Graduation Project Civil engineering master degree ...eprints2.insa-strasbourg.fr/2976/1/Mémoire_de_PFE.pdf · Voided slab systems..... 11 II.1. Historical development of reinforced

Research and evaluation on the use of voided reinfo rced concrete slab for residential high rise buildings

Ho Chi Minh City, July 2017

Author: Charlotte Defard

Tutor (INSA): M.Schaeffer

Tutor (Gbc Engineers): M.Bacon

4 Đường số 41, Bình An, Quận 2, TP Hồ Chí Minh, Viet Nam 24 Boulevard de la Victoire, 67000 Strasbourg, France

Graduation Project Civil engineering master degree

Graduation Projet 2017 - Civil engineering dffffffffffffffffffffffffffffffff Charlotte Defard

Research and evalutation on the use of voided reinforced concrete slab for residential high rise buildings

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Ackowledgement

I would like first and foremost to thank my tutor within the company, M. Daniel Bacon, for all the help and guidance he provided me. I would also like to thank M. Christoph Wolter for his support and valuable advices.

I thank my professor M. Claude Schaeffer, who supervised my work throughout the course of my graduation project.

At last, I would like to thank all the employees of the company and especially Mariusz Gorczyca, Hung Pham, Julia Siebe and Vinh Truong for their precious support and help.



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Abstract

Since 1990, Vietnam is experiencing a fast economic growth that goes along with a construction boom. Many residential high rise buildings are being constructed, especially in Ho Chi Minh City. In that context, gbc engineers, a Vietnamese based German engineering company, is interested in alternative solutions for high rise building slab, among which the voided slab. It is a bi-axially reinforced concrete slab with a grid of internal void formers that replace the concrete between the lower and the upper reinforcement. This system allows to reduce the self-weight, which is especially beneficial for foundations, and induces materials and cost savings. The aim of this report was to investigate on this system in order to fully understand its behavior and evaluate its efficiency in comparison to a solid slab for a high-rise residential building. For this purpose, a general presentation of this system has been carried out. Secondly, through the example of an actual high-rise project based in Ho Chi Minh City, two different kinds of voids have been implemented using a finite element analysis software. A comparison with a conventional solid slab has been conducted, in terms of structural behavior, material consumption, cost savings and installation. The results allow to evaluate the benefits resulting from this system and to determine the favorable conditions for its implementation.

Keywords: Voided slab, high-rise building, finite element, structural analysis, cost estimation

Résumé

Depuis les années 90, le Vietnam bénéficie d’une forte croissance économique qui s’accompagne d’un dynamisme sans précédent dans le domaine du bâtiment. De nombreux projets d’immeubles résidentiels de grande hauteur sont actuellement en construction, notamment à Hô-Chi-Minh-Ville. Dans ce contexte, gbc engineers, un bureau d’études allemand basé au Vietnam, est intéressé par les systèmes de plancher alternatifs, parmi lesquels les dalles allégées bidirectionnelles. Ces dalles ont la particularité d’incorporer des corps creux qui remplacent le béton entre les aciers inférieurs et supérieurs de la dalle. Ce procédé permet de réduire le poids propre de la dalle et aboutit ainsi une réduction des coûts. Le but de ce rapport est d’évaluer l’efficacité de ce système pour un immeuble résidentiel de grande hauteur. Dans une première partie, le comportement structurel de cette dalle a été développé, ainsi que ses propriétés. Dans une seconde partie, elle a été appliquée à un projet d’immeuble en utilisant le logiciel de calcul aux éléments finis Infocad. Une comparaison avec une dalle pleine quant à la consommation de matériaux, aux coûts et au comportement structurel a permis de quantifier les bénéfices de ce système et de mettre en lumière les situations favorables à son implantation.

Mots clés : Dalle allégée, immeuble de grande hauteur, éléments finis, dimensionnement, estimation des coûts



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Table of contents Ackowledgement ............................................................................................................. 2

Abstract ........................................................................................................................... 3

Résumé ........................................................................................................................... 3

Table of contents ............................................................................................................. 4

Table of figures ............................................................................................................... 7

Table of tables ................................................................................................................. 8

Introduction ...................................... ............................................................................. 9

I. Presentation of the company ......................................................................... 10

II. Voided slab systems ........................................................................................ 11

II.1. Historical development of reinforced concrete slab system .....................................1 1

II.1.1 Original systems........................................................................................................11

II.1.2 Evolution of the reinforced concrete slab ...................................................................12

II.1.3 Waffle slab ................................................................................................................14

II.I.4 Introduction of the voided slab....................................................................................15

II.2. General presentation of the voided slab ..... ................................................................17

II.2.1. Definition ..................................................................................................................17

II.2.2. Materials ..................................................................................................................17

II.2.3. Areas of application ..................................................................................................17

II.2.4. Design Codes ..........................................................................................................17

II.2.5. Construction methods ..............................................................................................17

III.3 Types of void makers available .............. .....................................................................18

II.4 Behavior of the voided slab .................. ........................................................................21

II.4.1. Flexural behavior and bending stiffness ...................................................................21

II.4.2. Shear .......................................................................................................................22

II.4.3 Crack behaviour .......................................................................................................24

II.4.4 Fire resistance ..........................................................................................................24

II.5 Benefits & Drawbacks ......................... ..........................................................................25

III.5.1 Benefits ....................................................................................................................25

II.5.2 Drawbacks ................................................................................................................26

III. Application on the Waterbay Project ......................................................... 27



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III.1 Introduction and scope of the study ......... ..................................................................27

III.2 Presentation of the Waterbay project......... .................................................................27

III.2.1 Project Parameters ..................................................................................................27

III.2.2 Initial design .............................................................................................................28

III.2.3 Value engineering solution .......................................................................................29

III.3 Specificities of structural design in Vietnam comparing to European standards ...29

III.3.1 Vietnamese standards..............................................................................................29

III.3.2 Concrete standards ..................................................................................................29

III.3.3 Steel standards ........................................................................................................30

III.3.4 Conclusion ...............................................................................................................30

III.4. Slab design on the software Infocad ........ ..................................................................30

III.4.1 Presentation of Infocad ............................................................................................30

III.4.2 Modellling of the slab on Infocad ..............................................................................31

III.5 Mechanical modeling and design of a voided sl ab ....................................................34

III.5.1 Practical modeling of a voided slab ..........................................................................34

III.5.2 Theoretical justification of the model ........................................................................37

III.5.3 Generic voided slab design process .........................................................................38

III.6 Slabs design ................................ .................................................................................39

III.6.1 Conventional reinforced concrete slab .....................................................................39

III.6.2 Bubbledeck slab .......................................................................................................39

III.6.3 U-boot ......................................................................................................................42

III.6.4 Conclusion ...............................................................................................................43

IV. Comparative study ............................. .................................................................... 44

