Lopes et al 2020a - Revision history

Rimni at 11:21, 17 September 2021

2021-09-17T11:21:58Z

Rimni at 11:20, 17 September 2021

2021-09-17T11:20:40Z

Show changes

Rimni at 10:10, 17 September 2021

2021-09-17T10:10:50Z

Rimni at 10:10, 17 September 2021

2021-09-17T10:10:07Z

Rimni at 10:09, 17 September 2021

2021-09-17T10:09:36Z

Rimni at 10:09, 17 September 2021

2021-09-17T10:09:03Z

Rimni at 10:06, 17 September 2021

2021-09-17T10:06:24Z

Rimni at 09:14, 17 September 2021

2021-09-17T09:14:58Z

Rimni: /* 4.2.2 Permeability coefficient effects */

2021-09-17T09:14:24Z

‎4.2.2 Permeability coefficient effects

Rimni: /* 4.2.2. Permeability coefficient effects */

2021-09-17T09:12:14Z

‎4.2.2. Permeability coefficient effects

@@ Line 10: / Line 10: @@
 *e-mail: [mailto:kronemberger.guilherme@laceo.coppe.ufrj.br kronemberger.guilherme@laceo.coppe.ufrj.br], Tel.: +55 24992272120
 -->
 ==Abstract==

@@ Line 804: / Line 804: @@
 Despite the insights obtained in the analyses of finless torpedo anchors, which may help design fixed points to anchor flexible lines, monobuoys or floating production systems in shallow waters, some important aspects were not addressed in this work. It is important to emphasize that the FE analyses did not consider thixotropic effects, and further investigations over this phenomenon are recommended. Thixotropy may rule the soil regain in the first instants of time after installation. Moreover, the effect of the setup when inclined loads are imposed on the anchor is another aspect that deserves future investigation. However, Sousa et al. [4] showed that, for inclinations between 40 degrees and 90 degrees (vertical), the holding capacity of the anchor can be obtained by simply projecting the pullout load in the considered direction. Finally, this study concentrated on finless torpedo anchors, but several torpedo anchors have fins that may also affect the soil stress state during installation. The effect of the fins has also to be considered in future studies.
-==6. Acknowledgments==
+==Acknowledgments==
 Authors also thank the National Council for Scientific and Technological Development (CNPq) for the research grants PQ-311084/2019-2 and PQ-306357/2018-6, the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior- Brasil (CAPES), Finance Code 001, and the Fundação Carlos Chagas de Amparo à Pesquisa do Estado do Rio de Janeiro (FAPERJ).

@@ Line 762: / Line 762: @@
 {| style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: auto;max-width: auto;"
 |-
-|style="padding:10px;"| [[Image:Draft_Kronemberger Lopes_857637204-image25.png|600px]]
+|style="padding:10px;"| [[Image:Draft_Kronemberger Lopes_857637204-image25.png|450px]]
 |- style="text-align: center; font-size: 75%;"
 | colspan="1" style="padding:10px;"| '''Figure 25'''. Comparison between methodologies – Soil A

@@ Line 741: / Line 741: @@
 {| style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: auto;max-width: auto;"
 |-
-|style="padding:10px;"| [[Image:Draft_Kronemberger Lopes_857637204-image24.png|450px]]
+|style="padding:10px;"| [[Image:Draft_Kronemberger Lopes_857637204-image24.png|400px]]
 |- style="text-align: center; font-size: 75%;"
 | colspan="1" style="padding:10px;"| '''Figure 24'''. Comparison between total radial stresses – Soils A and B

