# A Novel Integrated Approach to Solve Industrial Ground Floor Design Problems

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

_{s}(MPa/m) is the subgrade reaction coefficient.

_{s}is one of the most complex problems in geotechnical engineering. This coefficient is not just an index that characterizes the soil properties; it also depends on the subgrade loading scheme, foundation geometry, depth, and size [36,37].

_{s}—the influence factor depending on rigidity, the shape, and l/b ratio of the footing.

_{s}is subgrade stiffness coefficient.

_{1}(a compression ratio) and C

_{2}(a shear ratio), as depicted in Figure 1:

_{i}is the thickness of soil layer i; E

_{i}is the modulus of deformation of layer i.

_{i}of layer i.

_{s}is:

_{sz}—distributed load on a pile cap; k

_{s}is the pile stiffness according to pile static tests and the secant point on the Weibull curve. It is equal to the spring constant K

_{v}

_{0.33}of the model, and this quantity represents the pile stiffness under Serviceability Limit State conditions [28]:

_{v}

_{0.33}is dimensionless pile stiffness; D—pile diameter; R

_{u}—ultimate pile bearing capacity (or asymptotic ultimate bearing resistance R

_{cau}values).

## 3. Practical Application of Proposed Model

^{3}; the modulus of the RC slab deformation—31 GPa.

^{2}(this value without self-weight of the slab). This load was applied to all the surfaces of the RC slab. For values and layout of concentrated loads from shelving supports, see Figure 4. The following distribution and magnitude of the loads were specified in the design task of the analyzed logistics center.

#### 3.1. Calculations of the Slab with Plaxis 3D

#### 3.2. Calculations of the Slab Using FEM (Scad) Program

_{s}= 81 MN/m [28] was used to predict the subgrade reaction coefficients in the zone above the pile cap. Other parameters were the same as in the calculation with Plaxis 3D.

_{1}for the layer outside the pile cap will be 3137 kN/m

^{3}. The floor weight (4.8 kPa) and the storage load (50 kPa) 1.20 m, affect the thickness of the layer above the pile cap. The layer compression will be 1.00 mm.

_{s}= 81,000 kN/m. The deformations of the floor plate are calculated only from the additional loads—the weight of the floor slab and storage load. According to [5], the pile foundation settlement will be only 0.33 mm.

_{2}for the layer above the pile cap will be 41,221 kN/m

^{3}.

_{Σ}= 0.3188·10

^{−3}m

^{3}/kN and for the layers’ base δ

_{n}

_{+1}= 0. Table 4 shows the calculated values.

_{n}

_{+1}= 6.0494·10

^{−6}m

^{3}/kN.