IV.1 Structural behavior .......................... ............................................................................44

IV.1.1 Deflection.................................................................................................................44

IV.1.2 Bending behavior .....................................................................................................47

IV.1.3 Shear resistance ......................................................................................................47

IV.2 Installation ................................. ...................................................................................48

IV.3 Material consumption ......................... .........................................................................49

IV.3.1 Concrete and self-weight reduction ..........................................................................49

IV.3.1 Steel .......................................................................................................................49

IV.4 Cost Estimation .............................. ..............................................................................52

IV.4.1 Cost estimation per floor ..........................................................................................52



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IV.4.2 Summary comparison of economic efficiency ..........................................................53

IV.5 Conclusion of the comparison ................. ...................................................................54

V. Additional research ............................ .................................................................... 55

V.1 Beams consideration ........................... .........................................................................55

V.2 Foundation work in Ho Chi Minh City ........... ...............................................................56

V.3 Environmental impact .......................... .........................................................................56

Conclusion ........................................ ........................................................................... 58

References .................................................................................................................... 59

Annex A: Masterplan and elevation of the tower D6 o f the Waterbay project

Annex B: Layout of the 4 th floor of the Waterbay project

Annex C: Slab design procedure

Annex D: Design of the conventional reinforced-conc rete slab

Annex E: Design of the Bubbledeck slab

Annex F: Bubbledeck – Element design

Annex G: Design of the U-Boot slab

Annex H: U-Boot – Element section

Annex I: Layout – Location of the void

Annex J: Detailed Bills of Quantity



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Table of figures

Figure 1.1: Sample reference projects ......................................................................................10

Figure 2.1: One-way slab on beams .........................................................................................11

Figure 2.2: Two-way slab on beam ...........................................................................................11

Figure 2.3: Flat slab .................................................................................................................12

Figure 2.4: Required slab depth according to the span for a flat slab .......................................12

Figure 2.5: Hollow cylinder slab ...............................................................................................15

Figure 2.6: Biaxial voided slab modelisation .............................................................................15

Figure 2.7: In-situ application ...................................................................................................18

Figure 2.8: Semi-precast ..........................................................................................................18

Figure 2.9: Fully-precast ..........................................................................................................18

Figure 2.10: I-beams in the slab ...............................................................................................20

Figure 2.11: New Nautilus’s central cone .................................................................................20

Figure 2.12: Stress blocks in a BubbleDeck slab ......................................................................21

Figure 2.13: Illustration of the a/d ratio (Autocad) ......................................................................22

Figure 2.14: Shear capacity according to the a/d ratio ..............................................................23

Figure 2.15: Solid area around a column in a voided slab [ .......................................................24

Figure 3.1: Representation of the Waterbay project .................................................................27

Figure 3.2: Elevation of a tower of the Waterbay project ...........................................................28

Figure 3.3: Mesh generation of a square area ...........................................................................31

Figure 3.4: Internal force system with positive internal forces ...................................................31

Figure 3.5: Support system with positive support reactions ......................................................32

Figure 3.6: Downstand beams models with beam series ..........................................................32

Figure 3.7: Downstand beams models with beam series of T-beams .......................................33

Figure 3.8: Downstand beams models with beam element ......................................................33

Figure 3.9: Downstand beams models with shell element ........................................................33

Figure 3.10: Modeled slab on Infocad .......................................................................................34

Figure 3.11: Procedure for the determination of the solid areas ................................................36

Figure 3.12: Voided slab modelized on Infocad .........................................................................38

Figure 3.13: Generic voided slab design process .....................................................................38

Figure 3.14: Section of the Bubbledeck slab (Autocad) .............................................................41

Figure 3.15: Section of the U-Boot Slab from the design software Daliform ..............................43

Figure 4.1: Concrete tensile strength ........................................................................................44

Figure 4.2: Location of the maximum deflection for all three slabs ............................................45

Figure 4.3: Two-way behavior illustration with the bending moment mx for a voided slab .........47

Figure 4.4: Bubbledeck slab - Isoline of the shear acting in the slab ........................................48

Figure 4.5: Bubbledeck construction method ...........................................................................48

Figure 4.6: Local coordinates of the slab ...................................................................................50

Figure 5.1: Beam reinforcement ................................................................................................56



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Table of tables Table 2.1: Lightweight slab system ..........................................................................................14

Table 2.2: Comparison between waffle slab and Bubbledeck ...................................................16

Table 2.3 : Comparison between the voids makers ...................................................................19

Table 2.4: Structural behavior comparison between a Bubbledeck and a solid deck ................22

Table 3.1: Initial design for the podium floor ..............................................................................28

Table 3.2: Vietnamese concrete standards ..............................................................................29

Table 3.3: Vietnamese steel standards ....................................................................................30

Table 3.4: Summary table – Differences between solid and voided slab deisgn parameters .....39 Table 3.5: Conventional reinforced concrete slab parameters ...................................................39

Table 3.6: Resulted bending reinforcement ...............................................................................39

Table 3.7: Characteristics of the lattice girder ...........................................................................40 Table 3.8: Bubbledeck slab parameters ....................................................................................41

Table 3.9: Bubbledeck void parameters ....................................................................................41 Table 3.10: Bubbledeck slab design parameters .......................................................................42

Table 3.11: Resulted bending reinforcement .............................................................................42 Table 3.12: U-Boot slab parameters ..........................................................................................42

Table 3.13: U-Boot void parameter ...........................................................................................42

Table 3.14: U-Boot slab design parameters ..............................................................................43 Table 3.15: Resulted bending reinforcement .............................................................................43

Table 4.1: Non-linear analysis parameters ................................................................................45 Table 4.2: Deflection comparison ..............................................................................................45

Table 4.3: Deflections after establishment of the void layout .....................................................46 Table 4.4: Bending moment ......................................................................................................47

Table 4.5: Shear resistance ......................................................................................................47 Table 4.6: Concrete consumption per floor ................................................................................49

Table 4.7: Reduction in consumption of concrete per floor .......................................................49 Table 4.8: Load reduction due to the implementation of the voided slab comparing to the conventional slab .....................................................................................................................51

Table 4.9: Steel consumption ....................................................................................................51

Table 4.10: Steel consumption reduction compared to the conventional slab ............................51 Table 4.11: Material costs per floor for the conventional reinforced concrete slab .....................52

Table 4.12: Material costs per floor for the Bubbledeck slab .....................................................52

Table 4.13: Material costs per floor for the U-Boot slab .............................................................52

Table 4.14: Difference in costs per floor for the voided slab comparing to the conventional reinforced concrete slab ............................................................................................................53 Table 4.15: Estimated construction cost of the building .............................................................53

Table 4.16: Estimated savings resulting from the implemtation of the Bubbledeck slab ............54 Table 4.17: Estimated savings resulting from the implemtation of the U-Boot slab ....................54