@@ Line 757: / Line 757: @@
 In general, all methodologies have similar behavior, except for the initial instants of time for the ABS <span id='cite-_Ref51515640'></span>[[#_Ref51515640|[20]]] formulation, which starts with a lower holding capacity value. Results obtained from FEM analyses estimated pullout capacities slightly lower for a consolidation time of 18 000 days when compared to the other methodologies. It is emphasized that for all soils analyzed, only the ABS <span id='cite-_Ref51515640'></span>[[#_Ref51515640|[20]]] formulation and the analytical methodology based on α-method of API <span id='cite-_Ref502324791'></span>[[#_Ref502324791|[21]]] did not present a predominant linear behavior.
-Skov and Denver [17] empirical formulation, Eq. <span id='cite-_Ref52376815'></span>[[#_Ref52376815|(15)]], presented an excellent agreement for the first ten days after anchor installation. On the other hand, the analytical methodology based on the α-method of API <span id='cite-_Ref502324791'></span>[[#_Ref502324791|[21]]] showed better approaches for consolidation times over 100 days.
+Skov and Denver [[#_Ref534978548|[17]]] empirical formulation, Eq. <span id='cite-_Ref52376815'></span>[[#_Ref52376815|(15)]], presented an excellent agreement for the first ten days after anchor installation. On the other hand, the analytical methodology based on the α-method of API <span id='cite-_Ref502324791'></span>[[#_Ref502324791|[21]]] showed better approaches for consolidation times over 100 days.
 <div id='_Ref52371311'></div>
@@ Line 785: / Line 785: @@
 |}
 The undrained shear strength of the soil has a major impact on the ABS <span id='cite-_Ref51515640'></span>[[#_Ref51515640|[20]]] formulation compared to the other methodologies. As shown in <span id='cite-_Ref52371311'></span>[[#_Ref52371311|Figures 25]] to <span id='cite-_Ref52371314'></span>[[#_Ref52371314|27]], the pullout capacity increases at a higher rate compared to other formulations. For soil C, the ABS <span id='cite-_Ref51515640'></span>[[#_Ref51515640|[20]]] formulation approaches the Skov and Denver <span id='cite-_Ref534917435'></span>[[#_Ref534917435|[18]]] formulation for a consolidation time of 18 000 days, while, for soils A and B, it approaches the other formulations.