## 4. Results and Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Zolfani, S.H.; Zavadskas, E.K.; Turskis, Z. Design of products with both International and Local perspectives based on Yin-Yang balance theory and SWARA method. Econ. Res. Ekon. Istraž.
**2013**, 26, 153–166. [Google Scholar] [CrossRef] - Zavadskas, E.K.; Turskis, Z.; Volvačiovas, R.; Kildiene, S. Multi-criteria assessment model of technologies. Stud. Inf. Control.
**2013**, 22, 249–258. [Google Scholar] [CrossRef] [Green Version] - Concrete Industrial Ground Floors—A Guide to Design and Construction; Concrete Society Technical Report No. 34; The Concrete Society: Blackwater Camberley, UK, 2016.
- DIN 15185. Warehouse Systems with Guided Industrial Trucks: Requirements on the Ground, the Warehouse and Other Requirements; German Institute for Standardisation: Berlin, Germany, 1991; Volume 7. (In German) [Google Scholar]
- Piskunov, V.G.; Fedorenko, Y.M. A dynamic method for monitoring layered slabs on elastic beds. Archit. Constr. Belarus
**1994**, N5–6, 10–22. (In Russian) [Google Scholar] - Sadrekarimi, J.; Akbarzad, M. Comparative study of methods of determination of coefficient of subgrade reaction. Electron. J. Geotech. Eng.
**2009**, 14, 1–14. [Google Scholar] - Tomasovicova, D.; Jendzelovsky, N. Stiffness Analysis of the Subsoil under Industrial Floor. Proced Eng.
**2017**, 190, 365–370. [Google Scholar] [CrossRef] - Turskis, Z.; Lazauskas, M.; Zavadskas, E.K. Fuzzy multiple criteria assessment of construction site alternatives for non-hazardous waste incineration plant in Vilnius city, applying ARAS-F and AHP methods. J. Environ. Eng. Landsc. Manag.
**2012**, 20, 110–120. [Google Scholar] [CrossRef] - Bagočius, V.; Zavadskas, E.K.; Turskis, Z. Multi-person selection of the best wind turbine based on the multi-criteria integrated additive-multiplicative utility function. J. Civ. Eng. Manag.
**2014**, 20, 590–599. [Google Scholar] [CrossRef] - Zavadskas, E.K.; Kaklauskas, A.; Turskis, Z.; Kalibatas, D. An approach to multi-attribute assessment of indoor environment before and after refurbishment of dwellings. J. Environ. Eng. Manag.
**2009**, 17, 5–11. [Google Scholar] - Yepes, V.; Mart, J.V.; García, J. Black Hole Algorithm for Sustainable Design of Counterfort Retaining Walls. Sustainability
**2020**, 12, 2767. [Google Scholar] [CrossRef] [Green Version] - Kripka, M.; Yepes, V.; Milani, C.J. Selection of Sustainable Short-Span Bridge Design in Brazil. Sustainability
**2019**, 11, 1307. [Google Scholar] [CrossRef] [Green Version] - Seo, S.; Lee, B.; Won, J. Comparative Analysis of Economic Impacts of Sustainable Vertical Extension Methods for Existing Underground Spaces. Sustainability
**2020**, 12, 975. [Google Scholar] [CrossRef] [Green Version] - Sall, O.A.; Fall, M.; Berthaud, Y.; Ba, M. Influence of the Elastic Modulus of the Soil and Concrete Foundation on the Displacements of a Mat Foundation. Open J. Civ. Eng.
**2013**, 3, 228–233. [Google Scholar] [CrossRef] [Green Version] - Shadravan, S.; Ramseyer, C.; Kang, T.H.K. A long term restrained shrinkage study of concrete slabs on ground. Eng. Struct.
**2015**, 102, 258–265. [Google Scholar] [CrossRef] - Ye, W.; Liu, J.; Fang, H.; Lin, G. High-performance analysis of the interaction between plate and multi-layered elastic foundation using SBFEM-FEM. Compos. Struct.
**2019**, 214, 1–11. [Google Scholar] [CrossRef] - Ardah, A.; Chen, Q.; Abu-Farsakh, M. Evaluating the performance of very weak subgrade soils treated/stabilized with cementitious materials for sustainable pavements. Trans. Geotech.
**2017**, 11, 107–119. [Google Scholar] [CrossRef] - Jayarajan, P.; Kouzer, K.M. Analysis of Piled Raft Foundations. Indian J. Sci.
**2015**, 16, 51–57. [Google Scholar] - Al-Mhaidib, A.I. Experimental investigation of the behavior of pile groups in sand under different loading rates. Geotech. Geol. Eng.