Table 5.1: Deflection in the slab with and without downstand beams ........................................55

Table 5.2: Beam parameters and material reduction per floor due to its removal ......................56 Table 5.2: Beam parameters and material reduction per floor due to its removal ......................56



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Introduction

Vietnam is experiencing since about a decade a rapid growth of its economy as long as Asia’s fastest middle class expansion. As a result, there is a construction boom and Ho Chi Minh City is particularly affected by a rapid vertical construction. Projects of high-rise residential buildings are indeed numerous as the city is heading to become the next megacity in Asia after Singapore, Hong-Kong or Shangai. [30]

Gbc engineers is an actor of this development by contributing in projects as part of the design or the value engineering process. Therefore, it is essential for the company to maintain and improvevitsvknow-howvinvthevfieldvofvhighvrisevbuildings. The present report will study the implementation of the voided slab on a high-rise building. The voided slab is an innovative slab system where shapes made of high-density polyethylene are incorporatedvtovreducevthevvolumevofvconcrete. The first objective of the study is to increase the knowledge of the company in the field of voided slab. Furthermore, by establishing a clear procedure for the implementation of the voided slab on a finite element software, the aim is to ease its design. Finally, this study seeks to bring out the benefits that should be expected from the voided slab in the context of a high-rise residential building, thus evaluating its efficiency. It should allow to identify the key benefits to highlight while doing a proposal for this system.

For this purpose, the present report will be divided in three main parts. Firstly, the voided slab will be presented, from its historical context to its structural behavior. Then, on the basis of this theoretical knowledge, this system will be implemented through the example of the Waterbay project following the Eurocode. Finally, a comparison will be carried out between the voided slab and a conventional reinforced concrete slab regarding the material consumption, the installation and the cost.



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I. Presentation of the company Gbc Engineers is a german engineering company with its headquarter in Berlin and international offices in Ho Chi Minh City (Vietnam) and Phnom Penh (Cambodia). The company was founded in 2015.

The company provides the following services for German and South-Asian projects:

- Structural analysis and support for architects - Structural design for all types of buildings and materials - Structural examination of existing buildings - Detailed design work, Formwork, Rebar drawings and Structural layouts - Cost estimates - Bills of quantities - Cost saving – Structural value engineering - BIM - Building Information Modeling

The company currently employs around 85 people throughout its offices in Vietnam, Cambodia and Germany.

Allianz Headquarter

Berlin, Germany

The Sun Avenue Residence Ho Chi Minh City, Vietnam

It’s a complex made of 3 administrative and office buildings with a total gross floor area of 75 000 m2.

It’s an apartement complex that consists of 8 residential high-rise towers with a gross total floor area of 250 000 m2.

Services provided by gbc : Civil and structural Detailed Deisgn

Services provided by gbc : Structural value engineering design services, evaluation and design of alternative cost efficient construction methods

Figure 1.1: Sample reference projects



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II. Voided slab systems

II.1. Historical development of reinforced concrete slab system In this part, the evolution of slab will be developed in order to understand the logic reasoning that has led to the biaxial voided slab solution.

II.1.1 Original systems The original floor system in reinforced concrete buildings is a one-way or two-way solid slab supported by beams. Historically, there was no need for long span because the architecture of a building used to be limited by the reliance on natural light. Thus, the span was generally limited up to six meters.

Figur e 2.1: One-way slab on beams [4] Figure 2.2: Two-way slab on beams [4]

But this system has been brought to evolution for architectural, technical and cost efficiency reasons.

Evolution vofvthevarchitectural vdemand At the turn of the 20st century, space starts to be designed for artificial light. Large space and long span became therefore more common, especially for office buildings. Besides, requirements for architectural aesthetics became more and more stringent with long cantilever, large open floor or complex floor shapes. At last, some cities like Washington D.C. restricted the maximum height of buildings, thus requiring an optimized floor-to-floor height.

Technical vprogress - Improvement of the compressive strength of the concrete and the tensile strength of the steel. - Development of the formwork efficiency, allowing large slab area, reusability and the possibility of more complex sections. - More efficient construction methods such as powerful crane or construction lift.

Cost vefficiency In order to reduce the cost of building, it became more and more important to reduce the structural height by using slender structural systems, thus allowing more floors for the same total height. Moreover, contractors have sought to reduce the construction cost by reducing the construction time.



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To summarize, slab systems are asked to achieve longer span, without any increase of the thickness while allowing speeding up the construction time.

II.1.2 Evolution of the reinforced concrete slab Elimination vofvthevbeams The first idea was to eliminate beams in order to simplify the formwork, thus accelerated the construction time, and optimized the floor-to-floor height. The first flat slab has appeared almost simultaneously in the US (Turner, 1906) and in Switzerland (Maillart, 1910) at the beginning of the 20th century. Thanks to the advantages presented by this slab, including a simplified formwork and an optimized floor-to floor area, this system became very popular, even before a theoretical understanding of its behavior. [1]

Figure 2.3: Flat slab [4]

If this system allows improvements in terms of construction time and structural height compared to the two-way slab on beams, the increase of the span is limited by the deflection and it presents a critical punching shear behavior around columns

Improvement vofvthevstiffness vtovweight vratio As it is shown in the following graphic, the slab thickness will increase with the increase of the span.

Figure 2.4: Required slab depth according to the span for a flat slab [4]



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Longer span requires indeed a higher moment of inertia to deal with the deflection. This means that the member thickness must be increased which results to more structural self-weight. At a certain point, this becomes highly inefficient as the increasing self-weight is leading to more deflection. Thus, in order to achieve longer spans, the challenging problem was to improve the stiffness to weight ratio by providing lighter and stiffer slab. Different lightweight solutions have been then conceived in order to achieve this goal, some examples are developed in the following table (Table 2.1).



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System Illustration Advantages Disadvantages

Precast hollow-core slab

� Fast construction � Lightweight

structure

- Critical shear and punching shear resistance

- Very unfavorable in case of fire

Expanded polystyrene slab

� Long span � Fast construction � Lightweight

structure

- No design flexibility

- One-way spanning: must be supported by beam or wall

- Lack of structural integrity

Ribbed slab (One-way joist)

The concrete below the neutral axis is eliminated

� Profile may be expressed architecturally, or used for run services

� Lightweight structure

- One-way: limits the span

- Higher formwork cost

- Slow construction

- Slightly deeper section is required

Waffle slab (two-way

joist)

Two-way version of the ribbed slab

Among these systems, waffle slabs can be regarded as the most advanced and popular slab system. Thus, it will be further developed in the following

part.

Table 2.1: Lightweight slab system [4] [5]

II.1.3 Waffle slab Structural vBehavior The waffle slab behaves similarly to flat slab. Solid areas are set up around columns to provide



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the strength required for the shear transfer to the support. It allows medium to long spans from 9 to 14 meters.

