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Optimization of the performance of riprap apron to protect spur dikes against scouring using Taguchi and grey relational analysis methods

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Abstract

One of the most significant problems faced by hydraulic engineers is the local scouring of in-stream structures. The optimal design of scour protection methods requires time consuming, laborious and costly studies. Fractional factorial methods have been provided to formulate experimental designs which can optimize designs with fewer experiments and high accuracy. Therefore, this study aimed at using Taguchi and grey relational analysis (GRA) methods to investigate the effect of three factors: (1) spur dike angle, (2) size of riprap stones, and (3) riprap extent on the local scouring. An additional goal was to achieve an economical pattern for the riprap apron so that it delivers the best performance in protecting spur dikes with different angles. The results show that the riprap apron decreases the scouring depth and moves the scouring hole away from around the structure. However, increasing the spur dike angle decreases its performance in scouring reduction. Increasing the area of the riprap apron protected the downstream walls better and reduced the edge failure of the riprap; however, the erosion in the opposite wall increased. In addition, analysis of variance showed that the riprap extent and the spur dike angle, respectively, have the highest effects on the riprap performance, respectively. The comparison of the predictions of the Taguchi and GRA methods with observed values showed that these two methods have high capabilities to predict the results of scouring studies.

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Abbreviations

Ar :

Area of riprap extent (cm2)

B:

Flume width (cm)

Cf%:

Percentage contribution

\({\overline{A} }_{m}\), \({\overline{B} }_{m}\) and \({\overline{C} }_{m}\) :

Mean of response values for each factor at level m

Dr50 :

Median diameter of stable riprap aggregates (mm)

d50 :

Median diameter of bed particles (mm)

ds:

Maximum scour depth for protected tests (cm)

dsu :

Maximum scour depth for control tests (cm)

Fr1 :

Froude number at the abutment section

fx :

Response variable value in equation 6

g:

Gravitational acceleration (m/s2)

L:

Effective length of spur dike (cm)

n:

Number of response variables

nIm :

number of occurrences of factor I at level m

Q:

Flow discharge (lit/s)

Rds%:

Percentage reduction of maximum scour depth

RV% :

Percentage reduction of scour volume

T:

Sum of response variables

t:

Riprap layer thickness (cm)

U:

Mean velocity of flow (m/s)

U1 :

Mean velocity of flow at the abutment section (m/s)

Ucr :

Particle threshold velocity (m/s)

u*cr :

Critical shear velocity (cm/s)

Ss:

Relative density of the riprap aggregates

SSF :

Sum of squares for the factor F

SST :

Sum of squares of all factors

Vu :

Scour volume for control tests (cm3)

V:

Scour volume for unprotected tests (cm3)

W:

Distance from the tip of the spur dike to the edge of the riprap extent (cm)

xi(k):

Grey Relational Generation (GRN)

Y:

Flow depth (cm)

θ:

Spur dike installation angle

η:

predicted response variable

ζ:

Distinguishing coefficient

\({\upgamma }_{{\text{0,i}}} \left( {\text{k}} \right)\) :

Grey Relational Coefficient (GRC)

\({\upgamma }_{{\text{0,i}}}\) :

Grey Relational Grade (GRG)

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Authors and Affiliations

  1. Department of Water Engineering and Hydraulic Structures, Faculty of Civil Engineering, Semnan University, Semnan, Iran

    Amin Atarodi & Hojat Karami

  2. Department of Civil and Environmental Engineering, Amirkabir University of Technology, Tehran, Iran

    Abdollah Ardeshir & Khosrow Hosseini

  3. Department of Architectural and Environmental Engineering, Illinois Institute of Technology, Chicago, USA

    David Lampert

Authors
  1. Amin Atarodi
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  2. Hojat Karami
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  3. Abdollah Ardeshir
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  4. Khosrow Hosseini
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  5. David Lampert
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Correspondence to Hojat Karami.

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Atarodi, A., Karami, H., Ardeshir, A. et al. Optimization of the performance of riprap apron to protect spur dikes against scouring using Taguchi and grey relational analysis methods. Sādhanā 48, 18 (2023). https://doi.org/10.1007/s12046-022-02073-0

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  • DOI: https://doi.org/10.1007/s12046-022-02073-0

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