# Comparison of Prediction Methods for Axial Strength of Grouted Connections with Shear Keys

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methodology for Predicting Axial Strength

#### 2.1. Comparison of Application Range

_{cu}is the compressive strength of the grouted body.

#### 2.2. Method of Calculation

_{bk}of grouted connections considers the effects of radial stiffness, the length of the grouted seam, surface roughness, the dimensions of the shear key, and the cubic compressive strength of the grouted body; related formulas are shown as Equations (1) and (2)

_{cu}is the cubic compressive strength of the grouted body; C

_{S}is the surface state coefficient, and C

_{S}= 1.0 when h/s ≥ 0.005; m is the ratio of Young’s modulus for steel and for grout material, and m = 18 can be used if the Young’s modulus for grout material is not known. In the absence of geometric data of the steel tube and shear key, see Table 2 for C

_{L}parameter values, where L is the nominal length of the grouted connecting section. The parameter value between two data points in the table is calculated using the linear difference method.

_{bk}of grouted connections considers the influence of grouted material strength, shear key height, and the space of the shear key. Krahl et al. considered the failure mechanism of the pressure bar near the shear key in the grouted connecting section, and through linear regression analysis of the collected experimental data, the formula of shear strength is as shown in Equation (3). In order to ensure a certain safety factor, the API adjusts Equation (3) and adopts Equation (4) for design

_{g}is the length of the grouted connection section (mm); μ is the friction coefficient between the steel tube and the grouted material (0.6); E

_{g}and E are the elastic modulus of the steel tube and the grouted material, respectively; F is the radial flexibility coefficient; and N is the number of shear keys.

_{bk}, corresponding to the frictional sliding failure mode, and strength f

_{bkg}, determined by the failure of the grouted material itself, as expressed by Equations (7) and (8), respectively, in which f

_{bk}should not be greater than f

_{bkg},

## 3. Comparison of Calculation Results

_{cu}, and the radial stiffness of the grouted connection section k are changed in order to analyze the shear strength of the grouted connection. The main dimension information of specimens is as follows: D

_{s}= 2600 mm, t

_{s}= 70 mm, D

_{p}= 2270 mm, t

_{p}= 55 mm, D

_{g}= 2460 mm, t

_{g}= 95 mm, L

_{g}= 7000 mm, f

_{cu}= 130 MPa, E

_{g}= 55 GPa, E = 206 GPa, h = 20 mm, w = 40 mm, s = 500 mm (E

_{g}: Young’s modulus for grout material; E: Young’s modulus for steel).

#### 3.1. Space of Shear Key

_{bk}calculated by different codes and the applicable space of shear key s is shown in Figure 2, where a maximum value for s is not specified by API, HSE, and DNV-GL. In this study, s does not exceed 2 m. It can be found from the figure that within the selected value range of s, shear strength f

_{bk}calculated by HSE is the largest, followed by the calculated result of API, and the smallest is by DNV-GL. With increased s, the variation trend of shear strength obtained by different specifications is consistent. In the interval where s is less than 800 mm, the value of s has a significant effect on shear strength. As s increases, the calculated value of shear strength decreases rapidly, and the curve calculated by HSE is the most sensitive. After the value of s continues to increase beyond 1000 mm, shear strength f

_{bk}of the grouted connection slowly decreases, and the curve calculated by each code gradually flattens. Since the DNV calculation result is fixed, it is considered that the shear strength of the grouted joint is not related to the space of the shear key, which is inconsistent with Wimpey′s experimental phenomenon [16]. The Wimpey laboratory tested specimens with different shear key distances. The results showed that the shear strength of the grouted connections increased continuously when the space of the shear key s continued to decrease. However, as s was reduced to a certain extent, the failure mode of the grouted joint changed, and the shear strength of the grouted section decreased.