Material consumption & Cost efficiency It allows an economical material use: 15% concrete and 10% steel in less comparing to a solid slab of same thickness. But the high cost of formwork leads to an expensive solution

Construction The construction is on-site construction, but pre-cast pods can be used. The installation of the formwork and the reinforcement can be tedious, thus the construction required supervision and skilled labor.

Others drawbacks

- It reduces floor-to-floor height - It implies a low fire rating because of the slender section of the ribs - The numerical modeling is laborious

The waffle slab is a lightweight evolution of the solid slab that leads to savings, while exclusively considering material consumption. But this system still presents strong disadvantages, mainly the cost of construction, the reduced floor-to-floor height and the low fire resistance. [4]

II.I.4 Introduction of the voided slab In the 1950s, the first voided slab appears consisting of one way spanning concrete element with hollow cylinder set up prior to pouring. The problem was that it must be supported by beams or fixed to the wall. Besides, it provided few design flexibility.

Figure 2.5: Hollow cylinder slab [21]

An improved solution has been brought in the 1990s by Jorgen Breuning, a Danish structural engineer: the biaxial voided slab (Bubbledeck).

Figure 2.6: Biaxial voided slab modelisation [3]



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Unlike hollow core units, BubbleDeck voids are discrete shapes and not continuous voids running the length of the span. It means that they will not impact the slab strength in the way prismatic voids would. [3]

The idea was to avoid the negative implication of the waffle slab, while keeping the possibility to achieve longer spans with a cost and material reduction. In the following tables, a comparison between waffle slab and solid slab is conducted.

ADVANTAGES WAFFLE SLAB BUBBLEDECK

Concrete reduction (**) 15% (*) 30% (*)

Steel reduction (**) 10% (*) 15 % (*)

Span Up to 14 m

Up to 16m , 20m for multiple bays

Soffit finishing Can be exposed directly or be

covered by a ceiling Good

DISADVANTAGES WAFFLE SLAB BUBBLEDECK

Installation Complicated installation of formwork and reinforcement, Need of skilled labor

Simple installation, especially for pre-cast

system

Cost of construction The expensive formwork tends to increase the cost

Cost reduction expected, up to 10% (*)

Fire resistance Low fire resistance because

of the slender sections

Not fundamentally different from a solid flat, depends on

the concrete cover

Floor-to-floor height Reduced Potentially increased

(*) All the estimated percentage are determined according to a solid slab of same thickness (**) Calculated within the slab, thus without taking into account the indirect saving resulting from

the size reduction of bearing. Table 2.2: Comparison between waffle slab and Bubbledeck [3] [4]

As we can see, the biaxial voided slab tends to keep the advantages presented by the waffle slab while reducing the drawbacks.



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II.2. General presentation of the voided slab

II.2.1. Definition The biaxial voided slab is a bi-axially reinforced concrete system with a grid of internal void formers made of high-density polyethylene. Its isotropic behavior allows the engineers to use the same methods for structural analysis than for a solid two-way slab. The biaxial voided slab allows reducing the self-weight in order to achieve longer span and to reduce the size of the bearing. The aim is to reduce the overall cost of a structure.

II.2.2. Materials

Concrete Standard concrete grades can be used as long as the aggregate size if not exceeding 20 mm.

Steel There is no special requirement regarding the yield strength of the reinforcement.

Plastic The void shapes are made from recycled high-density polyethylene (HDPE). This material doesn’t react with the concrete and the reinforcement steel. [3]

II.2.3. Areas of application The typical case of application is for a building slab but it can also be implemented for foundation rafts. Following the recommendations from the void providers, this system can be implemented in a wide range of buildings: residential, school, hospital etc. But the use of such is system is actually limited by its structural capacity (see II.5).

II.2.4. Design Codes Since the voided slab will not present a structural behavior fundamentally different from a solid slab, it can be designed according standards international codes no matter the types of voided shapes.

II.2.5. Construction methods There are three different construction methods that can be applied to build a voided slab design, depending on the type of void (See II.3, Table 2.3).

• In-situ application • Semi-precast elements • Fully-precast elements



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Figure 2. 7: In-situ application [3]

Figure 2. 8: Semi-precast [3]

Figure 2. 9: Fully-precast [3]

In the following report, the in-situ application has been considered since precast solutions are not available in Vietnam. Using the in-situ method, the voids shapes are placed in modules with top and bottom steel. The modules are placed on conventional formwork and a first pour of concrete is carried out to provide enough weight to resist the uplift force on the bubbles. A second pour, usually one day after, completes the slab. The pouring is always in two layers in order to avoid the flotation of the void. This is the most common construction method for voided slab.

III.3 Types of void makers available Numerous studies have been carried out regarding the shape of the void. There are several criteria of optimization such as the storability or the load distribution on the surface. Some research aimed to create the most optimized shape that provides high shear strength and high reduction of self-weight. The diversity of the enhancement criterion results in a wide range of shapes for the void. [14] [31]

The following table identifies the different kind of voids available in the market and compares them according to: - the shape, - the range of void former height, - the range of slab thickness, - the span, - the availability in Vietnam.

Secondly, additional explanations will be given to develop the eventual specificities of each void. The voids are indeed following the same general structural behavior, but they also present specific features related to their shape or installation method.



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Tab

le 2

.3:

Com

paris

on b

etw

een

the

void

s m

aker

s

- :

No

figur

es h

ave

been

pro

vide

d by

the

com

pany



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Additional explanations: Cobiax :

The special feature with Cobiax is that steel construction cages are used to hold the void while pouring the concrete. The cages also act as shear reinforcement in the slab and so increase the shear strength. [13]

- The elliptical ball (slim-line) allows a better carrying capacity than BubbleDeck. U-Boot :

- The truncated pyramid shape allows a more efficient transportation and storage but the existence of corners can induce cracks.

- This shape has the characteristic to create a gridwork of mutually perpendicular I shape beams. [10]

Figure 2.10: I-beams in the slab [10]

New Nautilus :

- This product presents the same features than the U-Boot product. [11] - In addition, this shape has a central cone that provides several advantages: • Actual visual check of the lower slab finishing • Guarantee of the completeness of the structural section • Homogeneous and perfect intrados finishing • Lifting reduction during the pour • Prevention of the deflection. [14]

Figure 2.11: New Nautilus’s central cone [11]

Beeplate:

- The bumped shape provides an optimized distribution of the load on the void makers and greatly reduced the potential apparition of cracks.



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II.4 Behavior of the voided slab Even if this part aimed to remain general, as Bubbledeck has been the first void maker available on the market, most of the studies carried on the voided slab refer to this product. For this reason, the behavior of the voided slab is mostly illustrated through the example of this particular product. Since the void makers are made from the same material and are following the same structural principle, their behavior of the slab using different type of voids will be similar.

