completely uniform, the inlet weir crest elevations are level, and the outlet bottom elevations are the same. This layout is mature in gentle slopes or wide valley sections, but its direct application to steep slopes and straight river channels reveals several drawbacks. First, to meet the planar and longitudinal slope requirements of uniformly sloped spillways, large-scale slope cutting and excavation of steep banks are often required, along with extensive backfilling on the riverbanks to artificially construct site conditions that meet the layout requirements. This leads to a sharp increase in earthwork, significantly increasing project costs and greatly extending the construction period due to the complexity of construction on steep slopes. Second, with uniformly sloped spillways, the slopes of each outlet are the same, and the end spillway noses can only be staggered to a limited extent by their lengths. The dispersion of the water jet's impact point along the longitudinal direction of the river channel is extremely limited, resulting in a highly concentrated discharge energy. More seriously, under straight river conditions, this concentrated outflow pattern inevitably leads to high-speed water flow directly or laterally impacting the downstream bank slope. The intense scouring effect can easily cause bank slope instability, posing a serious threat to the long-term operational safety of the project. Furthermore, in existing spillway design practices, the determination of the bottom slope relies heavily on engineering experience and qualitative judgment, lacking a design method that incorporates terrain adaptability and engineering cost into a unified quantitative analysis. This makes it difficult to achieve economic optimization of the structural layout while ensuring flood discharge safety. Summary of the Invention

[0004] The purpose of this invention is to provide a longitudinal slope differentiation design method and spillway structure for high and steep slope spillways, so as to solve the problem that the bottom slope design of spillways under the condition of straight river channels with high and steep slopes in the prior art is difficult to simultaneously take into account the synergy between hydraulic safety and economy.

[0005] To achieve the above objectives, the present invention adopts the following technical solution: This invention discloses a longitudinal slope differentiation design method for spillways on steep slopes, comprising: The initial first longitudinal slope of the bottom slope of the spillway on the bank slope and the initial second longitudinal slope of the bottom slope of the spillway on the river channel side are proposed. A comprehensive cost function is constructed based on the excavation cost of the flood discharge hole on the bank slope and the backfilling cost of the flood discharge hole on the river channel side; Substitute the first longitudinal slope and the second longitudinal slope into the comprehensive cost function, and iteratively solve to obtain the minimum value of the comprehensive cost function; The minimum value corresponds to the longitudinal slope of the spillway bottom slope on the bank side and the longitudinal slope of the spillway bottom slope on the river channel side, which are determined as the optimal combination of bottom slope parameters. The target spillway structure is then designed based on the combination of bottom slope parameters.

[0006] Optionally, determining the initial first longitudinal slope of the bottom slope of the spillway on the bank side and the initial second longitudinal slope of the bottom slope of the spillway on the river channel side includes: Determine the hydraulic constraints of the bank slope side spillway and the river channel side spillway; The critical bottom slope is determined, and the relative slope relationships between the bottom slope of the spillway on the bank side, the bottom slope of the spillway on the river channel side, and the critical bottom slope are determined under the hydraulic constraints. Based on the engineering layout conditions, the initial first longitudinal slope of the bottom slope of the flood discharge hole on the bank slope is determined under the determined relative slope relationship. Based on the relative slope relationship and the initial first longitudinal slope of the bottom slope of the spillway on the bank slope, the initial second longitudinal slope of the bottom slope of the spillway on the river channel side is determined.

[0007] Optionally, determining the relative slope relationship between the bottom slope of the spillway on the bank side, the bottom slope of the spillway on the river channel side, and the critical bottom slope under the hydraulic constraints includes: Based on the aforementioned hydraulic constraints, the first relative relationships between the longitudinal slope of the spillway bottom slope on the bank slope side and the longitudinal slope of the spillway bottom slope on the river channel side and the critical longitudinal slope are determined respectively. Based on the original topographic conditions of the bank slope bottom slope and the original riverbed topographic conditions of the river channel bottom slope during the engineering layout, a second relative relationship between the longitudinal slope of the bank slope bottom slope and the longitudinal slope of the river channel bottom slope is determined. Based on the first relative relationship and the comprehensive slope ratio downstream of the preset dam, the relative slope relationships of the longitudinal slope of the spillway bottom slope on the bank slope side, the longitudinal slope of the spillway bottom slope on the river channel side, the longitudinal slope of the critical bottom slope, and the comprehensive slope ratio are determined. The expression for the relative slope relationship is as follows:

[0008] In the formula, This indicates the overall slope ratio downstream of the dam. This indicates the longitudinal slope of the bottom slope of the spillway on the river channel side. This indicates the longitudinal slope of the bottom slope of the spillway on the bank slope. This indicates the longitudinal slope of the critical bottom slope.

[0009] Optionally, determining the initial second longitudinal slope of the bottom slope of the river channel side spillway based on the relative slope relationship and the initial first longitudinal slope of the bottom slope of the spillway on the bank slope side includes: The bottom slope increment is preset based on the determined relative slope relationship; Based on the bottom slope increment and the first longitudinal slope, the second longitudinal slope is calculated. The functional expression for calculating the second longitudinal slope is as follows:

[0010] In the formula, This indicates the initial longitudinal slope of the bottom slope of the spillway on the river channel side. This indicates the initial second longitudinal slope of the bottom slope of the spillway on the bank slope. This indicates the increment of the bottom slope.

[0011] Optionally, the step of constructing a comprehensive cost function based on the excavation cost of the spillway on the bank slope and the backfilling cost of the spillway on the river channel includes: Based on the excavation volume, spoil transport distance, and excavation difficulty of the spillway on the bank slope, the excavation cost is determined with the longitudinal slope of the bottom slope of the spillway on the bank slope as the independent variable. Based on the backfill volume, unit price of backfill material, and compaction cost of the bottom slope of the flood discharge hole on the river side, the backfill cost is determined with the longitudinal slope of the bottom slope of the flood discharge hole on the river side as the independent variable. Obtain the additional costs of the project, and construct the comprehensive cost function by combining the excavation cost and the backfilling cost. The expression of the comprehensive cost function is as follows:

[0012] In the formula, This represents the combined cost with the longitudinal slope of the bottom slope of the spillway on the riverbank side and the longitudinal slope of the bottom slope of the spillway on the river channel side as independent variables. This represents the excavation cost with the longitudinal slope of the bottom slope of the spillway on the bank slope as the independent variable. This represents the backfill cost with the longitudinal slope of the bottom slope of the spillway on the river channel as the independent variable. This indicates the additional costs of the project.

[0013] Optionally, substituting the first longitudinal slope and the second longitudinal slope into the comprehensive cost function and iteratively solving to obtain the minimum value of the comprehensive cost function includes: The first longitudinal slope and the second longitudinal slope are substituted into the comprehensive cost function as the initial values ​​for iteration, and the first longitudinal slope and the second longitudinal slope are changed under the hydraulic constraints. Iteratively obtain the comprehensive cost of the corresponding longitudinal slope combination after each change, and take the minimum value from all the comprehensive costs.

