San Mauro et al 2018a - Revision history

Rimni at 13:14, 30 April 2020

2020-04-30T13:14:18Z

Rimni at 13:12, 30 April 2020

2020-04-30T13:12:43Z

Rimni at 14:06, 29 April 2020

2020-04-29T14:06:58Z

Rimni at 14:05, 29 April 2020

2020-04-29T14:05:08Z

Rimni at 13:44, 29 April 2020

2020-04-29T13:44:57Z

Rimni at 12:59, 29 April 2020

2020-04-29T12:59:22Z

Rimni at 12:52, 29 April 2020

2020-04-29T12:52:34Z

Rimni at 12:51, 29 April 2020

2020-04-29T12:51:50Z

Rimni at 12:51, 29 April 2020

2020-04-29T12:51:31Z

Rimni at 12:51, 29 April 2020

2020-04-29T12:51:00Z

@@ Line 355: / Line 355: @@
 </div>
-where: <math>q_i</math>: seepage flow; <math>\alpha</math>: toe slope; g: gravity acceleration and <math>d_{rr}</math>: rip-rap average diameter.
+where: <math>q_i</math>: seepage flow; <math>\alpha</math>: toe slope; <math>g</math>: gravity acceleration and <math>d_{rr}</math>: rip-rap average diameter.
 Another expression among those developed in the technical literature could be used by the designer to obtain the diameter of stone.

@@ Line 283: / Line 283: @@
 |}
-where ''GS:'' maximum saturation rate input; ''H<sub>t:</sub>'' height of toe and ''y<sub>t</sub>'': maximum seepage level under the flip bucket structure.
+where <math>GS</math>: maximum saturation rate input; <math>H_t</math>: height of toe and <math>y_t</math>: maximum seepage level under the flip bucket structure.
 ::* If the following expression is true then go to step 4
@@ Line 302: / Line 302: @@
 |}
-where ''GS:'' maximum saturation rate input; ''H<sub>t:</sub>'' height of toe and ''y<sub>p</sub>'': maximum seepage level into the dam.
+where <math>GS</math>: maximum saturation rate input; <math>H_t</math>: height of toe and <math>y_p</math>: maximum seepage level into the dam.
 ::* If the following expression is true then go to step 5
@@ Line 319: / Line 319: @@
 |}
-where ''GS: ''maximum saturation rate input and ''S'': saturated percentage of the drainage layer.
+where <math>GS</math>: maximum saturation rate input and <math>S</math>: saturated percentage of the drainage layer.
 ::* If the following expression [22] is true then increase thickness of drainage until reaching safety factor value.
@@ Line 327: / Line 327: @@
 |}
-where ''F<sub>d</sub>'': safety factor against mass sliding of drainage layer; ''γ<sub>e,sat</sub>:''  saturated specific weight of the material; ''β: ''dam slope angle; ''γ<sub>w</sub>:'' specific weight of water; ϕ'':'' friction angle; ''γ<sub>e,dry</sub>:'' dry specific weight of the material; ''GS: ''maximum saturation rate input; ''y<sub>d</sub>:'' seepage level into drainage layer; ''e<sub>t</sub>:'' thickness of drainage layer; ''λ:  ''homothetic factor; ''M: ''mass of block selected for design; ''g:'' gravity acceleration; ''A<sub>B</sub>:'' lengthwise of block tested to obtain infiltration data and ''B<sub>B</sub>:'' cross length of block tested to obtain infiltration data
+where <math>F_d</math>: safety factor against mass sliding of drainage layer; <math>{\gamma }_{e,sat}</math>: saturated specific weight of the material; <math>beta</math>: dam slope angle; <math>{\gamma }_{w}</math>: specific weight of water; <math>\phi</math>: friction angle; <math>{\gamma }_{e,dry}</math>: dry specific weight of the material; <math>GS</math>: maximum saturation rate input; <math>y_d</math>: seepage level into drainage layer; <math>e_t</math>: thickness of drainage layer; \lambda:  homothetic factor; <math>M</math>: mass of block selected for design; <math>g</math>: gravity acceleration; <math>{A}_{B}</math>: lengthwise of block tested to obtain infiltration data and <math>{B}_{B}</math>: cross length of block tested to obtain infiltration data
 ::* If the following expression is true then go back to step 1 and increase toe height.
@@ Line 335: / Line 335: @@
 |}
-where ''e<sub>t</sub>'': thickness of drainage layer; ''β: ''dam slope angle and ''H<sub>t</sub>:'' toe height.
+where <math>e_t</math>: thickness of drainage layer; <math>beta</math>: dam slope angle and <math>H_t</math>: toe height.
 ::* If the following expression is true then go to step 5
@@ Line 355: / Line 355: @@
 </div>
-where: ''q<sub>i</sub>:'' seepage flow; ''α: ''toe slope; g: gravity acceleration and d''<sub>rr</sub>:'' rip-rap average diameter.
+where: <math>q_i</math>: seepage flow; <math>\alpha</math>: toe slope; g: gravity acceleration and <math>d_{rr}</math>: rip-rap average diameter.
 Another expression among those developed in the technical literature could be used by the designer to obtain the diameter of stone.