The behavior of a voided slab can be described through a wide range of parameters. In this report, the aim is to implement this system and evaluate its efficiency. Thus, only the most important parameters to fulfill that goal will be developed below.

II.4.1. Flexural behavior and bending stiffness In bending, the stress level is relatively insignificant in the central core of the slab. Only the top compressive portion, the “stress block”, and the bottom reinforcement steel contribute to the flexural stiffness in bending. [15]

Figure 2.12: Stress blocks in a BubbleDeck slab [3]

That means that the biaxial voided slab will not present a bending behavior fundamentally different than the solid slab. This is the reason why this type of slab can be design with standard design codes (See II.2.4).

If the slab is highly stressed, the compression block may enter the void zone. In this case, the ratio of moment resisted by the void region Mu to the total moment resisted by the whole cross section Mvoid is represented by the variable µms. If this ratio is bigger than 0.2, the bending behavior will be greatly affected because the moment stress are not allowed to redistribute within the section. But in practice this situation is unlikely to occur since the voided slab is not cost-effective for very high-load. [3]

The Eindhoven University of Technology and the Technical University of Delft have conducted experiments of the bending stiffness of the BubbleDeck. They have confirmed that the flexural behavior of the BubbleDeck is the same as a solid concrete slab both theoretically and practically in short and long-term situation. [3]

The Technical University of Darmstadt in Germany also performed tests on the stiffness of a BubbleDeck slab. The results verified with the theoretical analysis and with the physical tests done in the Netherlands. [3]



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In % of a solid slab Bubbledeck versus solid slab

Same bending strength

Same bending stiffness Same concrete volume (*)

Bending strength 100 105 150 Bending stiffness 87 100 300

Volume of concrete 66 69 100 (*): On the condition of the same amount of steel

Table 2.4: Structural behavior comparison between a Bubbledeck and a solid slab [3]

The typical deflection was marginally higher than that of a solid slab because of the slightly lower stiffness of the Bubbledeck (approximately 90% of the solid slab with same thickness). But this is compensated by the lower dead load, giving the Bubbledeck a better carrying capacity. In practice, a stiffness reduction factor is applied to the stiffness of the slab. This factor is conservative and guarantees a safety margin. The stiffness reduction factor does not depend on the thickness of the section but on the ratio of the diameter of the void divided by the slab thickness. The reduction factor logically decreases as the ratio increase.

This ratio is provide by the company but can also be determined by the designer (See III.5.1).

II.4.2. Shear The shear strength depends only on the effective mass of concrete. Since some concrete is removed in the middle of the section, the voided slab will present a reduced shear stress.

The shear capacity of the BubbleDeck has been experimentally tested for different a/d ratio (with a the distance from imposed force to support and d the deck thickness), ranging from 1.4 to 3.7.

Figure 2.13: Illustration of the a/d ratio (Autocad)



23

a/d

Shear

capacity (in

% of solid

deck)

References [3]

1.4 81 Report from AEC Consulting Engineers Ltd.

/ Professor M.P. Nielsen - The Technical

University of Denmark – Enclosure B1.

2.3 76 Report "Optimising of Concrete

Constructions" / John Munk & Tomas

Moerk - The Engineering School in

Horsens / Denmark – Enclosure B4.

3 78 Report from A+U Research Institute /

Professor Kleinmann - the Eindhoven

University of Technology / the Netherlands

– Enclosure B2.

3.7 75 “Darmstadt Concrete” (Annual journal on

Concrete and Concrete Structures) -

Enclosure B3.

Figure 2.14: Shear capacity according to the a/d ratio [3]

These results show the reduced shear resistance of the voided slab compared to a conventional solid slab.

In practice, to determine the reduced shear resistance of a voided slab, a reduction factor is applied to the shear capacity for a solid deck of identical height. This factor is given by companies that are producing the void shape. It ranges between 0.5 and 0.6, which guaranty a safety margin with regard to the experimental results.

The reduced shear force provided by the voided slab is likely to be insufficient near the supports, resulting in puching shear failure. In these areas, the slab should remains solid and some shear reinforcement can be implemented if needed

81

7678

75

50

55

60

65

70

75

80

85

1 1,5 2 2,5 3 3,5 4

Sh

ea

r ca

pa

city

of

a b

ub

ble

de

ck

sla

b i

n %

of

soli

d s

lab

a/d ratio



24

Figure 2.15: Solid area around a column in a voided slab [15]

II.4.3 Crack behaviour According to a study conducted on Bubbledeck slab with a void former height of 230 and 450 mm [19], the crack pattern of the voided slab is similar to the solid slab in bending. Always following the documentation provided by the Bubbledeck Company, cracking in the bubbledeck slan is not badly affect by the presence of the void thanks to the continuous bottom and top mesh. [3] The procedure to ensure the serviceability limit state criteria for the crack limitation will be the same than for a conventional reinforced concrete slab, including the determination of the crack width.

II.4.4 Fire resistance The resistance of a slab depends on the ability of the steel to maintain sufficient strength during a fire when the temperature rises. The main parameter when considering fire resistance is the concrete cover of the reinforcement. The Eurocode 2 1-2 is providing the required concrete cover depending on the structural element and the desired fire resistance, which also applies to the voided slab.

Additionaly, recommendations for the void cover is provided by each company that commercializes void formers to be in compliance with fire resistance criteria of the aimed designed code.

Regarding the pressure of the void former during heating, calculations have been carried out by Jorgen Breuning for the Bubbledeck product. He showed that it is not a serious issue since in case of fire, all concrete is cracked and the air is likely to escape and the pressure dissipates. Besides, the products of combustion of the material used for the void (HDPE) are considered as non-hazardous with regards to health effects, according to the United Nations Globally Harmonized System of Classification and Labelling of Chemicals (UN GHS). [3] [29]



25

Conclusion

In terms of structural behavior and mechanical characteristics, the main differences between a solid slab and voided slab are as follows (no matter the kind of void used):

• A reduced self-weight • A reduced bending stiffness that will impact the deflection • A reduced shear resistance that will especially results in a weakness for punching shear

II.5 Benefits & Drawbacks

III.5.1 Benefits The benefits developed below are according the void providers (Bubbledeck, Daliform and Cobiax). [3] [6] [7] [8] [10]

Reduction of the dead weight: The first characteristic of a voided slab is the dead load reduction: about 30% compared to a solid slab with the same capacities. This will have many consequences on structural design.

Longer span: The voided slab allows achieving longer span without downstand beams.

Fewer columns: It will affect the design of column by reducing their number, their size and the quantity of reinforcement

Great design flexibility: The suppression of the downstand beams and the reduced number of columns provides a great design flexibility. Besides, the voids can adapt to all slab geometry.