[0014] Optionally, the longitudinal slope differentiation design method for high and steep slope spillways further includes verifying the optimal combination of bottom slope parameters after determining the optimal combination, including: A numerical simulation model is established based on the determined optimal combination of bottom slope parameters; The hydraulic numerical simulation of the numerical simulation model is used to obtain the flow characteristics of the simulation output, as well as the velocity distribution, wall pressure distribution and cavitation number distribution along the flow path during the discharge. Based on the flow characteristics, determine the flow type along the course of the flood discharge holes on the bank slope and the river channel. When it is determined that the flow pattern along the path of the flood discharge hole on the bank slope side and the flood discharge hole on the river channel side is a rapid flow, and the flow velocity distribution, wall pressure distribution and water cavitation number distribution along the path of the discharge channel meet the preset threshold, then the optimal combination of bottom slope parameters is verified as the target bottom slope parameters. When it is determined that the flow type of the flood discharge hole on the bank slope side and the flood discharge hole on the river channel side is not a rapid flow, or when any of the flow velocity distribution, the wall pressure distribution and the cavitation number distribution along the discharge channel do not meet the preset threshold, the first longitudinal slope and the second longitudinal slope are re-determined and the comprehensive cost function is iterated.

[0015] This invention also discloses a spillway structure, designed using the aforementioned longitudinal slope differentiation design method for high and steep slope spillways, including: The spillway body includes side-by-side spillway outlets on the river channel side and spillway outlets on the bank slope side, as well as a partition wall separating the spillway outlets on the river channel side and the spillway outlets on the bank slope side. The spillway body is divided into an inlet section, a channel section and an outlet section along the water flow direction. The bottom slope elevation of the river channel side spillway at the inlet section is the same as the bottom slope elevation of the bank slope side spillway at the inlet section, and the longitudinal slope of the bank slope side spillway at the spillway section is less than the longitudinal slope of the river channel side spillway at the spillway section. The outlet section corresponding to the river channel side flood discharge hole is located upstream of the outlet section corresponding to the bank slope side flood discharge hole, forming a stepped double outlet configuration.

[0016] Optionally, the spillway section and the outlet section are connected by an upstream gentle slope, and the upstream gentle slope is arc-shaped along the water flow direction. The end of the outlet section is provided with a diversion nose sill, the bottom plate of the diversion nose sill is inverted arc shape, and a flat footing body is provided on the bank-facing slope side of the diversion nose sill. The flat footing body is a sloping structure on the bank-facing slope side that is higher than the river-facing slope side.

[0017] Optionally, the outer sidewall of the river channel side spillway located at the outlet section and the outer sidewall of the bank slope side spillway located at the outlet section are asymmetrical structures. The outer sidewall of the river channel side spillway located at the outlet section is shorter than the bottom slope length of the river channel side spillway, while the outer sidewall of the bank slope side spillway located at the outlet section has the same bottom slope length as the bank slope side spillway. The intermediate partition wall is longer than the bottom slope length of the river channel side spillway but shorter than the bottom slope length of the bank slope side spillway.

[0018] Compared with the prior art, the beneficial effects of the longitudinal slope differentiation design method and spillway structure for high and steep slopes provided by the embodiments of the present invention are as follows: By constructing a comprehensive cost function that includes the excavation cost of the spillway outlets on the bank slope and the backfilling cost of the spillway outlets on the river channel, the design of the bottom slope is provided with a quantitative basis for optimization, solving the industry problem of lacking quantitative optimization methods in current design practices. By iteratively solving for the minimum value of the comprehensive cost function, the optimal bottom slope parameter combination with the lowest comprehensive cost can be selected from all feasible bottom slope combinations, achieving simultaneous minimization of the bank slope excavation and river channel backfilling volumes, reducing earthwork volume, lowering project costs, and shortening the construction period. Designing the target spillway structure based on the optimal bottom slope parameter combination allows the elevation difference between the bottom plates of the two outlets to naturally form, enabling the water jet to disperse longitudinally along the river channel, fully utilizing the longitudinal energy dissipation space of the river channel, and avoiding concentrated scouring of the bank slope by the discharged energy. Attached Figure Description

[0019] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. In the accompanying drawings: Figure 1 A schematic flowchart illustrating the steps of the longitudinal slope differentiation design method for high and steep slope spillways provided in this embodiment of the invention; Figure 2A schematic diagram of the engineering structure of the spillway structure on the river channel side and the spillway on the bank slope side provided in the embodiment of the present invention. Figure 3 A schematic diagram of the planar structure of the spillway structure on the river channel side and the spillway on the bank slope side, provided in an embodiment of the present invention; Figure 4 This is a schematic diagram of the cross-sectional structure of the spillway structure on the river channel side and the spillway on the bank slope side, provided in an embodiment of the present invention.

[0020] The markings in the attached diagram are as follows: 1. River channel side spillway; 2. Bank slope side spillway; 3. Intermediate partition wall; 4. Inlet section; 5. Spillway section; 6. Outlet section; 61. Flow-off nose sill; 62. Planar footing body; 7. Side wall. Detailed Implementation

[0021] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. The preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0022] This invention discloses a longitudinal slope differentiation design method for spillways on steep slopes, such as... Figure 1 As shown, it includes: S1. Determine the initial first longitudinal slope of the bottom slope of the flood discharge hole 2 on the bank slope side and the initial second longitudinal slope of the bottom slope of the flood discharge hole 1 on the river channel side; S2. Based on the excavation cost of the flood discharge hole 2 on the bank slope and the backfilling cost of the flood discharge hole 1 on the river channel, construct a comprehensive cost function; S3. Substitute the first and second longitudinal slopes into the comprehensive cost function and iteratively solve to obtain the minimum value of the comprehensive cost function; S4. Determine the optimal combination of bottom slope parameters by taking the longitudinal slope of the bottom slope of the flood discharge hole 2 on the bank slope and the longitudinal slope of the bottom slope of the flood discharge hole 1 on the river channel side corresponding to the minimum value, and design the target spillway structure based on the combination of bottom slope parameters.

[0023] By implementing the above-described embodiment of the longitudinal slope differentiation design method for high and steep slope spillways, a comprehensive cost function is first constructed, which includes the excavation cost of the bank-side spillway 2 and the backfilling cost of the river-side spillway 1. This incorporates terrain adaptability, engineering economics, and hydraulic requirements into a unified quantitative analysis framework. In traditional equal-slope layouts, the selection of the bottom slope often relies solely on qualitative judgment based on engineering experience, lacking systematic quantitative optimization methods, making it difficult to objectively evaluate the merits of the design scheme. The comprehensive cost function proposed in this embodiment fundamentally solves this industry problem, transforming bottom slope design from experience-driven to data-driven, providing a scientific objective function for subsequent iterative optimization.

[0024] Furthermore, by substituting the proposed first and second longitudinal slopes into the comprehensive cost function and iteratively solving for the minimum value, all feasible bottom slope combinations that meet the engineering layout conditions can be traversed. Preferably, this iterative solution can employ a numerical iterative method, systematically searching for the globally optimal solution within the range of values ​​defined by the constraints, rather than only seeking optimization in a local area, ensuring that the selected bottom slope parameter combination is the result with the lowest comprehensive cost among all feasible solutions.