@@ Line 237: / Line 237: @@
 {| class="formulaSCP" style="width: 100%; text-align: center;"
 |-
-| <math>{H}_{T}={{H}_{T}}^{0}+{\Delta H}_{T}</math>
+| <math>{H}_{T}={H}_{T}^{0}+{\Delta H}_{T}</math>
 |}

@@ Line 176: / Line 176: @@
 |style="padding:10px;"|  [[Image:Draft_San Mauro_130090090-image14.png|452px]]
 |- style="text-align: center; font-size: 75%;"
-| colspan="1" style="padding:10px;"| '''Figure 12'''. Flowchart of the algorithm of the design procedure proposed. <math>GS</math>: maximum saturation rate input; '<math>H_t</math>: height of toe; <math>y_t</math>: maximum seepage level under the flip bucket structure; <math>y_p</math>: maximum seepage level into the dam; <math>e_t</math>: thickness of drainage layer and <math>\beta </math>: dam slope angle
+| colspan="1" style="padding:10px;"| '''Figure 12'''. Flowchart of the algorithm of the design procedure proposed. <math>GS</math>: maximum saturation rate input; <math>H_t</math>: height of toe; <math>y_t</math>: maximum seepage level under the flip bucket structure; <math>y_p</math>: maximum seepage level into the dam; <math>e_t</math>: thickness of drainage layer and <math>\beta </math>: dam slope angle
 |}
@@ Line 190: / Line 190: @@
 |}
+where: <math>{F}_{r}</math> is safety factor against mass sliding of toe protection; <math>{\gamma }_{e,sat}</math>: saturated specific weight of the material; <math>\alpha</math>: toe slope angle; <math>{\gamma }_{w}</math>: specific weight of water and <math>\phi </math>: friction angle.
-Where: ''F<sub>r</sub> ''is safety factor against mass sliding of toe protection; ''γ<sub>e,sat</sub>:'' saturated specific weight of the material; ''α: ''toe slope angle; ''γ<sub>w</sub>'': specific weight of water and ϕ: friction angle.
 :* Calculation of an initial height of training walls from broad crested weir discharge equation:
@@ Line 207: / Line 206: @@
 |}
+where: <math>q</math>: unit discharge flow; <math>Q</math>: total discharge flow; <math>B</math>: width of spillway; <math>h</math>: height of training walls without safety factor; <math>{h}_{c0}</math>: height of training walls considering safety factor; <math>K</math>: safety factor and <math>g</math>: gravity acceleration.
-Where: ''q:'' unit discharge flow; ''Q:'' total discharge flow; ''B:'' width of spillway; ''h:'' height of training walls without safety factor; ''h<sub>c0</sub>:'' height of training walls considering safety factor; ''K:'' safety factor and ''g:'' gravity acceleration.
 :* Calculation of initial height of toe according to the expression:
@@ Line 216: / Line 214: @@
 |}
-where ''H<sub>t0</sub>:'' initial height of toe; ''h<sub>c0</sub>:'' initial height of training walls and ''β: ''dam slope angle.
+where <math>{H}_{T0}</math>: initial height of toe; <math>{h}_{c0}</math>: initial height of training walls and <math>\beta</math>: dam slope angle.
 A scheme of the geometrical meaning of the previous equation is shown in Figure 13.
@@ Line 223: / Line 221: @@
 |style="padding:10px;"|  [[Image:Draft_San Mauro_130090090-image15-c.png|348px]]
 |- style="text-align: center; font-size: 75%;"
-| colspan="1" style="padding:10px;"| '''Figure 13'''. Scheme of relation between parameters ''H<sub>t0</sub>:'' initial height of toe; ''h<sub>c0</sub>:'' initial height of training walls and ''β: ''dam slope angle
+| colspan="1" style="padding:10px;"| '''Figure 13'''. Scheme of relation between parameters <math>{H}_{T0}</math>: initial height of toe; <math>{h}_{c0}</math>: initial height of training walls and <math>\beta</math>: dam slope angle
 |}
 :* Calculation of homothetic factor
@@ Line 233: / Line 230: @@
 |}
+where: <math>\lambda</math>: homothetic factor; <math>M</math>: mass of block selected for design and <math>{M}_{B}</math>: mass of block tested to obtain infiltration data
-Where: ''λ:'' homothetic factor; ''M: ''mass of block selected for design and ''M<sub>B</sub>:'' mass of block tested to obtain infiltration data
 STEP 1 – Geometric update
@@ Line 244: / Line 240: @@
 |}
+where: <math>H_T</math> updated height of toe; <math>H_T^0</math>: height of toe for the previous iteration and <math>{\Delta H}_{T}</math>: increase of height fixed by designer (Figure 14). For the first run of step 1 <math>H_T^0 = {\Delta H}_{T}</math>; <math>{\Delta H}_{T}=0</math>.
-Where: ''H<sub>t:</sub>'' updated height of toe; ''H<sub>t</sub><sup>0</sup>:'' height of toe for the previous iteration and ''ΔH<sub>t</sub>:'' increase of height fixed by designer (Figure 14). For the first run of step 1 ''H<sub>t</sub><sup>0 </sup>''=''ΔH<sub>t</sub> ; ΔH<sub>t</sub>''=0
 :* Updating of training walls height:
@@ Line 253: / Line 248: @@
 |}
-where ''H<sub>t</sub>:'' toe height; ''h<sub>c</sub>'': training walls height and ''β: ''dam slope angle.
+where <math>H_t</math>: toe height; <math>H_c</math>: training walls height and <math>\beta</math>: dam slope angle.
 The geometrical relation between parameters is shown in Figure 14.
@@ Line 260: / Line 255: @@
 |style="padding:10px;"| [[Image:Draft_San Mauro_130090090-image16.png|348px]]
 |- style="text-align: center; font-size: 75%;"
-| colspan="1" style="padding:10px;"| '''Figure 14'''. Scheme of relation between parameters ''H<sub>t</sub><sup>0</sup>:'' height of toe for the previous iteration;  ''ΔH<sub>t</sub>:'' increase of height fixed by designer; ''h<sub>c</sub>'': training walls height and ''β: ''dam slope angle
+| colspan="1" style="padding:10px;"| '''Figure 14'''. Scheme of relation between parameters <math>H_T^0</math>: height of toe for the previous iteration;  <math>{\Delta H}_{T}</math>: increase of height fixed by designer; <math>H_c</math>: training walls height and <math>\beta</math>: dam slope angle
 |}

