Propose of Design Method on Level II load of open Sabo dam

. This study presents a load model of the Level II design for a steel pipe open Sabo dam. The Level II design is associated with a lower occurrence frequency than the conventional design concept, to the performance of debris flow trapping efficacy against higher discharge caused by heavy precipitation in recent years. A dynamic load model reveals experimental observations, and static models similar to the conventional design load models are evaluated from the viewpoint of a rational load. Dynamic and elastoplastic analyses are conducted for one structure, and three types of basin area models utilized Level II load models using a dynamic load. The safety evaluation results confirm that the design load models are composed of each other.


Introduction
In recent year, steel pipe open Sabo dams have been constructed to maintain continuity river for environment. However, there have been reports of damage by the generation of debris flows that exceed the design load [1]. Therefore, a system for a design load level larger than the current design load level (hereafter, Level-II) is studied [2,3]. Ishikawa et al. [3] proposed that a Level-II load can be set under excess probability (200-1000 years). Ishikawa [4] proposed a method for probabilistically estimating the planned peak debris flow by indicating the correlation between the amount of sediment and basin area. However, the definition of combining Level-II loads and structural responses remains unclear.
The study proposes a method for setting the Level-II load in the design of open Sabo dams, and examines the Level-II verification method which assumes that the limit state of the structural response is the limit value of the elasto-plastic response of the member. In addition, a static design load equivalent to the dynamic design one is examined.

Proposed Level-I load and Level-II load
The proposed design loads can be considered based on the form of the current design load in Fig.1. For Model-I as Level-I load, the debris flow fluid force statically acts on the upper part, and the sediment pressure load statically acts on the lower part. The debris flow load is determined from the rainfall of 100 year excess probability. The stability of the structure is an allowable stress design method that ensures that each member is within the elastic response value. Model-II is a dynamic load proposed by Komatsu et al. [5]. Because Model II * Corresponding author: htoshi@nda.ac.jp make the structural response a dynamic response, it is possible to reproduce close to the actual situation. If the limit state in the design is defined as the plastic rotation angle of the member reaching the allowable rotation angle, the verification is expressed below.
where, δi-max is the maximum deformation of the member, δαi is the allowable deformation of the member, δfi is the failure deformation of the member, γD is the safety factor corresponding to the dynamic response. The fracture deformation of a member is limit state. The safety factors corresponding to the dynamic response are those for Level II loads. This study utilizes the 99 % prediction line illustrated in Fig. 2.
The design of the open Sabo dam is based on data obtained from topographic surveys. The amount of sediment released is determined by comparing the amount of sediment that can be moved within the basin area, with the amount of sediment that can be transported by a planned debris flow based on the amount of rainfall. The peak flow can be expressed by the following equation: where QP is the peak flow rate (m 3 /s), C* is the volumetric concentration of deposited sediment, Vdqp is the sediment volume (m 3 ), Cd is the flow rate is planned at the installation location. The flow rate is initially planned at the installation location. The flow rate is obtained using the regression equation illustrated in Fig. 2(a) [4].
where QP I is the flow rate of the Level-I load (m 3 /s), AB is the basin area (km 2 ).
The velocity of the debris flow is determined using Manning's equation as follows: where v is the velocity of the debris flow (m/s), n is Manning's roughness coefficient (s･m -1/3 ) (n = 0.1 used in the design), Dr is the diameter depth (m) (Dr ≈ Dd (: water depth (m)), and θS is the slope of the stream bed. The equation of continuity is expressed as follows: where Q is the flow rate (m 3 /s), Ad is the cross-sectional area (m 2 ). The cross-sectional area of the flow can be expressed by the following equation: where Bda is the width of flow (m). The 99 % prediction line can be used to establish the planned sediment discharge and flow rate for Level-II load shown to Fig. 2 where, QP II is the flow rate (m 3 /s) of the Level-II load.
The debris flow fluid force is expressed below.
where F is the debris flow force (kN/m), Kh is the coefficient of debris flow force, γd is the unit volume weight of the debris flow (15.8 kN/m 3 ), g is the gravitational acceleration. Sediment pressure acts below the depth of the debris flow from the height of the dam.
where PeH is the sediment pressure (kN/m), Ce is the earth pressure coefficient (0.45), γe is the unit volume weight of the sediment (15.3 kN/m 3 ), he is the sediment height (m). The time required for the debris flow to reach the top of the open Sabo dam is defined.

Basin condition
Basin area is adopted as a parameter in the analysis. Three cases of basin area AB = 0.5, 1.0, 2.0 km 2 are adopted. The bed slope is set as the slope of the debris flow section (θs = 10 °). The design condition is a riverbed width of Bda = 10.7 m.