[0025] Since the comprehensive cost function includes both the excavation cost on the bank slope and the backfill cost on the river channel, and the two have an inverse relationship in the direction of bottom slope change, that is, reducing the first longitudinal slope of the bottom slope of the flood discharge hole 2 on the bank slope will reduce the excavation volume on the bank slope but increase the backfill volume on the river channel, and vice versa, the minimum comprehensive cost obtained by iterative solution is actually finding the optimal balance between the excavation volume on the bank slope and the backfill volume on the river channel. This avoids generating excessive excavation and backfill volumes at the same time in order to adapt to the equal longitudinal slope layout, thereby reducing the amount of earthwork, lowering the project cost and shortening the construction period at the source.

[0026] When designing the target spillway structure based on the optimal combination of bottom slope parameters, the difference between the first and second longitudinal slopes (i.e., longitudinal slope differentiation) results in a greater longitudinal slope at the bottom of the spillway 1 on the river channel side than at the bottom of the spillway 2 on the bank slope side. Therefore, with the same horizontal length of the spillway section 5, the elevation drop at the end of the bottom plate of the spillway 1 on the river channel side is greater than that at the end of the spillway 2 on the bank slope side. This naturally creates a height difference between the bottom plates at the outlets of the two outlets. This allows for separation of the downstream flow's landing points in the longitudinal direction of the river channel without relying on staggered nose sill lengths, significantly increasing the longitudinal dispersion of the water jet and fully utilizing the longitudinal energy dissipation space of the river channel, thus preventing concentrated energy scouring of the bank slope. Alternatively, different horizontal lengths of the spillway section 5 can be set so that the bottom plate elevations of the two outlets are similar, resulting in staggered nose sills in a stepped distribution, further dispersing the water jet's landing point. The arrangement can be flexibly adjusted according to the downstream energy dissipation zone conditions of the actual project.

[0027] Furthermore, the initial first longitudinal slope of the bottom slope of the spillway 2 on the bank slope and the initial second longitudinal slope of the bottom slope of the spillway 1 on the river channel side are determined, including: Determine the hydraulic constraints of the bank slope side spillway and the river channel side spillway; The critical bottom slope was determined, and the relative slope relationships between the bottom slopes of the 2nd spillway on the bank slope side, the bottom slope of the 1st spillway on the river channel side, and the critical bottom slope were determined under hydraulic constraints. Based on the engineering layout conditions, the initial first longitudinal slope of the bottom slope of the flood discharge hole 2 on the bank slope is determined under the established relative slope relationship. Based on the relative slope relationship and the initial first longitudinal slope of the bottom slope of the spillway 2 on the bank slope, the initial second longitudinal slope of the bottom slope of the spillway 1 on the river channel side is determined.

[0028] By implementing the above-described embodiment of the longitudinal slope differentiation design method for high and steep slope spillways, the hydraulic constraints of the bank slope side spillway and the river channel side spillway are first determined, providing a clear hydraulic safety boundary for the subsequent design of the bottom slope. Preferably, the hydraulic constraint is that both spillways must satisfy the rapid flow state. Its physical meaning is to ensure that the downstream flow is always in a supercritical flow state, so that the downstream water level changes cannot be transmitted upstream, thereby ensuring that the spillways can discharge stably under any operating conditions without being affected by the backwater effect of the downstream tailrace.

[0029] Under the rigid constraint of the rapid flow pattern, the critical bottom slope was further defined, and the relative slope relationships between the bottom slopes of the bank-side spillway 2, the river-side spillway 1, and the critical bottom slope were determined, i.e., the order of magnitude that must be satisfied among the three was determined. This relative slope relationship directly limits the allowable numerical range of the initial first longitudinal slope of the bank-side spillway 2 bottom slope and the initial second longitudinal slope of the river-side spillway 1 bottom slope, ensuring that all subsequent definition and optimization operations are carried out within this safe range, fundamentally eliminating the risk that the flow pattern of the spillway will not meet the rapid flow requirements due to improper bottom slope values.

[0030] Based on this, and according to the engineering layout conditions, the initial longitudinal slope of the bottom slope of the spillway 2 on the bank slope is determined under the established relative slope relationship. Since the bank slope is closely attached to a steep mountain, its bottom slope value directly determines the excavation outline and depth along the original bank slope topography. An excessively steep bottom slope will lead to extensive rock excavation, endangering slope stability and drastically increasing excavation costs. If the slope is gentle, the spillway 2 on the bank slope will require a longer outlet distance to reach the vicinity of the riverbed, similarly increasing the construction cost of the structure itself. Furthermore, the suitability of the outlet location needs to be determined in conjunction with the actual downstream topography and geology. Therefore, the initial longitudinal slope determined according to the engineering layout conditions is essentially the initial bottom slope value that minimizes excavation volume under the comprehensive constraints of outlet location suitability and slope stability.

[0031] The initial second longitudinal slope of the bottom slope of the spillway 2 on the river channel side is determined based on the relative slope relationship and the initial first longitudinal slope of the bottom slope of the spillway 2 on the bank slope side. This determination method directly links the bottom slope of the river channel side to the bottom slope of the bank slope side. For example, it ensures that the bottom slope of the river channel side is always greater than the bottom slope of the bank slope side, and that the rate of elevation drop of the bottom plate of the spillway 1 on the river channel side is greater than the rate of elevation drop of the bottom plate of the spillway 2 on the bank slope side. This lays the structural foundation for the subsequent formation of a longitudinally dispersed water jet outflow (see reference). Figures 2-4 ).

[0032] Meanwhile, since the value of the riverside bottom slope is determined based on the first longitudinal slope under the constraint of the relative slope relationship, the blindness in the process of proposing the riverside bottom slope is avoided. Furthermore, since the riverside bottom slope is obtained by adding a preset bottom slope increment to the relative bank slope bottom slope, the bottom plate elevation of the riverside flood discharge hole 1 can quickly approach the original riverbed elevation at an appropriate rate, effectively reducing the amount of backfilling on the riverside.

[0033] Furthermore, the relative slope relationships of the bottom slopes of the spillway 2 on the bank slope side, the spillway 1 on the river channel side, and the critical bottom slope were determined under hydraulic constraints, including: Based on the hydraulic constraints, the first relative relationship between the longitudinal slope of the bottom slope of the flood discharge hole 2 on the bank slope side and the longitudinal slope of the bottom slope of the flood discharge hole 1 on the river channel side and the critical bottom slope longitudinal slope is determined respectively. Based on the original topographic conditions of the bank slope of the spillway 2 and the original topographic conditions of the riverbed of the spillway 1 during the engineering layout, the second relative relationship between the longitudinal slope of the spillway 2 and the longitudinal slope of the spillway 1 is determined. Based on the first relative relationship and the first relative relationship, combined with the pre-set comprehensive slope ratio downstream of the dam, the relative slope relationships of the bottom slope of the spillway 2 on the bank slope side, the bottom slope of the spillway 1 on the river channel side, the critical bottom slope longitudinal slope, and the comprehensive slope ratio are determined. The expression for the relative slope relationship is:

[0034] In the formula, This indicates the overall slope ratio downstream of the dam. This indicates the longitudinal slope of the bottom slope of the spillway on the river channel side. This indicates the longitudinal slope of the bottom slope of the spillway opening on the bank slope. This indicates the longitudinal slope of the critical bottom slope.