@@ Line 517: / Line 517: @@
 [9] Rossi R., Larese A., Dadvand P., Oñate E. An efficient edge-based level set finite element method for free surface flow problems. International Journal for Numerical Methods in Fluids, 71(6):687-716, 2013.
-[10] Codina R. Stabilization of incompressibility and convection through orthogonal sub-scales in finite element method. Computer Methods in Applied Mechanics and Engineering.190, 1579–1599, 2000.
+[10] Codina R. Stabilization of incompressibility and convection through orthogonal sub-scales in finite element method. Computer Methods in Applied Mechanics and Engineering, 190:1579–1599, 2000.
-[11] Principe, J., Codina, R., Henke, F. The dissipative structure of variational multiscale methods for incompressible flows. Computer Methods in Applied Mechanics and Engineering.199 (13), 791-801, 2010.
+[11] Principe J., Codina R., Henke F. The dissipative structure of variational multiscale methods for incompressible flows. Computer Methods in Applied Mechanics and Engineering, 199(13):791-801, 2010.
-[12] Larese, A., Rossi, R., Oñate, E. Finite element modeling of free surface flow in variable porosity media. Archives of Computational Methods in Engineering, 22(4), 637-653, 2015.
+[12] Larese A., Rossi R., Oñate E. Finite element modeling of free surface flow in variable porosity media. Archives of Computational Methods in Engineering, 22(4): 637-653, 2015.
-[13] Larese, A., Rossi, R., Oñate, E., Toledo, M.A., Morán, R., Campos, H. Numerical and experimental study of overtopping and failure of rockfill dams. International Journal of Geomechanics.15(4), 04014060, 2013.
+[13] Larese A., Rossi R., Oñate E., Toledo M.A., Morán R., Campos H. Numerical and experimental study of overtopping and failure of rockfill dams. International Journal of Geomechanics, 15(4):04014060, 2013.
-[14] San Mauro, J., Salazar, F., Toledo, M. A., Caballero, F. J., Ponce-Farfan, C., Ramos, T. Physical and numerical modeling of labyrinth weirs with polyhedral bottom. Ingeniería del Agua, 20(3), 127-138, 2016.
+[14] San Mauro J., Salazar F., Toledo M.A., Caballero F.J., Ponce-Farfan C., Ramos T. Physical and numerical modeling of labyrinth weirs with polyhedral bottom. Ingeniería del Agua, 20(3):127-138, 2016.
-[15] Salazar, F., San Mauro, J., Oñate, E., Toledo, M. Á. CFD analysis of flow pattern in labyrinth weirs. I International Seminar on Dam Protection Against Overtopping. Madrid, 24-25 November 2014.
+[15] Salazar F., San Mauro J., Oñate E., Toledo M.Á. CFD analysis of flow pattern in labyrinth weirs. I International Seminar on Dam Protection Against Overtopping, Madrid, 24-25 November 2014.
-[16] ES 2595852 B2. Ministerio de Industria Energía y Turismo. Oficina Española de Patentes y Marcas, Tomo II: Invenciones,  Boletín Oficial de la Propiedad Industrial, no. 4915, 8 de Mayo de 2017.
+[16] ES 2595852 B2. Ministerio de Industria Energía y Turismo. Oficina Española de Patentes y Marcas. Tomo II: Invenciones,  Boletín Oficial de la Propiedad Industrial, no. 4915, 8 de Mayo de 2017.
-[17] Morán, R., Toledo, M. A. Design and construction of the Barriga Dam spillway through an improved wedge-shaped block technology. Canadian Journal of Civil Engineering, 41(10), 924-927, 2014.