#### 3.2. Height of Shear Key

_{bk}of the grouted joint. When the minimum value of h is taken, it means there is no shear key on the grouted joint, and the maximum value of h is generally half the thickness of the grouted material, which is generally greater than the value in an actual project. The curve of shear strength f

_{bk}calculated by different codes and shear key height h is shown in Figure 3, where the specifications of API, DNV, and DNV-GL do not set a maximum value of h, and only the case when h less than 50 mm is compared. It can be seen from the data that the DNV takes f

_{bk}as 0, when h = 0, ignoring the cohesive force and friction force between grouted material and the steel pipe surface. With increased h, the slope of the HSE curve becomes the largest and f

_{bk}grows the fastest. However, the application scope of h in HSE is limited. Compared with DNV and DNV-GL, the API curve increases faster with increased h, reflecting that the influence of h becomes more obvious. The DNV-GL code requires that the height of shear key h is greater than 5 mm, to avoid slippage damage on the interface of steel pipe and grouted material in the grouted section. The slope of the curve of the DNV code is the smallest, and shear strength f

_{bk}of the calculation is the smallest with increased h. In addition, the API, DNV, and DNV-GL codes assume that shear strength f

_{bk}will continue to increase with the growth of h, which disagrees with the actual situation.

#### 3.3. Ratio of Height to Distance of Shear Key

_{bk}of a grouted connection. The relationship curve of shear strength f

_{bk}calculated by different codes and the h/s ratio are shown in Figure 4. It can be concluded that the slope of the HSE curve is the largest, and with increased h/s ratio, the growth rate of f

_{bk}is the largest, but h/s in HSE is less applicable. However, the application scope of the h/s ratio in the HSE code is relatively low. When a large h/s ratio is required in the test, the HSE code is inapplicable. The curves of the API, DNV, and DNV-GL codes generally show a linear growth trend. When the h/s ratio is large, the API calculation value is the largest, while the DNV counterpart is the smallest. The maximum h/s ratio applicable to the specification is 0.1.

#### 3.4. Compressive Strength of Grouted Material

_{cu}plays a significant role in f

_{bk}. Billington showed through data analysis that f

_{bk}is directly proportional to the 0.5 power of f

_{cu}[9]. The relationship curve between the shear strength f

_{bk}calculated using different codes and the compressive strength of grouted material f

_{cu}is shown in Figure 5. It can be found that API considers that f

_{bk}and f

_{cu}show a linear relationship, which is not consistent with the results of Billington’s analysis. API overestimates the effect of f

_{cu}on f

_{bk}, and f

_{cu}is less applicable in the API code. When the compressive strength of larger or smaller grouted materials is used in the test, the formula in the API code is not necessarily applicable. In contrast, HSE, DNV, and DNV-GL agree that the ultimate shear strength of the grouted junction is proportional to the 0.5, 0.4, and 0.3 power cubic compressive strength of the grouted material, and the DNV code is constantly reducing the impact of f

_{cu}on f

_{bk}.

#### 3.5. Radial Stiffness Coefficient

_{bk}obtained by different codes and radial stiffness K is shown in Figure 6. It can be concluded that the API code holds that there is no direct relationship between f

_{bk}and K, that is, the change of radial stiffness of the grouted connection section will not affect the shear strength of the grouted joint. In contrast, the HSE and DNV codes assume that f

_{bk}of the grouted junction is proportional to radial stiffness K. The DNV-GL code assumes that f

_{bk}is proportional to the 0.6 power of radial stiffness coefficient K, which reduces the effect of K on the shear strength of the grouted connection.

_{p}/t

_{p}, the diameter-to-thickness ratio of steel sleeve D

_{s}/t

_{s}, the D

_{g}/t

_{g}ratio, and the ratio of elastic modulus of steel pipe to grouted material E/E

_{g}. Hence, the analysis results of radial stiffness K are presented in Figure 7 by changing the parameters above. It can be found that a D

_{g}/t

_{g}ratio between 0 and 15 shows a significant effect on radial stiffness K, but this effect gradually decreases when the ratio is more than 15. The D

_{p}/t

_{p}and D

_{s}/t

_{s}ratios have less effect on radial stiffness K. The E/E

_{g}ratio can only achieve a relatively small change range because the value only relates to the material properties, but it can also effectively enhance radial stiffness K in the variation range.