Open Sabo dam model
As shown to Fig. 3, an open Sabo dam model is 9.0 m height, 9.5 m width, and 3.5 m depth. All the joints are of the same cross-section, and joint pipes are not considered in open Sabo dam model. The spacing between each member is set with a maximum gravel diameter 1.0 m. The cross section of the steel pipe is set to a diameter D = 508 mm, wall thickness t = 22 mm. The open Sabo dam model for the basin area is assumed under the same conditions. The steel pipe material used is STK490. The compression and tension are set to the same value for computational efficiency. Bending failure is considered instead of failure. The sectioning method is employed to obtain the bending momentcurvature relationship, axial force-strain relationship, and torsional moment-torsional rate relationship for a circular tube cross-section. FEM is utilized for this analysis, which is capable of simulating large deformations of structures. The amount of plastic deformation is determined using the associated flow law.
The limit value of the plastic rotation angle is set to the limit corresponding to the local buckling during compression. In addition, the function Φy representing the elastic limit and plasticization function are expressed by the following equations: where M1 is the bending moment around the crosssectional principal axis, M2 is the bending moment around the cross-sectional axis, N is the axial force, T is the torsional moment, MY is the yield moment, MP is the plastic moment, NY is the yield axial force, NP is the plastic axial force, TY is the yield torsional moment, and TP is the plastic torsional moment. Table 1 presents the parameters for Level-I load. Eqs (4)-(7), (9), (10) are adopted to determine the debris flow load and sediment pressure in each basin area. The structural response of the structure is investigated by static analysis under the influence of debris flow forces and sediment pressure. The Level-I load is 'static load'. Table 2 present the parameters for Level-II load. Eqs (5)-(11) are adopted to determine the debris flow forces and time to reach the top of the open Sabo dam for each basin area. The load-time relationship acting on each node is illustrated in Fig.4. The maximum total load for a basin area of AB = 0.5 km 2 is 57.1 kN/m 2 . The maximum total load for a basin area of AB = 1.0 km 2 is 77.2 kN/m 2 . The maximum total load for a basin area of AB = 2.0 km 2 is 128.7 kN/m 2 . The load reduction after the maximum total load decreased is similar to the slope at which the maximum load is reached. This is a dynamic loading model that remains constant when the sediment pressure load is reached. The Level-I load is 'dynamic load'.

Level-I load
The analysis resulted in an elastic response. Fig.5 illustrates the locations of the members. Fig.6 illustrates the stresses in the members by basin area. Stresses in the members are indicated at the top, and stresses in the upstream and downstream column members and firststage joint are indicated. The stresses are expressed using the following equations: where, σi is the stress in member i (N/m 2 ), Mmax is the maximum bending moment in the cross section (N･m), Z is the section modulus (m 3 ), N is the axial force (N), Am is the cross-sectional area of the member (m 2 ). Fig.7 shows the simulated structural response of Model II (AB = 2.0 km 2 ). Fig.7(a) illustrates that the height reaches 2.7 m above the bottom of the open Sabo dam.  Bending moments close to the yield bending moment occur in the upstream and downstream column members and in the first-stage horizontal joint. In particular, the first-stage horizontal joint material is plasticized. Fig. 9 illustrates a study of the limit rotation angle due to the local buckling of the steel pipes. Suganuma et al.

Model-II
[7] illustrated a bending moment and rotation angle relationship for a diameter-to-thickness ratio D/t = 40.1. The angle of rotation corresponding to the maximum bending moment is θf_1 = 17.5 × 10 -2 rad (≈ 10 °). Hoshikawa et al. [8] proposed the following equation for the critical rotation angle θf_2, which corresponds to local buckling: Substituting D/t = 23.1 for this analytical model into this equation, we obtain θf_2 = 10.5 × 10 -2 rad (≈ 6 °). The ratios of the respective plastic rotation angles are approximately 30 and 18, respectively. Therefore, the following description is based on the most stressed basin area AB = 2.0 km 2 .

Conclusions
The results are summarized as follows: (1) Level-II loads were considered assuming a 99 % non-exceedance probability.
(2) The proposed design load models were Model-II for dynamic analysis of structural response. The characteristics of each design load model were evaluated by numerical analysis on a typical structural model.
(3) In Model-II, the dynamic effect was negligible, and the plastic rotation angle generated in the member was evaluated to be approximately 1/20 of the rotation angle limit value, which is sufficient to provide a safety margin.
This study evaluated the response from structural stability based on the worst load, and the effects of actual sediment/soils need to be investigated.