**2006**, 24, 889–902. [Google Scholar] [CrossRef] - Poulos, H.G. Piled raft foundation: Design and applications. Geotechnique
**2001**, 51, 95–113. [Google Scholar] [CrossRef] - El-Garhy, B.; Galil, A.A.; Mari, M. Analysis of flexible raft resting on soft soil improved by granular piles considering soil shear interaction. Comput. Geotech.
**2018**, 94, 169–183. [Google Scholar] [CrossRef] - Bhaduri, A.; Choudhury, D. Serviceability-Based Finite-Element Approach on Analyzing Combined Pile-Raft Foundation. Int. J. Geomech.
**2020**, 20. [Google Scholar] [CrossRef] - Gunerathne, S.; Seo, H.; Lawson, W.D.; Jayawickrama, P.W. Variational approach for settlement analysis of circular plate on multilayered soil. Appl. Math. Model.
**2019**, 70, 152–170. [Google Scholar] [CrossRef] - Han, X.; Xiao, C.; Li, J.; Feng, J. Spring constitutive model of rigid pile composite foundation and application in design of raft foundation. J. Cent. South Univ.
**2013**, 20, 1079–1084. [Google Scholar] [CrossRef] - Akpila, S.B.; Jaja, G.W.T. Reliability of Soil and Ground Improvement Techniques on Peaty Clay Soil—A Review. Int. J. Trend Sci. Res. Dev.
**2019**, 3, 682–690. [Google Scholar] - Al-Adhadh, A.R.; Kadhim, Z.J.; Naeem, Z.T. Reviewing the most suitable Soil Improvement Techniques for treating soft clay soil. J. Eng. Res. Appl.
**2019**, 9, 1–11. [Google Scholar] - Briancon, L.; Kastner, R.; Simon, B.; Dias, D. Etat des connaissances: Amélioration des sols par inclusions rigides. In Proceedings of the Am Élioration Des Sols En Place, Paris, France, 9–10 September 2004; pp. 15–43. [Google Scholar]
- Urbonas, K.; Sližytė, D.; Mackevičius, R. Influence of the pile stiffness on the ground slab behaviour. J. Civ. Eng. Manag.
**2016**, 22, 690–698. [Google Scholar] [CrossRef] - Xu, M.; Ni, P.; Ding, X.; Mei, G. Physical and numerical modelling of axially loaded bored piles with debris at the pile tip. Comput. Geotech.
**2019**, 114. [Google Scholar] [CrossRef] - Luo, R.; Yang, M.; Li, W. Normalized settlement of piled raft in homogeneous clay. Comput. Geotech.
**2018**, 103, 165–178. [Google Scholar] [CrossRef] - Moayed, R.Z.; Janbaz, M. Foundation size effects on modulus of subgrade reaction on clayey soil. Electron. J. Geotech. Eng.
**2008**, 13, 1–8. [Google Scholar] - Nejad, F.P.; Jaksa, M.B. Load-settlement behavior modeling of single piles using artificial neural networks and CPT data. Comput. Geotech.
**2017**, 89, 9–21. [Google Scholar] [CrossRef] - Xu, L.; Shao, W.; Xue, Y.; Cai, F.; Li, Y. A simplified piecewise-hyperbolic softening model of skin friction for axially loaded piles. Comput. Geotech.
**2019**, 108, 7–16. [Google Scholar] [CrossRef] - Xu, L.; Cai, F.; Pan, J.; Xue, Y. Generalized nonlinear model describing softening and hardening behaviors of skin friction for axially loaded piles. Comput. Geotech.
**2019**, 116. [Google Scholar] [CrossRef] - Winkler, E. Die Lehre von Elastizitat and Festigkeit (on Elasticity and Fixity); Dominicus: Prague, Czech Republic, 1867; Volume 18. [Google Scholar]
- Elsamee, W.N.A. An Experimental Study on the Effect of Foundation Depth, Size and Shape on Subgrade Reaction of Cohessionless Soil. Engineering
**2013**, 5, 785–795. [Google Scholar] [CrossRef] [Green Version] - Terzaghi, K.V. Evaluation of coefficient of subgrade reaction. Geotechnique
**1995**, 5, 41–50. [Google Scholar] - Pasternak, P.L. Basics of a New Method for Analyzing Foundations on Elastic Beds using Two Subgrade Reaction Coefficients; “Gosstroyizdat”: Moscow, Russia, 1954; Volume 56. (In Russian) [Google Scholar]
- Shashkin, K.G. Using Simplified Foundation Models for Coupled Analysis of a Structure Together with Its Foundation. Available online: http://www.georec.narod.ru/mag/1999n1/9.htm (accessed on 10 December 2019). (In Russian).
- de Normalisation , C.E. Design of Concrete Structures—Part 1-1: General Rules and Rules for Buildings. Eurocode 2, EN 1992-1-1. 2004. E. Available online: https://www.phd.eng.br/wp-content/uploads/2015/12/en.1992.1.1.2004.pdf (accessed on 10 June 2020).