+[17] Morán R., Toledo M.A. Design and construction of the Barriga Dam spillway through an improved wedge-shaped block technology. Canadian Journal of Civil Engineering, 41(10):924-927, 2014.
-[18] Toledo, M.A. Embankment dams slip failure due to overtopping. XIX International Congress on Large Dams, ICOLD, Florence, Italy 1997.
+[18] Toledo M.A. Embankment dams slip failure due to overtopping. XIX International Congress on Large Dams, ICOLD, Florence, Italy 1997.
-[19] Salazar, F., Morán, R., Rossi, R., and Oñate, E. “Analysis of the discharge capacity of radial-gated spillways using CFD and ANN–Oliana Dam case study,” Journal of Hydraulic Research, 51 (3), 244–252, 2013.
+[19] Salazar F., Morán R., Rossi R., Oñate E. Analysis of the discharge capacity of radial-gated spillways using CFD and ANN–Oliana Dam case study. Journal of Hydraulic Research, 51(3):244–252, 2013.
-[20] Venables, W. N., Ripley, B. D. Modern Applied Statistics with S. Fourth Edition.Springer, New York. 2002. ISBN 0-387-95457-0
+[20] Venables W.N., Ripley B.D. Modern Applied Statistics with S. Fourth Edition, Springer, New York, 2002. ISBN 978-0-387-95457-8.
-[21] Ergun, S., Orning, A.A.Fluid flow through randomly packed columns and fluidized beds. Industrial & Engineering Chemistry, 41(6), 1179-1184, 1949.
+[21] Ergun S., Orning A.A. Fluid flow through randomly packed columns and fluidized beds. Industrial & Engineering Chemistry, 41(6):1179-1184, 1949.
-[22] San Mauro, J., Larese, A., Salazar, F., Irazábal, J., Morán, R., Toledo, M. A. Hydraulic and stability analysis of the supporting layer of wedge-shaped blocks. II International Seminar on Dam Protection Against Overtopping. Ft. Collins, Colorado, USA, 7-9 September 2016.
+[22] San Mauro J., Larese A., Salazar F., Irazábal J., Morán R., Toledo M.A. Hydraulic and stability analysis of the supporting layer of wedge-shaped blocks. II International Seminar on Dam Protection Against Overtopping, Ft. Collins, Colorado, USA, 7-9 September 2016.
-[23] Knauss, J.  Computation of maximum discharge at overflow rockfiil dams, a comparison of different model test results. ICOLD congress New Delhi 1979.
+[23] Knauss J.  Computation of maximum discharge at overflow rockfiil dams, a comparison of different model test results. ICOLD congress New Delhi, 1979.
 [24] RStudioTeam. RStudio: Integrated Development Environment for R. RStudio, Inc., Boston, MA. <URL: [http://www.rstudio.com/ http://www.rstudio.com/]>.
@@ Line 549: / Line 549: @@
 [25] R Core Team. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. <URL: [https://www.R-project.org/ https://www.R-project.org/]>.
-[26] Chang W, Cheng J, Allaire J, Xie Y and McPherson J. Shiny: Web Application Framework for R. R package version 1.0.5, <URL: [https://CRAN.R-project.org/package=shiny https://CRAN.R-project.org/package=shiny]>.
+[26] Chang W., Cheng J., Allaire J., Xie Y.,  McPherson J. Shiny: Web Application Framework for R. R package version 1.0.5, <URL: [https://CRAN.R-project.org/package=shiny https://CRAN.R-project.org/package=shiny]>.
 </div>