[0035] By implementing the above-described embodiment of the longitudinal slope differentiation design method for high and steep slope spillways, the first relative relationship between the longitudinal slope of the spillway 2 on the bank slope side and the longitudinal slope of the spillway 1 on the river channel side and the critical longitudinal slope is determined according to the hydraulic constraints. Essentially, this transforms the rapid flow regime required by the hydraulic constraints into a specific numerical constraint: the longitudinal slopes of both the spillway 2 on the bank slope side and the spillway 1 on the river channel side must be greater than the critical longitudinal slope. The critical longitudinal slope, serving as the critical value distinguishing between rapid and slow flow, has a specific value that depends on hydraulic parameters such as the design discharge flow rate, cross-sectional shape, and slope roughness of the spillway, and is a fixed value under given engineering conditions.

[0036] The establishment of the first relative relationship defines a common lower limit boundary for the longitudinal slope values ​​of the bottom slope of the 2nd flood discharge hole on the bank slope and the 1st flood discharge hole on the river channel side. This ensures that any combination of bottom slopes that satisfies this relationship can guarantee that the water flow in the discharge channel is in a rapid flow state, avoiding the occurrence of slow flow or critical flow due to excessively gentle bottom slopes, thereby ensuring the discharge stability of the discharge channel under any working conditions.

[0037] Because the bottom slope of the spillway 2 on the bank slope side is closely attached to the steep bank slope, the original bank slope topography dictates that the gentler the bottom slope, the greater the excavation depth and the larger the excavation volume. Conversely, the bottom slope of the spillway 1 on the river channel side is located near the river channel, and the original riverbed topography dictates that the gentler the bottom slope, the greater the bottom slab overhang and the larger the backfill volume. There is a natural contradiction between the two in terms of longitudinal slope orientation. The second relative relationship transforms this contradiction into a quantitative constraint that the longitudinal slope of the bottom slope of the spillway 1 on the river channel side is greater than that of the bottom slope of the spillway 2 on the bank slope side. That is, a relatively steep bottom slope is used on the river channel side, while a relatively gentle bottom slope is used on the bank slope side, thus reflecting adaptability to the original topography from the bottom slope design stage.

[0038] The comprehensive slope ratio downstream of the pre-set dam is used as the upper limit constraint of the longitudinal slope of the spillway bottom slope. This ensures that the longitudinal slopes of the spillway bottom slope on both the bank slope side and the river channel side are less than the comprehensive slope ratio downstream of the dam. This prevents the spillway bottom slope from being too steep, which would cause the bottom plate elevation at the end of the spillway to be lower than the foundation elevation of the downstream structure of the dam. It also avoids the spillway excavation or structural layout from encroaching on the stability influence range of the dam body, thus ensuring the structural safety of the dam from the root of slope value selection. The relative slope relationship is determined by combining the first and second relative relationships. This relative slope relationship unifies the safety requirements of rapid flow under hydraulic constraints and the longitudinal slope differentiation requirements under topographic conditions into a single mathematical expression. It serves as the overall constraint framework for subsequently determining the initial first longitudinal slope of the bottom slope of the spillway 2 on the bank side and the initial second longitudinal slope of the bottom slope of the spillway 1 on the river channel side. This ensures that the final determined relative slope relationship not only meets the safety requirements of the rapid flow state but also reflects the engineering economic logic of reducing excavation volume on the bank side and reducing backfill volume on the river channel side with the gentle slope. At the same time, it ensures that the bottom slope value of the spillway is always within the safe range allowed by the stability of the dam structure.

[0039] Furthermore, based on the relative slope relationship and the initial first longitudinal slope of the bottom slope of the spillway 2 on the riverbank side, the initial second longitudinal slope of the bottom slope of the spillway 1 on the river channel side is determined, including: The bottom slope increment is preset based on the determined relative slope relationship; Based on the bottom slope increment and the first longitudinal slope, the second longitudinal slope is calculated. The functional expression for calculating the second longitudinal slope is as follows:

[0040] In the formula, This indicates the initial longitudinal slope of the bottom slope of the spillway 1 on the river channel side. This indicates the initial second longitudinal slope of the bottom slope of the spillway 2 on the bank slope. This indicates the increment of the bottom slope.

[0041] By implementing the above-described embodiment of the longitudinal slope differentiation design method for high and steep slope spillways, a bottom slope increment is preset based on the determined relative slope relationship. This bottom slope increment is used to control the increase in the initial second longitudinal slope of the bottom slope of the river-side spillway 1 relative to the initial first longitudinal slope of the bottom slope of the bank-side spillway 2.

[0042] Since the relative slope relationship only specifies the qualitative order of the second longitudinal slope being greater than the first longitudinal slope, without giving a quantitative difference between the two, the preset bottom slope increment transforms the qualitative relationship into a quantitative difference that can be used for engineering calculations, thus providing a clear operational basis for determining the second longitudinal slope. Preferably, the bottom slope increment is determined comprehensively based on the elevation difference between the original bank slope topography and the original riverbed topography in the engineering layout conditions, as well as the horizontal length of the spillway section. Its value directly affects the degree of longitudinal slope difference between the bottom slope of the spillway 1 on the river channel side and the bottom slope of the spillway 2 on the bank slope side.

[0043] The second longitudinal slope is calculated based on the bottom slope increment and the first longitudinal slope, specifically using an additive function expression, where the second longitudinal slope equals the sum of the first longitudinal slope and the bottom slope increment. This linear calculation method ensures that the second longitudinal slope changes synchronously and in the same direction as the first longitudinal slope, while maintaining a constant difference in bottom slope increment between the two. This guarantees that when the first longitudinal slope is numerically adjusted in subsequent iterative optimization processes, the second longitudinal slope follows suit with the same change step size, simplifying the coupling relationship between optimization variables and reducing the computational complexity of iterative optimization.

[0044] Meanwhile, by pre-setting the bottom slope increment, the difference between the second longitudinal slope and the first longitudinal slope can be flexibly adjusted within the safety allowable range according to the actual needs of the project. This controls the elevation difference of the bottom plate of the two outlets, the relative position of the outlets, and the longitudinal drop distance of the water tongue, so as to adapt to the energy dissipation space conditions and water flow scour protection requirements of different straight channels and avoid concentrated scour of the bank slope by the discharged energy.

[0045] Furthermore, based on the excavation cost of the bank slope spillway 2 and the backfilling cost of the river channel spillway 1, a comprehensive cost function is constructed, including: Based on the excavation volume, spoil transport distance, and excavation difficulty of the spillway 2 on the bank slope side, the excavation cost is determined with the longitudinal slope of the bottom slope of the spillway 2 on the bank slope side as the independent variable. Based on the backfill volume, unit price of backfill material, and compaction cost of the bottom slope of the river channel side spillway 1, the backfill cost is determined with the longitudinal slope of the bottom slope of the river channel side spillway 1 as the independent variable. Obtain the additional costs of the project, and construct a comprehensive cost function by combining excavation costs and backfilling costs. The expression of the comprehensive cost function is as follows:

[0046] In the formula, This represents the combined cost with the longitudinal slopes of the bottom slopes of both the bank-side spillway 2 and the river-side spillway 1 as independent variables. This represents the excavation cost with the longitudinal slope of the bottom slope of the spillway 2 on the bank slope as the independent variable. This represents the backfill cost with the longitudinal slope of the bottom slope of the river channel spillway 1 as the independent variable. This indicates the additional costs of the project.