**Figure 4.**Layout: (

**a**) Values of concentrated loads (section A-A see Figure 6 and Figure 8a); (

**b**) Fragment “A” with the position of the piles and the cap of the piles.

**Figure 8.**Settlement distribution in cross-section A-A when the layer of soil is 1.20 m thick: (

**a**) Results according to FEM and Plaxis3D; (

**b**) Thickness of RC slab is 0.15, 0.20, 0.40 m.

Truck Width S (m) | S ≤ 1.0 | 1 < S ≤ 1.5 | 1.5 < S ≤ 2.0 | 2.0 < S ≤ 2.5 |
---|---|---|---|---|

Truck lifting height ≤6.0 m | 2.0 mm | 2.5 mm | 3.0 mm | 3.5 mm |

Truck lifting height >6.0 m | 1.5 mm | 2.0 mm | 2.5 mm | 3.0 mm |

Length of simulated straight edge | 1.0 m | 2.0 m | 3.0 m | 4.0 m |

Flatness tolerance | 2.0 mm | 3.0 mm | 4.0 mm | 5.0 mm |

Layer | Crushed Stone | Sand with Crushed Stone | Sand, Compacted | Clay 1 | Clay 2 |
---|---|---|---|---|---|

H, m | 0.25 | 0.35 | 1.00 | 0.60 | 7.8 |

c, kPa | 1 | 1 | 1 | 25 | 28 |

φ, deg | 43 | 40 | 38 | 19 | 22 |

γ, kN/m^{3} | 19.8 | 19.2 | 19 | 19.4 | 19.4 |

ν, - | 0.3 | 0.3 | 0.3 | 0.3 | 0.3 |

E_{ref}, MPa | 180 | 80 | 32 | 16 | 22 |

Parameter | 1 Layer | 2 Layer | 3 Layer | 4 Layer | 5 Layer |
---|---|---|---|---|---|

s_{i}, mm | 0.0565 | 0.1781 | 1.2721 | 1.5266 | 14.433 |

G_{i}, MPa | 69.23 | 30.77 | 12.31 | 6.15 | 8.46 |

δ_{i}, m^{3}/kN 10^{−6} | 1.0318 | 3.250 | 23.21 | 27.86 | 263.4 |

C_{2,i} MN/m^{3} | 969.230 | 307.692 | 43.077 | 35.897 | 3.797 |

Area of Application | C_{1}, MN/m^{3} | C_{2}, MN/m^{3} |
---|---|---|

Outside pile foundation | 3.14 | 16.06 |

Above pile cap | 41.22 | 48.14 |

Settlement | The Thickness of the Plate, m/% (Compared to a 0.15 m Thick Slab) | ||
---|---|---|---|

0.15 | 0.20 | 0.40 | |

s_{min} 10^{−3}, m | 8.277/100 | 8.945/108.1 | 11.865/143.3 |

s_{max} 10^{−3}, m | 16.971/100 | 16.481/97.1 | 16.107/94.9 |

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**MDPI and ACS Style**

Turskis, Z.; Urbonas, K.; Sližytė, D.; Medzvieckas, J.; Mackevičius, R.; Šapalas, V.
A Novel Integrated Approach to Solve Industrial Ground Floor Design Problems. *Sustainability* **2020**, *12*, 4809.
https://doi.org/10.3390/su12124809

**AMA Style**

Turskis Z, Urbonas K, Sližytė D, Medzvieckas J, Mackevičius R, Šapalas V.
A Novel Integrated Approach to Solve Industrial Ground Floor Design Problems. *Sustainability*. 2020; 12(12):4809.
https://doi.org/10.3390/su12124809

**Chicago/Turabian Style**

Turskis, Zenonas, Kęstutis Urbonas, Danutė Sližytė, Jurgis Medzvieckas, Rimantas Mackevičius, and Vaidotas Šapalas.
2020. "A Novel Integrated Approach to Solve Industrial Ground Floor Design Problems" *Sustainability* 12, no. 12: 4809.
https://doi.org/10.3390/su12124809