## 4. Comparison between Calculation and Test Results

#### 4.1. Data Acquisition and Verification

#### 4.2. HSE (2002)

#### 4.3. API (2007)

#### 4.4. DNV (2013)

#### 4.5. DNV-GL (2016)

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- The European Wind Energy Association. The European Offshore Wind Industry Key Trends and Statistics; EWEA: Brussels, Belgium, 2010–2013.
- HSE. Pile/Sleeve Connections; Health & Safety Executive (HSE): Norwich, UK, 2001. [Google Scholar]
- API. API Recommended Practice: Recommended Practice for Planning, Designing, and Constructing Fixed Offshore Platforms-Working Stress Design (API RP 2A-WSD); American Petroleum Institute (API): Washington, DC, USA, 2007. [Google Scholar]
- ISO. Petroleum and Natural Gas Industries- Fixed Steel Offshore Structures (ISO 19902); International Organization for Standardization (ISO): Geneva, Switzerland, 2007. [Google Scholar]
- The Norwegian Oil Industry Association. Norsok Standard: Design of Steel Structures (N-004); The Norwegian Oil Industry Association: Norway, Norway, 2013. [Google Scholar]
- DNV GL. Support Structures for Wind Turbines (DNVGL-ST-0126); Det Norske Veritas (DNV): HØvik, Norway, 2016. [Google Scholar]
- DNV. Offshore Standard. Design of Offshore Wind Turbine Structures (DNVS-OS-J101); Det Norske Veritas (DNV): HØvik, Norway, 2013. [Google Scholar]
- Billington, C.J.; Lewis, G.H. The strength of large diameter grouted connections. In Proceedings of the Offshore Technology Conference, Houston, TX, USA, 8–11 May 1978; pp. 291–301. [Google Scholar]
- Billington, C.; Tebbett, I. The basis for new design formulae for grouted jacket to pile connections. In Proceedings of the Offshore Technology Conference, Houston, TX, USA, 5–8 May 1980; pp. 449–458. [Google Scholar]
- Karsan, D.I.; Krahl, N.W. New API equation for grouted pile-to-structure connections. In Proceedings of the Offshore Technology Conference, Houston, TX, USA, 7–9 May 1984; pp. 49–56. [Google Scholar]
- Lotsberg, I.; Serednicki, A.; Cramer, E.; Bertnes, H.; Haahr, P.E. On the structural capacity of grouted connections in offshore structures. In Proceedings of the ASME 2011 30th International Conference on Ocean, Offshore and Arctic Engineering, Rotterdam, The Netherlands, 19–24 June 2011; pp. 667–677. [Google Scholar]
- Dallyn, P.; El-Hamalawi, A.; Palmeri, A.; Knight, R. Knight. Experimental testing of grouted connections for offshore substructures: A critical review. Structures
**2015**, 3, 90–108. [Google Scholar] [CrossRef] [Green Version] - Dallyn, P.; El-Hamalawi, A.; Palmeri, A.; Knight, R. Experimental investigation on the development of wear in grouted connections for offshore wind turbine generators. Eng. Struct.
**2016**, 113, 89–102. [Google Scholar] [CrossRef] [Green Version] - Wang, G. The Axial Bearing Capacity of Large-Diameter Grouted Connections for Offshore Wind Turbines. Doctoral Thesis, Zhejiang University, Hangzhou, China, 2017. [Google Scholar]
- Zhang, Y.; Wang, G.; Yang, L.; Chen, F.; Jiang, J.; Wang, Z. Axial bearing capacity of high strength grouted connections with shear keys. Acta Energ. Sol. Sin.
**2017**, 38, 3117–3122. [Google Scholar] - Wimpey Laboratories Limited. Review of Offshore Grout Strengths (Report ST 55/79); Department of Energy: London, UK, 1979. [Google Scholar]
- Forsyth, P.; Tebbett, I. New test data on the strength of grouted connections with closely spaced weld beads. In Proceedings of the Offshore Technology Conference, Houston, TX, USA, 2–5 May1988; pp. 237–245. [Google Scholar]
- Aritenang, W.; Elnashai, A.S.; Dowling, P.J.; Carroll, B.C. Failure mechanisms of weld-beaded grouted pile/sleeve connections. Mar. Struct.
**1990**, 3, 391–417. [Google Scholar] [CrossRef] - UK-Department of Energy. Report of the Working Party on the Strength of Grouted Pile/Sleeve Connections for Offshore Structures (OTP- 11); Offshore Technology Publication: London, UK, 1982. [Google Scholar]
- UK-Department of Energy. The Strength of Grouted Pile-Sleeve Connections (OTH 86210); Offshore Technology Publication: London, UK, 1986. [Google Scholar]
- Lamport, W.B.; Jirsa, J.O.; Yura, J.A. Strength and behavior of grouted pile-to-sleeve connections. J. Struct. Eng.
**1991**, 117, 2477–2498. [Google Scholar] [CrossRef] - Sele, A.; Skjolde, M. Design Provisions for Offshore Grouted Construction. In Proceedings of the Offshore Technology Conference, Houston, TX, USA, 3–6 May 1993; pp. 165–179. [Google Scholar]
- Anders, S.; Lohaus, L. Optimized high-Performance concrete in grouted connections. In Proceedings of the International Fib Symposium, London, UK, 7 May 2008; Volume 8, pp. 369–374. [Google Scholar]
- Li, W.; Bian, E.L.; Zhong, W.Q.; Fang, T.; Jiang, P.; Xu, J. Model teset of grouted connection for monopole of offshore wind turbin under static axial load. Hydro Sci. Eng.
**2014**, 5, 41–46. [Google Scholar] - Lee, J.H.; Won, D.H.; Jeong, Y.J.; Kim, S.H.; Kang, Y.J. Interfacial shear behavior of a high-strength pile to sleeve grouted connection. Eng. Struct.
**2017**, 151, 704–723. [Google Scholar] [CrossRef]