[0047] Furthermore, substituting the first and second longitudinal slopes into the comprehensive cost function, the minimum value of the comprehensive cost function is obtained through iterative solution, including: The first and second longitudinal slopes are substituted into the comprehensive cost function as the initial values ​​for iteration, and the first and second longitudinal slopes are changed under the constraints of water conservancy. Iteratively obtain the comprehensive cost of the corresponding longitudinal slope combination after each change, and take the minimum value from all comprehensive costs.

[0048] By implementing the above-described embodiment of the longitudinal slope differentiation design method for high and steep slope spillways, firstly, the excavation volume of the spillway outlet 2 on the bank slope side increases with the increase of the longitudinal slope of the bottom slope of the spillway outlet 2 on the bank slope side. The greater the longitudinal slope, the faster the bottom plate of the spillway descends along the path, and the excavation range close to the high and steep bank slope increases accordingly, thus increasing the excavation volume. Conversely, the excavation volume decreases. The spoil transport distance is determined by the location of the spoil disposal site in the project area and is not directly related to the longitudinal slope of the bottom slope of the spillway outlet 2 on the bank slope side. However, under the condition of a fixed excavation volume, it acts as a linear multiplier factor that directly affects the total excavation cost. The greater the spoil transport distance, the higher the transportation cost per unit excavation volume. The excavation difficulty is determined by the rock mass type, weathering degree, etc. in the geological survey report. Different excavation depths correspond to different rock mass types, and the excavation difficulty changes accordingly, thus affecting the construction cost per unit excavation volume. The superposition effect of the positive correlation among the three factors makes the excavation cost exhibit a nonlinear response characteristic when the longitudinal slope of the bottom slope of the spillway outlet 2 on the bank slope side changes.

[0049] As mentioned above, since a small amount of backfilling is required after the actual excavation of the bank slope, part of the backfill serves as the foundation for constructing the spillway bank slope side openings. Therefore, the excavation cost of the bank slope side spillway opening 2 also includes the additional cost of backfilling.

[0050] Similarly, the backfill volume of the bottom slope of the spillway 1 on the river channel side decreases as the longitudinal slope of the bottom slope of the spillway 1 on the river channel side increases. The greater the longitudinal slope, the faster the bottom slab approaches the original riverbed elevation, the smaller the gap between the bottom slab and the riverbed, and the less backfill is required. The unit price of backfill material is determined by the building materials market and transportation conditions at the project site, and is not directly related to the longitudinal slope of the bottom slope of the spillway 1 on the river channel side, but it directly affects the total backfill cost as a linear multiplier factor. The compaction cost is determined by the design compaction requirements and construction technology. Different backfill thicknesses correspond to different compaction difficulties and compaction passes, thus affecting the construction cost per unit backfill volume. The superimposed effect of the positive correlation among these three factors can be expressed as a backfill cost function with the longitudinal slope of the bottom slope of the spillway 1 on the river channel side as the independent variable.

[0051] Subsequently, the additional costs of the project were obtained, and the excavation cost, backfill cost, and additional costs were combined to construct a comprehensive cost function. This function accurately maps the variation of the total project cost in a dual-variable space of the longitudinal slope of the bottom slope of the spillway 2 on the bank slope and the bottom slope of the spillway 1 on the river channel side. Since the excavation cost and backfill cost show opposite trends in the direction of slope variation, the comprehensive cost needs to be determined from the perspective of the entire project.

[0052] The first and second longitudinal slopes are used as initial values ​​in the iterative process and substituted into the comprehensive cost function. Under hydraulic constraints, the first and second longitudinal slopes are then varied. Preferably, this iterative variation can be performed within the range defined by the hydraulic constraints. The first longitudinal slope is adjusted sequentially along the increasing direction of the slope of the bottom slope of the spillway 2 on the bank slope side, with a preset step size. Simultaneously, the corresponding second longitudinal slope is determined based on the relative slope relationship. All combinations of longitudinal slopes satisfying the hydraulic constraints are iterated over. The comprehensive cost of the corresponding longitudinal slope combination after each variation is obtained iteratively. The minimum comprehensive cost is then selected from all comprehensive costs. The first and second longitudinal slopes corresponding to this minimum value are the optimal solution that minimizes the comprehensive cost among all feasible combinations of longitudinal slopes satisfying the hydraulic constraints.

[0053] Through the above construction and iterative solution process, the positive product effect of excavation volume, spoil transport distance and excavation difficulty in excavation cost and the positive product effect of backfill volume, backfill unit price and compaction cost in backfill cost are accurately quantified and optimally balanced in the same objective function, ensuring that the design parameters with the lowest comprehensive cost are accurately locked among all feasible longitudinal slope combinations that meet the hydraulic constraints.

[0054] Furthermore, the longitudinal slope differentiation design method for spillways on steep slopes also includes verifying the optimal combination of bottom slope parameters after determining it, including: A numerical simulation model is established based on the determined optimal combination of bottom slope parameters; The hydraulic numerical simulation model is used to obtain the flow characteristics of the simulation output, as well as the velocity distribution, wall pressure distribution and cavitation number distribution along the flow path during discharge. Based on the flow characteristics, the flow patterns along the course of the bank slope spillway 2 and the river channel spillway 1 were determined. When the flow pattern along the spillway 2 on the bank slope and the spillway 1 on the river channel is determined to be a rapid flow, and the velocity distribution, wall pressure distribution and cavitation number distribution along the spillway meet the preset threshold, then the optimal combination of bottom slope parameters is verified as the target bottom slope parameters. When the flow type of the bank slope spillway 2 and the river channel spillway 1 is determined to be not a rapid flow, or when any of the velocity distribution, wall pressure distribution and cavitation number distribution along the spillway do not meet the preset threshold, the first longitudinal slope and the second longitudinal slope are re-determined and the comprehensive cost function is iterated.

[0055] By implementing the above-described embodiment of the longitudinal slope differentiation design method for spillways with steep slopes, relying solely on the theoretical optimization of the comprehensive cost function can only ensure that the combination of bottom slope parameters achieves optimal economic efficiency, but it cannot predict the hydraulic safety performance of the downstream flow under actual engineering boundary conditions. Numerical simulation models can fully consider the coupled effects of multiple factors, such as the variation of the spillway cross-sectional shape along the spillway, the non-uniform distribution of sidewall roughness, and local disturbances at the slope transition section, thus overcoming the limitations of theoretical analytical methods in terms of applicability under complex boundary conditions.

[0056] By establishing a numerical simulation model based on the determined optimal combination of bottom slope parameters and running hydraulic numerical simulation, the entire flow process of the downstream water flow in the flood discharge hole 2 on the bank slope side and the flood discharge hole 1 on the river channel side can be reproduced in the virtual environment. The flow characteristics, as well as the velocity distribution, wall pressure distribution and cavitation number distribution along the discharge channel, can be obtained. This provides a comprehensive and objective evaluation basis for the actual effect of the bottom slope parameter combination and avoids hydraulic safety hazards caused by the simplification of the boundary conditions of theoretical calculation.