@@ Line 732: / Line 732: @@
 Another important aspect that should be observed in <span id='cite-_Ref34133953'></span>[[#_Ref34133953|Table 3]] is the variation of consolidation ratio over time. It can be noted that, in the transition between the consolidation ratios chosen, a change of an order of magnitude into time scale occurs. The succeeding values of time are not precisely the previous value multiplied by a factor of 10, but they are relatively close to that.
-==4.2.3. Comparison between FEM and analytical methodologies==
+====4.2.3 Comparison between FEM and analytical methodologies====
 For this investigation, a unique permeability coefficient of <math display="inline">2.5\times {10}^{-5}</math> m/day was employed in all analyses. Moreover, different undrained shear strength profiles were considered, and the effects of these profiles on the holding capacity of the torpedo anchors were assessed.
-<span id='cite-_Ref52371266'></span>[[#_Ref52371266|Fig.  24]] compares the radial stresses obtained with the FEM and the CEM analytical formulation, Eqs. <span id='cite-_Ref52371242'></span>[[#_Ref52371242|(7)]] and <span id='cite-_Ref52371231'></span>[[#_Ref52371231|(10)]]. In this figure, the radial stress was normalized by the undrained shear strength of the soil. Furthermore, the radial distance was normalized against the external radius of the anchor. In general, both methodologies are in good agreement throughout the radial distance within the soil. Although, a significant difference can be noticed in the region close to the anchor shaft in soil B.
+<span id='cite-_Ref52371266'></span>[[#_Ref52371266|Figure  24]] compares the radial stresses obtained with the FEM and the CEM analytical formulation, Eqs. <span id='cite-_Ref52371242'></span>[[#_Ref52371242|(7)]] and <span id='cite-_Ref52371231'></span>[[#_Ref52371231|(10)]]. In this figure, the radial stress was normalized by the undrained shear strength of the soil. Furthermore, the radial distance was normalized against the external radius of the anchor. In general, both methodologies are in good agreement throughout the radial distance within the soil. Although, a significant difference can be noticed in the region close to the anchor shaft in soil B.
-<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
+<div id='_Ref52371266'></div>
- [[Image:Draft_Kronemberger Lopes_857637204-image24.png|450px]] </div>
+{| style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: auto;max-width: auto;"
 Aiming at employing the analytical methodology based on the α-method from API <span id='cite-_Ref502324791'></span>[[#_Ref502324791|[21]]], CEM equations were used to obtain the effective radial stress over the external anchor wall along time and, thus, to calculate the values of the remaining parameters at each instant of time selected.
@@ Line 750: / Line 753: @@
 Input parameters of combined holding capacity <math display="inline">{R}_{0}</math> and <math display="inline">{R}_{EOD}</math>, used in the empirical formulations of Skov and Denver <span id='cite-_Ref534917435'></span>[[#_Ref534917435|[18]]], Eq. <span id='cite-_Ref52376815'></span>[[#_Ref52376815|(15)]], and Svinkin and Skov <span id='cite-_Ref534917465'></span>[[#_Ref534917465|[19]]], Eq. <span id='cite-_Ref52376819'></span>[[#_Ref52376819|(16)]], were obtained from the analyses using the FEM for time instants of 1 day and 0.01 day, respectively, after the installation of the anchor.
-<span id='cite-_Ref52371311'></span>[[#_Ref52371311|Fig.  25]] to <span id='cite-_Ref52371314'></span>[[#_Ref52371314|Fig.  27]] present comparative plots, for different soil undrained shear strength profiles considering the FE and analytical predictions. In these figures, the holding capacity of the anchor was normalized by the submerged weight of the anchor (500 kN).
+<span id='cite-_Ref52371311'></span>[[#_Ref52371311|Figures  25]] to <span id='cite-_Ref52371314'></span>[[#_Ref52371314|27]] present comparative plots, for different soil undrained shear strength profiles considering the FE and analytical predictions. In these figures, the holding capacity of the anchor was normalized by the submerged weight of the anchor (500 kN).