@@ Line 499: / Line 499: @@
 <div class="auto" style="width: auto; margin-left: auto; margin-right: auto;font-size: 85%;">
-[1] Pravdivets, Y. P., Slissky, S. M. Passing floodwaters over embankment dams. Water Power & Dam Construction, 33(7), 30-32, 1981.
+[1] Pravdivets Y.P., Slissky S.M. Passing floodwaters over embankment dams. Water Power & Dam Construction, 33(7):30-32, 1981.
-[2] Hewlett, H., Baker, R., May, R., and Pravdivets, Y. P. Design of stepped-block spillways. Construction Industry Research and Information Association. London, U.K 1997.
+[2] Hewlett H., Baker R., May R., Pravdivets Y.P. Design of stepped-block spillways. Construction Industry Research and Information Association, London, U.K, 1997.
-[3] Frizell, K. H. Protecting embankment dams with concrete stepped overlays. Hydro Review,  16(5), 1997.
+[3] Frizell K.H. Protecting embankment dams with concrete stepped overlays. Hydro Review,  16(5), 1997.
-[4] Relvas, A. T., Pinheiro, A. N. Inception point and air concentration in flows on stepped chutes lined with wedge-shaped concrete blocks.  Journal of Hydraulic Engineering, 134(8), 1042-1051, 2008.
+[4] Relvas A.T., Pinheiro A.N. Inception point and air concentration in flows on stepped chutes lined with wedge-shaped concrete blocks.  Journal of Hydraulic Engineering, 134(8):1042-1051, 2008.
-[5] Caballero, J., Salazar, F., San Mauro, J., Toledo, M.A. Physical and Numerical modeling for understanding the hydraulic behaviour of Wedge-Shaped-Blocks spillways. I International Seminar on Dam Protection Against Overtopping. Madrid, 24-25 November 2014.
+[5] Caballero J., Salazar F., San Mauro J., Toledo M.A. Physical and Numerical modeling for understanding the hydraulic behaviour of Wedge-Shaped-Blocks spillways. I International Seminar on Dam Protection Against Overtopping, Madrid, 24-25 November 2014.
-[6] Morán, R. Wedge-shaped blocks: a historical review. II International Seminar on Dam Protection Against Overtopping. Ft. Collins, Colorado, USA, 7-9 September 2016.
+[6] Morán R. Wedge-shaped blocks: a historical review. II International Seminar on Dam Protection Against Overtopping, Ft. Collins, Colorado, USA, 7-9 September 2016.
-[7] Caballero, F. J., Toledo, M. Á., Morán, R., San Mauro, J., Salazar, F. Advances in the understanding of the hydraulic behavior of wedge-shape block spillways. II International Seminar on Dam Protection Against Overtopping. Ft. Collins, Colorado, USA, 7-9 September 2016.
+[7] Caballero F.J., Toledo M.Á., Morán R., San Mauro J., Salazar F. Advances in the understanding of the hydraulic behavior of wedge-shape block spillways. II International Seminar on Dam Protection Against Overtopping, Ft. Collins, Colorado, USA, 7-9 September 2016.
-[8] Dadvand, P., Rossi,R., and Oñate,E. An object-oriented environment for developing finite element codes for multi-disciplinary applications. Archives of Computational Methods in Engineering, 17, 253–297, 2010.
+[8] Dadvand P., Rossi R., Oñate E. An object-oriented environment for developing finite element codes for multi-disciplinary applications. Archives of Computational Methods in Engineering, 17(3):253–297, 2010.
-[9] Rossi, R., Larese, A., Dadvand, P., Oñate, E. An efficient edge-based level set finite element method for free surface flow problems. International Journal for Numerical Methods in Fluids, 71(6), 687-716, 2013.
+[9] Rossi R., Larese A., Dadvand P., Oñate E. An efficient edge-based level set finite element method for free surface flow problems. International Journal for Numerical Methods in Fluids, 71(6):687-716, 2013.
 [10] Codina R. Stabilization of incompressibility and convection through orthogonal sub-scales in finite element method. Computer Methods in Applied Mechanics and Engineering.190, 1579–1599, 2000.