[0057] The acquired flow characteristics are used to determine the flow type along the spillway at the bank slope side (slide 2) and the channel side (slide 1), and to determine whether a true rapid flow is maintained throughout the entire process. A rapid flow is a prerequisite for the stable operation of the spillway, ensuring that downstream water level changes are not transmitted upstream, and that the spillway can discharge water stably under any operating condition without being affected by tailrace backwater. However, a rapid flow is only the most basic safety threshold. Even if the flow is rapid, if any of the velocity distribution, wall pressure distribution, or cavitation number distribution along the spillway does not meet the design requirements, the bottom slope parameter combination cannot be directly used for engineering design.

[0058] Specifically, the velocity distribution determines whether the discharged water flow can be delivered to the outlet section with sufficient kinetic energy. If the velocity along the flow path is too low, the effective ejection and delivery capacity of the water flow cannot be guaranteed, easily causing the water jet to fail to reach the expected landing point. The wall pressure distribution determines the load state borne by the lining structure of the spillway. Excessive pressure may cause structural overload, while excessively low pressure or even negative pressure can easily trigger cavitation erosion. The cavitation number distribution of the water flow is a key indicator for judging whether cavitation damage has occurred. When the cavitation number of the water flow is too low, dissolved gases in the high-speed water flow precipitate to form bubbles. The shock waves generated by the collapse of these bubbles in the high-pressure area have extremely strong erosion capabilities, and long-term effects will damage the surface of the spillway. Preferably, the numerical simulation model can adopt computational fluid dynamics methods, and by solving the Reynolds-averaged Navier-Stokes equations and the standard two-equation turbulence model, the flow characteristics along the spillway section and the distribution of the three hydraulic parameters can be simulated with high precision.

[0059] When it is determined that the flow patterns of both the bank slope spillway 2 and the river channel spillway 1 are rapid flows, and the velocity distribution, wall pressure distribution, and cavitation number distribution along the spillway all meet the preset thresholds, the optimal bottom slope parameter combination is verified as the target bottom slope parameter. This means that the bottom slope parameter combination, while minimizing the overall cost, fully meets the multi-dimensional hydraulic design standards such as the stable flow pattern of the rapid flow in the spillway section, kinetic energy transport capacity, structural load safety, and cavitation resistance safety, and can be directly used for the design of the target spillway structure.

[0060] When the flow type is determined to be not a rapid flow, or when any of the velocity distribution, wall pressure distribution, and cavitation number distribution along the spillway does not meet the preset threshold, it indicates that although the current optimal bottom slope parameter combination has the lowest overall cost, there are potential hydraulic safety hazards. It is necessary to identify the locations and extents of non-compliance based on the numerical simulation results, and then specifically redetermine the first and second longitudinal slopes and substitute them into the overall cost function for iterative solution until the optimal bottom slope parameter combination passes the verification of all hydraulic parameters.

[0061] The aforementioned verification and feedback iteration mechanism incorporates the results of hydraulic numerical simulation as constraints into the optimization process, ensuring that the final output target slope parameters not only meet the economic objective of minimizing overall cost, but also satisfy the multi-dimensional hydraulic design requirements of flow stability, kinetic energy transport safety, structural load safety, and cavitation resistance safety.

[0062] This invention also discloses a spillway structure, designed using the aforementioned longitudinal slope differentiation design method for high and steep slope spillways, such as... Figures 2-4 As shown, it includes: The spillway body includes side-by-side spillway 1 and bank slope spillway 2, as well as a partition wall 3 separating the side-by-side spillway 1 and bank slope spillway 2. The spillway body is divided into an inlet section 4, a channel section 5 and an outlet section 6 along the direction of water flow. The bottom slope elevation of the river channel side spillway 1 located in the inlet section 4 is the same as the bottom slope elevation of the bank slope side spillway 2 located in the inlet section 4, and the longitudinal slope of the bank slope side spillway 2 located in the spillway section 5 is less than the longitudinal slope of the river channel side spillway 1 located in the spillway section 5. Among them, the outlet section 6 corresponding to the flood discharge hole 1 on the river channel side is located upstream of the outlet section 6 corresponding to the flood discharge hole 2 on the bank slope side, and forms a stepped double outlet configuration.

[0063] By implementing the above-described spillway structure embodiment, the river-side spillway 1 and the bank-side spillway 2 are arranged side by side in the spillway body and separated by a partition wall 3. The two spillways share a single inlet in the inlet section 4. The bottom slope elevation of the river-side spillway 1 in the inlet section 4 is flush with that of the bank-side spillway 2 in the inlet section 4. This flush arrangement ensures that the two spillways obtain the same initial bottom elevation and water inlet conditions in the inlet section 4, allowing upstream water to be evenly distributed to the river-side spillway 1 and the bank-side spillway 2. This avoids unfavorable flow patterns such as flow deviation or backflow caused by uneven inflow due to inconsistent inlet bottom elevations, and provides uniform initial inflow conditions for the stable water transport in the subsequent spillway section 5.

[0064] The two outlets are arranged with different longitudinal slopes in the spillway section 5. Because the bottom slopes of the two outlets in the inlet section 4 are at the same elevation, while the longitudinal slopes of the spillway section 5 are different, the rate of descent of the channel-side spillway 1 in the spillway section 5 is greater than that of the bank-side spillway 2. This causes a gradual difference in the bottom elevation of the two outlets along the flow direction, and this difference accumulates and increases. Secondly, the outlet section 6 corresponding to the channel-side spillway 1 is located upstream of the outlet section 6 corresponding to the bank-side spillway 2. This arrangement is directly determined by the difference in the longitudinal slopes of the two outlets in the spillway section 5—the channel-side spillway 1 has a steeper longitudinal slope, thus reaching the outlet bottom elevation within a shorter horizontal length of the spillway, while the bank-side spillway 2 has a gentler longitudinal slope, requiring a longer horizontal length of the spillway to achieve the same drop in outlet bottom elevation. Therefore, the two outlet sections 6 naturally form a misalignment in the longitudinal direction of the river, and this misalignment is determined by the difference in the longitudinal slopes of the two outlets and the horizontal length of the spillway section 5.

[0065] This staggered arrangement creates a stepped, dual-outlet configuration downstream of the spillway. Two streams of water are ejected from outlet sections 6 at different longitudinal positions into the downstream channel, with the water jets naturally offset longitudinally. The degree of dispersion of the water jets' longitudinal landing points is determined by the longitudinal distance between the two outlet sections 6, which is controlled by adjusting the difference between the longitudinal slope of the bank-side spillway 2 located in the spillway section 5 and the longitudinal slope of the river-side spillway 1 located in the spillway section 5. The increased distance between the landing points of the two water jets in the longitudinal direction of the channel disperses the total downstream energy over a larger area of ​​the downstream river, significantly reducing the impact energy per unit area of ​​the riverbed. This avoids the excessively deep local scour pits or bank root scouring damage caused by concentrated water jet landing points in multi-hole, same-slope spillways, and fully utilizes the energy dissipation space of the downstream river's longitudinal water body without the need for artificial auxiliary energy dissipation structures.