Optimized floor-to-floor area: A voided slab is generally thicker than a traditional flat slab, but it doesn’t require any beams. The cumulative height of the slab and the beams tends to be higher than the height of a solid slab. That means that a voided slab tends to increase the floor-to-floor height.

Improved seismic behavior: Since weight is a leading factor in determining how much seismic force acts on a building during an earthquake, the weight reduction of a voided slab will have consequences on its seismic performance. Reducing the weight of the slabs can lead to a large reduction in the overall seismic force induced in the building. Less seismic force leads to smaller components in the lateral force resisting system. (*)

Fast construction time: The reduction of the amount of steel and concrete and the easy implementation of the void former is leading to a reduction of the cycle time for each floor, which will have a great impact for high-rise buildings.

Reduction of the overall cost of the building: Due to the fact that less material is used, the biaxial voided slab should allow a reduction of the cost of the building.



26

Environmentally green & sustainable: The recycled plastic shape and the reduction of the material consumption will reduce the energy and carbon emission.

II.5.2 Drawbacks In addition to present a reduced stiffness and a reduced shear resistance, the structural behavior of the voided slab imposes some requirements regarding the type of load distribution.

Thevamount vofvlive vload vshould vbevlimited vover vthevdeadvload As we saw earlier (See II.4.1), the deflection of a voided slab is likely to be higher because of the reduced stiffness.

The reduction of dead load can compensate this loss of stiffness, which can lead to a smaller deflection. But if the proportion of live load is way above the dead load, the compensation does not happen and the impact on deflection is very unfavorable.

It means that the voided slab is not suitable when high live loads are applied to the slab, which is the case in the following examples:

- Industrial buildings with storage areas or heavy machines - Buildingsvthatvhostvgatheringv(theater,vmuseum,vschool)

Thevlive vload vapplied vdirectly vonvthevslab vhasvtovbevrelatively vstationary If the live load highly varied in location and time, for example a vibrating industrial machine that is likely to be moved on the floor, the solid area cannot be located properly, which could lead to punching shear failures. Thus, because of its reduced stiffness, the voided slab cannot be applied for every configuration of slabs.

Conclusion From these two points it is clear that the voided slab should be mainly implemented on category A according Eurocode 0, which are residential buildings. This confirmed the focus of the report on residential buildings.



27

III. Application on the Waterbay Project

III.1 Introduction and scope of the study In the previous part, a general presentation of the voided slab has been conducted. In the present part, this system will be implemented through the example of the Waterbay project. The following study will be from now on focused on two types of void: Bubbledeck and U-Boot (see Table 2.3).The choice has been based mainly on their availability in Vietnam. Besides, two different shapes have been chosen, one sphere and one truncated pyramid, in order to obtain a relevant comparison.

The aim in this part is to establish a detailed procedure for the design of a voided slab on finite element software. The study is specifically focused on slab and does not include the design of the supports (beams and columns).

The design has been carried out with the use of different software: - Infocad, a finite element software, - Frilo, a modular software for structural analysis.

III.2 Presentation of the Waterbay project

III.2.1 Project Parameters The Waterbay is a residential and office building project based in Ho-Chi-Minh-City. It is located in an upcoming district dedicated to become one of the new administrative centers of the city.

The project consists of 10 identical towers (see masterplan in Annex A) with a gross floor area of 646 000 m2. It includes three types of spaces: apartments, offices and shops. Each block consists of 3 podium floors for shops and offices and of a tower with 21 to 24 typical floors for apartments (see figure 3.2). The studied tower is the Tower D6, its elevation can be seen in figure 3.2 and in the appendix (Annex A).

Figure 3.1: Representation of the Waterbay project [22]



28

III.2.2 Initial design The building has been designed as a frame reinforced concrete structure. The wall system bears the horizontal load caused by the wind and the earthquakes as well as the load due to the vertical weight.

The difference between the podium floors and the typical floors is the category of use (according to Eurocode 1 Section 6):

- Category A for typical floors (residential area) - Category B, C or D for the podium (offices, departments stores, areas where people may aggregate)

Figure 3.2: Elevation of a tower of the Waterbay project

In the first place, the podium floors have been designed as a one-way pre-stressed slab with 250x500mm edges beams. The initial thickness of the slab is 21 cm.

Type of slab Thickness Concrete Strength Steel strength Fire resistance

Prestressed slab on beams

21 cm

B30 (Vietnamese classification)

Equivalent concrete strength according to Eurocode = C30/37

AIII (Vietnamese classification):

- fyk = 295 Mpa for

D<10 mm

- fyk = 390 Mpa for D>10 mm

REI120 with a minimum thickness of 200 mm

Table 3.1 : Initial design for the podium floor



29

III.2.3 Value engineering solution The pre-stressed slab was the first designed solution. As a part of a value engineering study, the solution of solid conventional reinforced concrete slab has been suggested by gbc Engineers, for both podium and typical floors.

This solution will be studied and compared to the voided slab in the following report. The layout of the conventional slab is provided in Annex B.

The study is focused on the 4th floor, which is the first typical floor of the tower, just above the podium (see figure 3.2). The voided solution is not implemented for podium floors since the category of use is assumed to be not suitable for that system.

III.3 Specificities of structural design in Vietnam comparing to European standards Before further developments, the specificities of structural design in Vietnam will be briefly explained.

III.3.1 Vietnamese standards Vietnamese construction codes (TCVN, Tiêu Chuẩn Việt Nam) are allowing the designers to apply several international codes, including Eurocodes. The choice belongs to the clients. For the Waterbay project, the Eurocode has been used to design the horizontal and vertical structural element, which is the case in most of the Vietnamese projects. Thus, this code will be used in the following report.

III.3.2 Concrete standards

Vietnamese Standards for concrete

Compressive strength at 28 days [MPa]

Equivalent in Eurocode standards

M 10 10 - M 12.5 12.5 - M 15 15 - M 20 20 C20/25 M 25 25 C25/30 M 30 30 C30/37 M 40 40 C40/50 M 60 60 C50/60

Table 3.2 : Vietnamese concrete standards [23]



30

III.3.3 Steel standards

Vietnamese Standards for steel Yield strength of reinforcement [MPa] CI, AI 225

CII, AII 280 AIII 355

AIIIB 490 CIII 510

CIV, AIV 680 AV 815 AVI 980

ATVII 980 Table 3.3 : Vietnamese steel standards [24]

Note: Prefabricated meshes are not available in Vietnam. All the reinforcement is assembled in-situ.

III.3.4 Conclusion The fact that the project is based in Vietnam will not fundamentally change the design procedure in comparision with the European one, since the Eurocode is applied and the Vietnamese standards can easily find Eurocode equivalent for concrete and steel. For the following study, the steel strength CIII has been chosen. In the sake of simplification and for the use of the software, fyk will be taken equal to 500 MPa.