 In general, all methodologies have similar behavior, except for the initial instants of time for the ABS <span id='cite-_Ref51515640'></span>[[#_Ref51515640|[20]]] formulation, which starts with a lower holding capacity value. Results obtained from FEM analyses estimated pullout capacities slightly lower for a consolidation time of 18 000 days when compared to the other methodologies. It is emphasized that for all soils analyzed, only the ABS <span id='cite-_Ref51515640'></span>[[#_Ref51515640|[20]]] formulation and the analytical methodology based on α-method of API <span id='cite-_Ref502324791'></span>[[#_Ref502324791|[21]]] did not present a predominant linear behavior.
@@ Line 756: / Line 759: @@
 Skov and Denver [17] empirical formulation, Eq. <span id='cite-_Ref52376815'></span>[[#_Ref52376815|(15)]], presented an excellent agreement for the first ten days after anchor installation. On the other hand, the analytical methodology based on the α-method of API <span id='cite-_Ref502324791'></span>[[#_Ref502324791|[21]]] showed better approaches for consolidation times over 100 days.
-<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
+<div id='_Ref52371311'></div>
- [[Image:Draft_Kronemberger Lopes_857637204-image25.png|600px]] </div>
+{| style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: auto;max-width: auto;"
-<div id="_Ref52371311" class="center" style="width: auto; margin-left: auto; margin-right: auto;">
+<div id='_Ref52371314'></div>
-''Fig.  25 – Comparison between methodologies – Soil A.''</div>
+{| style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: auto;max-width: auto;"
 <div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
@@ Line 774: / Line 797: @@
 ''Fig.  27 – Comparison between methodologies – Soil C.''</div>
-The undrained shear strength of the soil has a major impact on the ABS <span id='cite-_Ref51515640'></span>[[#_Ref51515640|[20]]] formulation compared to the other methodologies. As shown in <span id='cite-_Ref52371311'></span>[[#_Ref52371311|Fig.  25]] to <span id='cite-_Ref52371314'></span>[[#_Ref52371314|Fig.  27]], the pullout capacity increases at a higher rate compared to other formulations. For soil C, the ABS <span id='cite-_Ref51515640'></span>[[#_Ref51515640|[20]]] formulation approaches the Skov and Denver <span id='cite-_Ref534917435'></span>[[#_Ref534917435|[18]]] formulation for a consolidation time of 18 000 days, while, for soils A and B, it approaches the other formulations.
+The undrained shear strength of the soil has a major impact on the ABS <span id='cite-_Ref51515640'></span>[[#_Ref51515640|[20]]] formulation compared to the other methodologies. As shown in <span id='cite-_Ref52371311'></span>[[#_Ref52371311|Figures 25]] to <span id='cite-_Ref52371314'></span>[[#_Ref52371314|27]], the pullout capacity increases at a higher rate compared to other formulations. For soil C, the ABS <span id='cite-_Ref51515640'></span>[[#_Ref51515640|[20]]] formulation approaches the Skov and Denver <span id='cite-_Ref534917435'></span>[[#_Ref534917435|[18]]] formulation for a consolidation time of 18 000 days, while, for soils A and B, it approaches the other formulations.
 <span id='_GoBack'></span>Finally, it is emphasized that the FE analyses presented a setup curve with a predominantly linear behavior with the ''log'' of time. Among the empirical methodologies, the Svinkin and Skov <span id='cite-_Ref534917465'></span>[[#_Ref534917465|[19]]] empirical formulation, Eq. <span id='cite-_Ref52376819'></span>[[#_Ref52376819|(16)]], presented a better match to those obtained with the FE approach. This indicates that a reasonable approach to obtain the setup curve is to conduct a pair of analyses with the FE approach, ''e. g.'', for consolidation times of zero (i.e., immediately after the installation of the anchor) and several days after the installation (typically, 5 000 or 10 000 days). Then, the coefficient ''B'', Eq. <span id='cite-_Ref52376819'></span>[[#_Ref52376819|(16)]], can be calibrated using these two points of the curve. In this study, a value of 0.2 for the coefficient ''B'' was found adequate to simulate the setup for all soils considered.