[0066] Furthermore, the spillway section 5 and the outlet section 6 are connected by an upstream gentle slope, and the upstream gentle slope is arc-shaped along the direction of water flow. At the end of the outlet section 6, a diversion nose sill 61 is provided. The bottom plate of the diversion nose sill 61 is inverted arc shape, and a planar footing body 62 is provided on the bank-facing slope side of the diversion nose sill 61. The planar footing body 62 is a sloping structure on the bank-facing slope side that is higher than the river-facing slope side.

[0067] By implementing the above-described spillway structure embodiment, the water flow in the spillway section 5 is a high-speed rapid flow. If a direct broken line is used to connect the end of the spillway section 5 and the outlet section 6, the high-speed water flow is prone to generating shock waves and local negative pressure at the turning point, resulting in turbulent water flow and affecting the diversion effect of the outlet section 6. By using a gentle upstream slope with an arc shape, the high-speed water flow undergoes a smooth directional adjustment and velocity redistribution before entering the outlet section 6, and the water flow streamline gradually changes direction, avoiding water flow separation and shock waves caused by abrupt changes in the channel boundary. This ensures that the water flow enters the diversion nose sill 61 of the outlet section 6 in a stable flow state, providing a prerequisite for the diversion nose sill 61 to obtain a stable outflow state.

[0068] At the end of outlet section 6, a flow-propelling nose sill 61 with a reverse-arc bottom plate is installed. This reverse-arc bottom plate guides the water jet upwards as it flows, causing the water jet to be projected obliquely upwards at a preset launch angle into the downstream river channel. The radius of curvature of the reverse-arc shape directly affects the launch angle and projection distance of the water jet. By adjusting the radius of curvature, the lateral distance between the water jet's landing point and the bank slope can be controlled, ensuring that the water jet's landing point avoids the bank slope root.

[0069] A planar foot-attaching body 62 is provided on the bank-facing slope side of the diversion nose sill 61. Its inclined structure forms an asymmetrical constraint boundary on the bank-facing slope side of the diversion nose sill 61, which applies additional lateral lifting and guiding effect to the water flow on the bank-facing slope side. This causes the water flow on the bank-facing slope side to have a lateral component pointing towards the center of the river, while the water flow on the river-facing side is less constrained by the inclined structure and its outward direction remains relatively straight. Due to the difference in outward direction, the water flow on both sides begins to disperse laterally at the outlet, forming a fan-shaped water tongue shape with the center of the river as the axis.

[0070] The fan-shaped water tongue significantly increases the coverage area of ​​the downstream flow in the lateral plane, reducing the energy density per unit width of the flow in the direction of the river center, thus preventing energy from concentrating in a single direction and directly impacting the bank slope root. Simultaneously, the longitudinal projection provided by the inverted arc-shaped bottom plate and the lateral guidance provided by the 62-sloping structure of the planar footwork combine to give the water tongue both upward and center-direction velocity components, achieving energy dispersion in both longitudinal and lateral dimensions. This fundamentally avoids the problem of high-speed water flowing directly onto the bank slope side, effectively reducing the risk of scouring and damage to the bank slope root.

[0071] Furthermore, the outer sidewall 7 of the channel-side spillway 1 located in the outlet section 6 and the outer sidewall 7 of the bank slope-side spillway 2 located in the outlet section 6 are asymmetrical structures. The outer sidewall 7 of the channel-side spillway 1 located in the outlet section 6 is shorter than the bottom slope length of the channel-side spillway 1, while the outer sidewall 7 of the bank slope-side spillway 2 located in the outlet section 6 has the same bottom slope length as the bank slope-side spillway 2. The intermediate partition wall 3 is longer than the bottom slope length of the channel-side spillway 1 and shorter than the bottom slope length of the bank slope-side spillway 2.

[0072] By implementing the above-described spillway structure embodiment, the river-side spillway 1 has an outer sidewall 7 shorter than its bottom slope length, and the bank-side spillway 2 has an intermediate partition wall 3 shorter than its bottom slope length. Therefore, both spillways have a structure where one side wall is shorter than the corresponding bottom slope length, allowing the water flow from both spillways to escape the constraint of the shorter sidewall at the outlet in advance, thereby increasing the diffusion space in the plane.

[0073] Based on the longitudinal jetting and lateral guidance provided by the anti-arc bottom plate of the outlet section 6 and the inclined structure of the planar foot-attaching body 62, the asymmetrical sidewall 7 structure further enhances the planar dispersion effect of the water jet, making the water jet cover a larger area in the lateral space and dispersing the water flow energy in a wider lateral plane, thus avoiding the energy concentration in a narrow area in the river center and forming concentrated scouring. At the same time, the sidewall 7 on the bank slope has the same length as the bottom slope, so that the water flow on the bank slope side is still constrained and guided by the sidewall 7 in the outlet section 6, ensuring that the direction of the water flow near the bank slope side is controllable and will not deviate from the preset direction and rush directly to the root of the bank slope due to premature diffusion. This achieves the dispersion of the downstream water flow along the direction of the river center while ensuring the safety of the bank slope.

[0074] It should be understood that the above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit them. Those skilled in the art can modify the technical solutions described in the above embodiments, or make equivalent substitutions for some of the technical features; and all such modifications and substitutions should fall within the protection scope of the appended claims of the present invention.

Claims

1. A method for longitudinal slope differentiation design of spillway on steep slopes, characterized in that: The longitudinal slope differentiation design method for spillways on steep slopes includes: The initial first longitudinal slope of the bottom slope of the spillway on the bank slope and the initial second longitudinal slope of the bottom slope of the spillway on the river channel side are proposed. A comprehensive cost function is constructed based on the excavation cost of the flood discharge hole on the bank slope and the backfilling cost of the flood discharge hole on the river channel side; Substitute the first longitudinal slope and the second longitudinal slope into the comprehensive cost function, and iteratively solve to obtain the minimum value of the comprehensive cost function; The minimum value corresponds to the longitudinal slope of the spillway bottom slope on the bank side and the longitudinal slope of the spillway bottom slope on the river channel side, which are determined as the optimal combination of bottom slope parameters. The target spillway structure is then designed based on the combination of bottom slope parameters.

2. The longitudinal slope differentiation design method for spillways on steep slopes according to claim 1, characterized in that: The proposed initial first longitudinal slope of the bottom slope of the spillway on the bank slope side and the initial second longitudinal slope of the bottom slope of the spillway on the river channel side include: Determine the hydraulic constraints of the bank slope side spillway and the river channel side spillway; The critical bottom slope is determined, and the relative slope relationships between the bottom slope of the spillway on the bank side, the bottom slope of the spillway on the river channel side, and the critical bottom slope are determined under the hydraulic constraints. Based on the engineering layout conditions, the initial first longitudinal slope of the bottom slope of the flood discharge hole on the bank slope is determined under the determined relative slope relationship. Based on the relative slope relationship and the initial first longitudinal slope of the bottom slope of the spillway on the bank slope, the initial second longitudinal slope of the bottom slope of the spillway on the river channel side is determined.