@@ Line 482: / Line 482: @@
 It should be noted that there is an option in the tool to carry out an economical optimization of a WSB spillway, regarding the provider’s range of blocks and several widths of discharge channel.
-==4 Summary and conclusions==
+==4. Summary and conclusions==
 A design procedure for WSB spillways based on numerical modeling of infiltration was presented. This procedure defines the appropriate geometry of the spillway to ensure the stability of the dam against sliding with a sloping toe protection, and to ensure the stability of blocks avoiding water pressure under it.

@@ Line 376: / Line 376: @@
 '''Table 1'''. Input and output parameters of the design process.</div>
-{| style="width: auto;margin: 1em auto 0.1em auto;border-collapse: collapse;font-size:85%;width:85%;"
+{| style="width: auto;margin: 1em auto 0.1em auto;border-collapse: collapse;font-size:85%;width:75%;"
 |- style="border: 2pt solid black;border-bottom: 2pt solid black;"
 |  style="text-align: center;vertical-align: top;"|'''INPUT'''

@@ Line 381: / Line 381: @@
 |  style="text-align: center;vertical-align: top;"|'''OUTPUT'''
 |-
-|  style="border-left: 1pt solid black;border-right: 1pt solid black;text-align: center;vertical-align: top;width:200px;"|Type of dam
+|  style="border-left: 1pt solid black;border-right: 1pt solid black;text-align: center;vertical-align: top;width:180px;"|Type of dam
-|  style="border-left: 1pt solid black;border-right: 1pt solid black;text-align: center;vertical-align: top;width:200px;"|Toe slope
+|  style="border-left: 1pt solid black;border-right: 1pt solid black;text-align: center;vertical-align: top;width:180px;"|Toe slope
 |-
 |  style="border: 1pt solid black;text-align: center;vertical-align: top;"|Downstream slope of dam

@@ Line 411: / Line 411: @@
 |  style="border: 1pt solid black;text-align: center;vertical-align: top;"|
 |-
-|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|Safety factor of drainage layer against mass sliding
+|  style="border: 1pt solid black;text-align: center;vertical-align: top;"|Safety factor of drainage layer against mass sliding (only for homogeneous dam)
-−
 (only for homogeneous dam)
 |  style="border: 1pt solid black;text-align: center;vertical-align: top;"|
 |-