III.4. Slab design on the software Infocad

III.4.1 Presentation of Infocad Infocad is a civil engineering software for finite element analysis of 2D and 3D structures. It allows to calculate and checking a wide range of structures such as 2D or 3D beams, shell structures, cable structures and solid model. The calculation can be run according to European standards (Eurocodes, DIN, OENORM and SIA). For reinforced concrete construction, the software allows the designer to check the Ultimate Limit State as well as the Serviceability Limit State. The software can also run a non-linear analysis to check the long-term deformation or the internal forces. [26]

Infocad offers several ways to model a structure. The designer has to choose between different options for each component of its structure. Its choices have to be based on the aim of the study and on the level of accuracy and complexity required. The overall mechanical behavior of the structure has to be understood in order to produce an accurate and optimized model, which meets the needs of the designer.



31

In our case, we want to model a slab and the aim is to be able to analyze accurately the shear behavior and the deflection, which are the two most important design parameters for a voided slab.

III.4.2 Modellling of the slab on Infocad

III.4.2.1 Mesh generation The mesh has been created with a direct description of the area, using the mesh generators “Grid on four edges”. It generates a square area where all edges can be freely divided. The element properties and the support conditions are assigned manually.

Figure 3.3: Mesh generation of a square area with a variable numbers of elements at the edges

[26]

III.4.2.2 Slab On the finite element software, the designer can choose among different elements when he wants to generate the mesh for a slab:

- Slab element: the software will lead the calculation with forces acting at a right angle of the element.

- Plain element: the software will only consider the forces acting in the plane. - Shell element: the software will run the calculation in both directions.

In our case, there is no need to save calculation memory so it is simpler to choose the shell element.

Figure 3.4: Internal force system with positive internal forces [26]

The properties of the area are described through its section, where among other the following parameters can be specified: - Section form - Specifications for determination of shear stresses - Material - Bedding - Specification for reinforced concrete



32

III.4.2.3 Wall Infocad allows modeling the wall as an object or with a shell element. In our case, the study is focused on the behavior of the slab only. In order to simplify the model, the wall will be just represented as line jointed support. By doing that, the designer is still able to carry out punching shear verification by considering the support reaction.

Figure 3.5: Support system with positive support reactions [26]

III.4.2.4 Beam The obtained deflection will be greatly impacted by the way the downstand beams are modeled. Infocad offers options to represent the downstand beams:

The first option is to design the downstand beams with the feature “beams series” that will allow a rapid design in two dimensions.

Figure 3.6: Downstand beams models with beam series [26]

But in this case, the eccentricity of the downstand beams is not taken into account. It means that according to the Huygens-Steiner theorem, d will be taken as 0 (with d the distance from the centroid of the beam to the neutral axis).

I � I∆ � S ∗ d

As a result, the stiffness of the slab will be underestimated and the model will give an excessively conservative estimation of the deflection.

Another way to design then is to use the feature “beam series” of T-beams. As in the previous case, the input is easy and quick. But on the contrary, this model will overestimate the stiffness of the structure, because of the important proportion of redundant stiffness. Therefore, it will not place the model on the safe side.



33

Figure 3.7: Downstand beams models with beam series of T-beams [26]

The most accurate way to represent those beams is to use beam elements connected to the slab thanks to link element. That way, the induced stiffness will be accurate. But this model is complex and very long to implement in a large structure.

Figure 3.8: Downstand beams models with beam element [26]

Lastly, they can be modeled with a shell element which represents the actual dimension of the downstand beams. The resulted stiffness will be close to the actual stiffness since the eccentricity is taken into account and the redundant stiffness is limited.

Figure 3.9: Downstand beams models with shell element [26]

Since this study is focused on slab design, the last possibility has been chosen. It allows the model to remain simple while being close to the actual stiffness of the slab

It should be noted that if the design has to include the analysis of the beam, it is better to model the downstand beams with beams series.



34

III.4.2.5 Resulted slab

Figure 3.10: Modeled slab on Infocad

III.5 Mechanical modeling and design of a voided sl ab

III.5.1 Practical modeling of a voided slab The practical model of a voided slab on Infocad consists of two different sections of same thickness, the voided section and the solid section. The solid section is located along the supports and around the columns where the shear strength is critical. The voided section is located everywhere else and presents the same characteristic parameters than a voided slab: reduced self-weight and reduced stiffness.

This method allows the designers to obtain a practical model which is accurately reflecting the behavior of the voided slab.

Determination of the reduced shear resistance In order to calculate the shear resistance of the voided slab VRd,c, the article 6.2.2 of the EC2 1-1 is applied. The following formulas are valid for members that don’t require shear reinforcement.

V��,� � �C��,�k�100ρ�f�� k�σ�� b d�6.2a�

And the minimum value:

V��,� � %v'() �k�σ��*b d�6.2b�

Where: fck is the characteristic compressive strength of concrete

k � 1 �+,,� with d the effective depth in mm



35

ρ� =A.�b d

≤ 0.02

Asl is the area of the tensile reinforcement, defined in the figure 6.3 (EC2 1-1 Art. 6.2.2)

bw is the smallest width of the cross-section of the tensile area

Ac is the area of the cross section

C��,� =,.�0

12 with γ� the partial factor for concrete

v'() = 0.035 ∗k�6 ∗ f��

�6

σ�� =789:2Mpa, the compressive stress in the concrete from axial load

The influence of imposed deformation by Ned is ignored in this calculation, as it is allowed in the Eurocode.

By applying the reduction factor due to the reduced stiffness of the voided slab, we can get the reduced shear resistance. It ranges between 0.5 and 0.6.

V��,�=>(�?� = Reductionfactor ∗V��,�

Location of the solid area The location of the solid area mainly depends on the shear resistance of the slab. The procedure is as described in the following figure.



36

Figure 3.11: Procedure for the determination of the solid areas

This assumes that the shear resistance of the slab has previously been check regarding the design value of the maximum shear force VRd,max. The dimension of the solid area should be further check with the required punching shear perimeter.

Determination of the voided slab parameters Calculation of the reduced bending stiffness:

The reduced stiffness can be calculated by determining the moment of inertia of a solid slab of equivalent thickness I. and the moment of inertia of the void shape I�. For example, in the case of round void shape:

I. =bh�12

With b the width of the solid section surrounding a void shape and h the total thickness of the slab.

I� � πyL4

With y the radius of the void area.

The stiffness reduction factor of a section with void is equals to NOPN2NO . Assuming the slab

consists of 90% of void, the resulted reduction factor is equals to:



37

I. − I�

I.

∗ 0.9 + 1 ∗ 0.1

This calculation can be used to verify the factors given by the providers. But the determination can get more complicated in case of a complex shape like the truncated pyramid.

In practice, the applied reduction factor is according to the recommendations of the company. Its value ranges between 0.8 and 0.9

Calculation of the reduced dead weight:

This calculation is possible by using the weight of the void shape. The providers also communicate the load reduction by square meters or per ball.