**Figure 1.**Geometric parameters of grouted connection. D

_{p}, diameter of steel pile; D

_{g}, diameter of grout; D

_{s}, diameter of sleeve; R

_{p}, radius of steel pile; R

_{g}, radius of grout; R

_{s}, radius of sleeve; t

_{p}, thickness of steel pile; t

_{g}, thickness of grout; t

_{s}, thickness of sleeve; w, width of shear key; h, height of shear key; s, spacing of shear key.

**Figure 4.**Relationship between interface shear strength (f

_{bk}) and height-to-distance ratio of shear key (h/s).

**Figure 5.**Relationship between interface shear strength (f

_{bk}) and grouted material strength (f

_{cu}).

**Figure 7.**Relationship between radial stiffness factor (k) and D

_{p}/t

_{p}, D

_{s}/t

_{s}, E/E

_{g}, and D

_{g}/t

_{g}ratios.

**Figure 12.**Comparison of test load–displacement curves: (

**a**) S75; (

**b**) S50; (

**c**) S100; (

**d**) H2.5; (

**e**) T38; (

**f**) T63; (

**g**) N2.

**Figure 15.**Comparison of shear strength calculated using API and tested results: (

**a**) API fitting formula; (

**b**) formula under extreme conditions.

**Table 1.**Geometric and material parameters in different codes. DNV-GL, Det Norske Veritas–Germanischer Lloyd; API, American Petroleum Institute; ISO, International Organization for Standardization; HSE, Health and Safety Executive.

Parameter | DNV GL-ST-0126 (2016) | DNV (2013) | NORSOK (2013) | API (2007) | ISO (2007) | HSE (2007) | |
---|---|---|---|---|---|---|---|

Jackets | Single Pile | Jackets/Single Pile | Jackets | Jackets | Jackets | Jackets | |

D_{p}/t_{p} | 20–60 | 20–60 | 10–60 | 20–40 | ≤40 | 20–40 | 24–40 |

D_{s}/t_{s} | 30–140 | 18–140 | 18–140 | 30–140 | ≤80 | 30–140 | 50–140 |

D_{g}/t_{g} | 10–45 | / | / | 10–45 | 7–45 | 10–45 | 10–45 |

t_{g} | / | / | / | / | ≥38 mm | ≥40 mm | / |

f_{cu} (MPa) | / | / | / | 20–80 | 17.25–110 | 20–80 | / |

L_{g}/D_{p} | 1.0–10.0 | 1.5–2.5 | / | 1.0–10.0 | / | 1.0–10.0 | ≥2.0 |

h | ≥5 mm | ≥5 mm | / | 0–0.012 D_{p} | / | 0–0.012 D_{p} | 0–0.006 D_{p} |

s | ≥0.8$\sqrt{{R}_{p}{t}_{p}}$ | ≥$\sqrt{{R}_{p}{t}_{p}}$ | ≥$\sqrt{{R}_{p}{t}_{p}}$ | ≥D_{p}/16 | ≥D_{p}/8 | ≥D_{p}/16 | ≥D_{p}/8 |

h/s | ≤0.1 | ≤0.1 | ≤0.1 | 0–0.1 | 0–0.1 | 0–0.1 | ≤0.04 |

w/h | 1.5–3.0 | 1.5–3.0 | / | / | 1.5–3.0 | 1.5–3.0 | 1.5–3.0 |

_{g}, length of grout; f

_{cu}, cubic compressive strength of grouted body.