3. The longitudinal slope differentiation design method for spillways on steep slopes according to claim 2, characterized in that: Determining the relative slope relationships of the bottom slopes of the spillway on the bank side, the spillway on the river channel side, and the critical bottom slope under the hydraulic constraints includes: Based on the aforementioned hydraulic constraints, the first relative relationships between the longitudinal slope of the spillway bottom slope on the bank slope side and the longitudinal slope of the spillway bottom slope on the river channel side and the critical longitudinal slope are determined respectively. Based on the original topographic conditions of the bank slope bottom slope and the original riverbed topographic conditions of the river channel bottom slope during the engineering layout, a second relative relationship between the longitudinal slope of the bank slope bottom slope and the longitudinal slope of the river channel bottom slope is determined. Based on the first relative relationship and the comprehensive slope ratio downstream of the preset dam, the relative slope relationships of the longitudinal slope of the spillway bottom slope on the bank slope side, the longitudinal slope of the spillway bottom slope on the river channel side, the longitudinal slope of the critical bottom slope, and the comprehensive slope ratio are determined. The expression for the relative slope relationship is as follows: In the formula, This indicates the overall slope ratio downstream of the dam. This indicates the longitudinal slope of the bottom slope of the spillway on the river channel side. This indicates the longitudinal slope of the bottom slope of the spillway on the bank slope. This indicates the longitudinal slope of the critical bottom slope.

4. The longitudinal slope differentiation design method for spillways on steep slopes according to claim 2, characterized in that, The step of determining the initial second longitudinal slope of the bottom slope of the river channel spillway based on the relative slope relationship and the initial first longitudinal slope of the bottom slope of the spillway on the bank slope side includes: The bottom slope increment is preset based on the determined relative slope relationship; Based on the bottom slope increment and the first longitudinal slope, the second longitudinal slope is calculated. The functional expression for calculating the second longitudinal slope is as follows: In the formula, This indicates the initial second longitudinal slope of the bottom slope of the spillway on the river channel side. This indicates the initial longitudinal slope of the bottom slope of the spillway on the bank slope. This indicates the increment of the bottom slope.

5. The longitudinal slope differentiation design method for spillways on steep slopes according to claim 2, characterized in that, The comprehensive cost function is constructed based on the excavation cost of the flood discharge outlet on the bank slope and the backfilling cost of the flood discharge outlet on the river channel side, including: Based on the excavation volume, spoil transport distance, and excavation difficulty of the spillway on the bank slope, the excavation cost is determined with the longitudinal slope of the bottom slope of the spillway on the bank slope as the independent variable. Based on the backfill volume, unit price of backfill material, and compaction cost of the bottom slope of the flood discharge hole on the river side, the backfill cost is determined with the longitudinal slope of the bottom slope of the flood discharge hole on the river side as the independent variable. Obtain the additional costs of the project, and construct the comprehensive cost function by combining the excavation cost and the backfilling cost. The expression of the comprehensive cost function is as follows: In the formula, This represents the combined cost with the longitudinal slope of the bottom slope of the spillway on the riverbank side and the longitudinal slope of the bottom slope of the spillway on the river channel side as independent variables. This represents the excavation cost with the longitudinal slope of the bottom slope of the spillway on the bank slope as the independent variable. This represents the backfill cost with the longitudinal slope of the bottom slope of the spillway on the river channel as the independent variable. This indicates the additional costs of the project.

6. The longitudinal slope differentiation design method for spillways on steep slopes according to claim 5, characterized in that, The step of substituting the first longitudinal slope and the second longitudinal slope into the comprehensive cost function and iteratively solving to obtain the minimum value of the comprehensive cost function includes: The first longitudinal slope and the second longitudinal slope are substituted into the comprehensive cost function as the initial values ​​for iteration, and the first longitudinal slope and the second longitudinal slope are changed under the hydraulic constraints. Iteratively obtain the comprehensive cost of the corresponding longitudinal slope combination after each change, and take the minimum value from all the comprehensive costs.

7. The longitudinal slope differentiation design method for spillways on steep slopes according to claim 5, characterized in that, The longitudinal slope differentiation design method for high and steep slope spillways also includes verifying the optimal combination of bottom slope parameters after determining the optimal combination, including: A numerical simulation model is established based on the determined optimal combination of bottom slope parameters; The hydraulic numerical simulation of the numerical simulation model is used to obtain the flow characteristics of the simulation output, as well as the velocity distribution, wall pressure distribution and cavitation number distribution along the flow path during the discharge. Based on the flow characteristics, determine the flow type along the course of the flood discharge holes on the bank slope and the river channel. When it is determined that the flow pattern along the path of the flood discharge hole on the bank slope side and the flood discharge hole on the river channel side is a rapid flow, and the flow velocity distribution, wall pressure distribution and water cavitation number distribution along the path of the discharge channel meet the preset threshold, then the optimal combination of bottom slope parameters is verified as the target bottom slope parameters. When it is determined that the flow type of the flood discharge hole on the bank slope side and the flood discharge hole on the river channel side is not a rapid flow, or when any of the flow velocity distribution, the wall pressure distribution and the cavitation number distribution along the discharge channel do not meet the preset threshold, the first longitudinal slope and the second longitudinal slope are re-determined and the comprehensive cost function is iterated.

8. A spillway structure, designed using the longitudinal slope differentiation design method for high and steep slope spillways as described in any one of claims 1-7, characterized in that, The spillway structure includes: The spillway body includes side-by-side spillway outlets on the river channel side and spillway outlets on the bank slope side, as well as a partition wall separating the spillway outlets on the river channel side and the spillway outlets on the bank slope side. The spillway body is divided into an inlet section, a channel section and an outlet section along the water flow direction. The bottom slope elevation of the river channel side spillway at the inlet section is the same as the bottom slope elevation of the bank slope side spillway at the inlet section, and the longitudinal slope of the bank slope side spillway at the spillway section is less than the longitudinal slope of the river channel side spillway at the spillway section. The outlet section corresponding to the river channel side flood discharge hole is located upstream of the outlet section corresponding to the bank slope side flood discharge hole, forming a stepped double outlet configuration.

9. The spillway structure according to claim 8, characterized in that: The spillway section and the outlet section are connected by an upstream gentle slope, and the upstream gentle slope is arc-shaped along the water flow direction. The end of the outlet section is provided with a diversion nose sill, the bottom plate of which is inverted arc-shaped, and a flat footing body is provided on the bank-facing slope side of the diversion nose sill. The flat footing body is a sloping structure where the bank-facing slope side is higher than the river-facing slope side.

10. The spillway structure according to claim 8, characterized in that: The river-side spillway located on the outer sidewall of the outlet section and the bank-side spillway located on the outer sidewall of the outlet section are asymmetrical structures. The outer sidewall of the river-side spillway located on the outlet section is shorter than the bottom slope length of the river-side spillway, while the outer sidewall of the bank-side spillway located on the outlet section has the same bottom slope length as the bank-side spillway. The intermediate partition wall is longer than the bottom slope length of the river-side spillway but shorter than the bottom slope length of the bank-side spillway.

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