@@ Line 728: / Line 728: @@
 |  style="text-align: center;vertical-align: top;"|1.12E+05
 |}
 Another important aspect that should be observed in <span id='cite-_Ref34133953'></span>[[#_Ref34133953|Table 3]] is the variation of consolidation ratio over time. It can be noted that, in the transition between the consolidation ratios chosen, a change of an order of magnitude into time scale occurs. The succeeding values of time are not precisely the previous value multiplied by a factor of 10, but they are relatively close to that.

@@ Line 674: / Line 674: @@
 {| style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: auto;max-width: auto;"
 |-
-|style="padding:10px;"| [[Image:Draft_Kronemberger Lopes_857637204-image22.png|534px]]
+|style="padding:10px;"| [[Image:Draft_Kronemberger Lopes_857637204-image22.png|434px]]
 |- style="text-align: center; font-size: 75%;"
 | colspan="1" style="padding:10px;"| '''Figure 22'''. Consolidation ratio over time in Soil A
@@ Line 687: / Line 687: @@
 {| style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: auto;max-width: auto;"
 |-
-|style="padding:10px;"| [[Image:Draft_Kronemberger Lopes_857637204-image23.png|486px]]
+|style="padding:10px;"| [[Image:Draft_Kronemberger Lopes_857637204-image23.png|386px]]
 |- style="text-align: center; font-size: 75%;"
 | colspan="1" style="padding:10px;"| '''Figure 23'''. Consolidation ratios for different permeability coefficients at 7.5m from the top of the anchor
@@ Line 702: / Line 702: @@
 !  rowspan='2' |<math display="inline">\mathit{\boldsymbol{k}}</math> (m/dia) !! colspan='6'  style="vertical-align: top;"|Consolidation ratio, <math display="inline">\mathit{\boldsymbol{U}}</math>
 |-
-|  style="text-align: center;vertical-align: top;"|'''0.10'''
+!  '''0.10''' !! '''0.25'''!!'''0.50'''!!'''0.75'''!!'''0.90'''!!'''0.99'''
-|  style="text-align: center;vertical-align: top;"|'''0.25'''
-|  style="text-align: center;vertical-align: top;"|'''0.50'''
-|  style="text-align: center;vertical-align: top;"|'''0.75'''
-|  style="text-align: center;vertical-align: top;"|'''0.90'''
-|  style="text-align: center;vertical-align: top;"|'''0.99'''
 |-
 |  style="text-align: center;vertical-align: top;"|2.50E-04