L/D_{p} | 2 | 4 | 8 | ≥12 |

C_{L} | 1.0 | 0.9 | 0.8 | 0.7 |

No. | D_{s} (mm) | t_{s} (mm) | D_{p} (mm) | t_{p} (mm) | L_{g} (mm) | h (mm) | W (mm) | s (mm) |
---|---|---|---|---|---|---|---|---|

GC-N2 | 600 | 12 | 480 | 12 | 350 | 5 | 10 | 75 |

GC-S75 | 600 | 12 | 480 | 12 | 500 | 5 | 10 | 75 |

GC-S50 | 600 | 12 | 480 | 12 | 400 | 5 | 10 | 50 |

GC-S100 | 600 | 12 | 480 | 12 | 600 | 5 | 10 | 100 |

GC-H2.5 | 600 | 12 | 480 | 12 | 500 | 2.5 | 5 | 75 |

GC-T38 | 580 | 12 | 480 | 12 | 500 | 5 | 10 | 75 |

GC-T63 | 630 | 12 | 480 | 12 | 500 | 5 | 10 | 75 |

Material | Young’s Modulus (MPa) | Yield Strength (MPa) | Ultimate Strength (MPa) | Poisson’s Ratio |
---|---|---|---|---|

Steel | 2.06 × 10^{5} | 380 | 565 | 0.31 |

Grout (GC-S75) | 5.1 × 10^{4} | / | 149.1 | 0.2 |

Grout (GC-S50) | 5.1 × 10^{4} | / | 149.3 | 0.2 |

Grout (GC-S100) | 5.1 × 10^{4} | / | 154.2 | 0.2 |

Grout (GC-H2.5) | 5.1 × 10^{4} | / | 150.2 | 0.2 |

Grout (GC-N2) | 5.1 × 10^{4} | / | 131.2 | 0.2 |

Grout (GC-T38) | 5.1 × 10^{4} | / | 150.2 | 0.2 |

Grout (GC-T63) | 5.1 × 10^{4} | / | 150.3 | 0.2 |

No. | GC-S75 | GC-S50 | GC-S100 | GC-H2.5 | GC-N2 | GC-T38 | GC-T63 |
---|---|---|---|---|---|---|---|

P_{TEST} | 5887 | 5204 | 7196 | 4683 | 2437 | 5843 | 5753 |

P_{FEA} | 6127 | 5481 | 6954 | 4712 | 2563 | 6315 | 6251 |

Error | 4% | 5% | −3% | 1% | 5% | 8% | 9% |

_{TEST}is the experimental peak load; P

_{FEA}is the numerical peak load.

ψ | K_{c} | α_{f} | ε | μ |
---|---|---|---|---|

30 | 2/3 | 1.16 | 0.1 | 0.0001 |

_{c}is the second stress invariant; α

_{f}is the biaxial/uniaxial ratio; ε is the eccentricity; μ is the viscosity parameter.

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**MDPI and ACS Style**

Xianhui, Y.; Zhaoqi, W.; Zehao, C.
Comparison of Prediction Methods for Axial Strength of Grouted Connections with Shear Keys. *Appl. Sci.* **2020**, *10*, 1942.
https://doi.org/10.3390/app10061942

**AMA Style**

Xianhui Y, Zhaoqi W, Zehao C.
Comparison of Prediction Methods for Axial Strength of Grouted Connections with Shear Keys. *Applied Sciences*. 2020; 10(6):1942.
https://doi.org/10.3390/app10061942

**Chicago/Turabian Style**

Xianhui, You, Wu Zhaoqi, and Chen Zehao.
2020. "Comparison of Prediction Methods for Axial Strength of Grouted Connections with Shear Keys" *Applied Sciences* 10, no. 6: 1942.
https://doi.org/10.3390/app10061942