@@ Line 665: / Line 665: @@
 By comparing <span id='cite-_Ref34065797'></span>[[#_Ref34065797|Table 2]] and <span id='cite-_Ref52285415'></span>[[#_Ref52285415|Figure 21]], it is possible to affirm that the regain rates of the holding capacity are higher in the initial moments. Immediately after, these rates start to decrease. It is important to emphasize that this conclusion is only valid because the same permeability coefficient was considered for all soils analyzed.
-==4.2.2. Permeability coefficient effects==
+====4.2.2 Permeability coefficient effects====
 In the investigation of the impact of the soil permeability coefficient in the ultimate holding capacity of the torpedo anchor, only the undrained shear strength profile of Soil A (<span id='cite-_Ref32422685'></span>[[#_Ref32422685|Table 1]]) was considered. All other properties of the model were the same described in section 4.1.
-<span id='cite-_Ref52371035'></span>[[#_Ref52371035|Fig. 22]] shows the soil consolidation ratio considering a permeability coefficient of <math display="inline">2.5\times {10}^{-5}</math> m/day. The figure shows three different consolidation curves related to a specific point located along the anchor length. These points are also illustrated in this figure. It is emphasized that the points were chosen to ensure that the anchor geometry's boundaries do not influence the results.
+<span id='cite-_Ref52371035'></span>[[#_Ref52371035|Figure 22]] shows the soil consolidation ratio considering a permeability coefficient of <math display="inline">2.5\times {10}^{-5}</math> m/day. The figure shows three different consolidation curves related to a specific point located along the anchor length. These points are also illustrated in this figure. It is emphasized that the points were chosen to ensure that the anchor geometry's boundaries do not influence the results.
-<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
+<div id='_Ref52371035'></div>
- [[Image:Draft_Kronemberger Lopes_857637204-image22.png|534px]] </div>
+{| style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: auto;max-width: auto;"
-As can be observed in <span id='cite-_Ref52371035'></span>[[#_Ref52371035|Fig. 22]], the rate of excess pore pressure dissipation is slightly different at each of the points analyzed. However, all curves follow the same trend. Moreover, complete soil consolidation occurred practically at the same time. In this case, a time of 10 000 days is representative of this phenomenon.
+As can be observed in <span id='cite-_Ref52371035'></span>[[#_Ref52371035|Figure 22]], the rate of excess pore pressure dissipation is slightly different at each of the points analyzed. However, all curves follow the same trend. Moreover, complete soil consolidation occurred practically at the same time. In this case, a time of 10 000 days is representative of this phenomenon.
-[[#_img-23|Fig. 23]]<span id='cite-_Ref52371035'></span> compares the consolidation ratio along time for soil A, considering different permeability coefficients. These results refer to the point located at 7.5 m distant from the top of the anchor, as illustrated in [[#_Ref52371035|Fig. 22]]. It can be observed that the time needed to achieve a certain consolidation ratio of the soil is lower when the permeability coefficient increases. On the other hand, full consolidation time is higher when the permeability coefficient decreases.
+[[#_img-23|Figure 23]]<span id='cite-_Ref52371035'></span> compares the consolidation ratio along time for soil A, considering different permeability coefficients. These results refer to the point located at 7.5 m distant from the top of the anchor, as illustrated in [[#_Ref52371035|Figure 22]]. It can be observed that the time needed to achieve a certain consolidation ratio of the soil is lower when the permeability coefficient increases. On the other hand, full consolidation time is higher when the permeability coefficient decreases.
-<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
+<div id='_img-23'></div>
- [[Image:Draft_Kronemberger Lopes_857637204-image23.png|486px]] </div>
+{| style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: auto;max-width: auto;"
 The total times needed for consolidation ratios of 0.1 to 0.99 are summarized in <span id='cite-_Ref34133953'></span>[[#_Ref34133953|Table 3]] for the different permeability coefficients considered. This table indicates that when the permeability coefficient increases an order of magnitude, the time needed to achieve a specific consolidation ratio decreases at the same ratio. Analogously, when decreasing one order of magnitude of the permeability coefficient, the total time required to achieve a certain consolidation ratio is increased by the same ratio.
-<div id="_Ref34133953" class="center" style="width: auto; margin-left: auto; margin-right: auto;">
+<div class="center" style="font-size: 75%;">'''Table 3'''. Time (in days) needed to achieve different consolidation ratios: 7.5 m above the top of the anchor</div>
-''Table 3 – Time (in days) needed to achieve different consolidation ratios: 7.5 m above the top of the anchor.''</div>
-{| style="width: 100%;margin: 1em auto 0.1em auto;border-collapse: collapse;"
+<div id='_Ref34133953'></div>
-|-
+{| class="wikitable" style="margin: 1em auto 0.1em auto;border-collapse: collapse;font-size:85%;width:auto;"
-|  rowspan='2' style="border-top: 1pt solid black;text-align: center;"|<math display="inline">\mathit{\boldsymbol{k}}</math> (m/dia)
+|-style="text-align:center"
-|  colspan='6'  style="border-top: 1pt solid black;text-align: center;vertical-align: top;"|Consolidation ratio, <math display="inline">\mathit{\boldsymbol{U}}</math>
+!  rowspan='2' |<math display="inline">\mathit{\boldsymbol{k}}</math> (m/dia) !! colspan='6'  style="vertical-align: top;"|Consolidation ratio, <math display="inline">\mathit{\boldsymbol{U}}</math>
 |-
 |  style="text-align: center;vertical-align: top;"|'''0.10'''
@@ Line 720: / Line 725: @@
 |  style="text-align: center;vertical-align: top;"|1.52E+04
 |-
-|  style="border-bottom: 1pt solid black;text-align: center;vertical-align: top;"|2.50E-06
+|  style="text-align: center;vertical-align: top;"|2.50E-06
-|  style="border-bottom: 1pt solid black;text-align: center;vertical-align: top;"|3.09E+00
+|  style="text-align: center;vertical-align: top;"|3.09E+00
-|  style="border-bottom: 1pt solid black;text-align: center;vertical-align: top;"|3.18E+01
+|  style="text-align: center;vertical-align: top;"|3.18E+01
-|  style="border-bottom: 1pt solid black;text-align: center;vertical-align: top;"|4.04E+02
+|  style="text-align: center;vertical-align: top;"|4.04E+02
-|  style="border-bottom: 1pt solid black;text-align: center;vertical-align: top;"|6.32E+03
+|  style="text-align: center;vertical-align: top;"|6.32E+03
-|  style="border-bottom: 1pt solid black;text-align: center;vertical-align: top;"|3.10E+04
+|  style="text-align: center;vertical-align: top;"|3.10E+04
-|  style="border-bottom: 1pt solid black;text-align: center;vertical-align: top;"|1.12E+05
+|  style="text-align: center;vertical-align: top;"|1.12E+05
 |}