Summary of differences in design between solid and voided slab

Solid slab Voided slab

Shear resistance VRd,c VRd,c voided = VRd,c . Reduction factor

Reduction factor ~ 0.5 – 0.6

Bending stiffness EI EI voided = EI . Reduction factor

Reduction factor ~ 0.8 - 0.9

Self-Weight γ = 25 kN/m3 Reduced of around 30% depending on the slab parameters and the

type of voids

Table 3.4: Summary table – Differences between solid and voided slab design parameters

III.5.2 Theoretical justification of the model As it has already been developed (see II.3.1), the behavior of the voided slab will not be fundamentally different than a solid slab.

The main differences are:

- The reduced stiffness, that is easily implemented as a rigidity factor in the model - The reduced shear resistance, which is taken into account while calculating the shear

resistance - The reduced dead weight, which is an input in the section parameters

Thus, by taking into account these parameters, the obtain model in Infocad will reflect the behavior of the voided slab.



38

Figure 3.12: Voided slab modelized on Infocad

The previous figure is showing an example of the voided slab. The blue parts are solid areas while the green parts are voided areas.

III.5.3 Generic voided slab design process

Figure 3.13: Generic voided slab design process [9]

11



39

III.6 Slabs design In this part, the design of three slabs will be developed.

• One conventional solid slab (see the layout of the slab in Annex B) • Two voided slab:

- Bubbledeck slab - U-Boot slab

The design of slabs has been carried out following the procedure developed in the Annex C along with the previous flow chart for voided slabs (figure 3.13).

Only the results of the design will be developed in this part, but the full analysis are available in annex D, E and G respectively. The sections about the two solutions of voided slab will be more extensive in order to explain the design and detailing the specificities.

III.6.1 Conventional reinforced concrete slab The structural design report is provided in Annex D.

Thickness Concrete Grade Steel Grade Concrete Cover

20 cm C25/30 500 Mpa 3 cm

Table 3.5: Conventional reinforced concrete slab parameters

Bending reinforcement

Top x-direction Top y-direction Bottom x-direction

Bottom y-direction

Main Ø8/12 Ø8/12 Ø8/12 Ø8/12

Additional Ø8/10, Ø8/20, Ø8/25, Ø20/15

Ø8/15, Ø8/20, Ø8/25, Ø20/15

- -

Table 3.6: Resulted bending reinforcement

The plan view of the slab with the position of the bending reinforcement is available at the end of the annex D.

III.6.2 Bubbledeck slab The structural design report is provided in Annex E. III.6.2.1 Detailing Constructive solution As we saw in Part II.2.6, there are three different ways to implement the Bubbledeck slab: semi-precast, in-situ and fully precast. The semi-precast method is not available in Vietnam and the



40

fully precast method is not very common due to the fact that the two-way behavior is difficult to reach in that case. Therefore, the in-situ method has been chosen.

The width of the manufactured element, which consists of the bubble and the top and bottom mesh, is up to 3 meters wide and the length depends on the standards of the country. In Vietnam, the length is limited to 12 meters.

Reinforcement -vMesh The spacing between the bubble and the distance to the top and bottom of the slab will be determined by the position of the mesh, which restrain the movement of the bubble laterally and vertically. Loose bars can be added in order to locally increase the steel area. They must fit between the mesh bars and be secured by tying wire.

-vConnectionvbetweenvmodules The reinforcement modules are connected to each other with splice bars and joints mesh in order to ensure a monolithic behavior to the slab and a two-way spanning. The splice bars are simply placed on the top of the bottom reinforcement. It will punctually reduce the effective depth of the slab. It will only induce a marginal effect on the structural capacity of the slab since the reduction is at infrequent interval and localized. A narrow top mesh is used to lay over the joints to ensure a continuous reinforcement. According to the Bubbledeck’s recommendation, the diameter and number of bars of the mesh should be chosen identically to the main mesh. The required anchorage length must be calculated according to the standards. The joint mesh is hand-ligated.

-vGirder In the studied case, the girder is not necessary as shear reinforcement since the bubbles are installed in the area that doesn’t require shear reinforcement. Thus, the girders have only to comply with the functional requirement during transportation and lifting and will act as distance order. For this purpose, a single leg girder can be used. It will be welded to the top and the bottom reinforcement. Following the recommendation from Bubbledeck company, the girder should not be spaced by more than two elements.

Upper chord Ø10

Lower chord Ø10

Diagonal Ø8

Distance between welding points

20 cm

Length of the girder 4 m

Height of the girder 13 cm

Table 3.7: Characteristics of the lattice girder



41

III.6.2.2 Design parameters


23 cm C25/30 500 Mpa 3 cm

Table 3.8: Bubbledeck slab parameters

Diameter Axis spacing

Rigidity factor

Shear factor

Estimated self-weight

Max. load reduction

18 cm 20 cm 0.88 0.6 16.7 kN/m3 1.91 kN/m2

Table 3.9: Bubbledeck void parameters

The void parameters have been obtained using the Bubbledeck Technical Manual [3].

Figure 3.14: Section of the Bubbledeck slab (Autocad)

Equivalent solid slab (*) Bubbledeck slab

Shear resistance VRd,c = 99 kN

VRd,c voided = VRd,c . 0.6

VRd,c voided = 59 kN Bending stiffness EI EI voided = EI . 0.88

Self -Weight γ = 25 kN/m3 γ voided = 16.7 kN/m 3 (*): solid slab of same thickness and same concrete grade

Table 3.10: Bubbledeck slab design parameters



42

III.6.2.3 Results

Bending reinforcement

Top x-direction Top y-direction Bottom x-direction

Bottom y-direction

Main Ø7/10 Ø7/10 Ø7/10 Ø7/10

Additional Ø8/25, Ø20/15 Ø8/20, Ø8/25,

Ø20/15 - -


The plan view of the slab with the position of the bending reinforcement is available at the end of the annex E.

The element section is available in annex F. The layout showing the location of the voided area within the slab is available in Annex I.

III.6.3 U-boot The structural design report is provided in annex G.

III.6.3.1 Detailing Constructive vsolution The U-Boot slab is a fully in-situ solution, in order to take advantage as much as possible of the storability of this type of void.

Reinforcement The position of the void in the slab is not depending on the mesh reinforcement, as for the Bubbledeck slab. The voids are indeed placed on foot height that determined their position within the section. It allows a less binding choice and detailing of reinforcement.

Similarly to the Bubbledeck, vertical girder has to be placed at a maximum spacing of two voids.

III.6.3.2 Design parameters


20 cm C25/30 500 Mpa 3 cm

Table 3.12: U-Boot slab parameters

U-Boot height

U-Boot width

Rib width between each U-Boot module

Rigidity factor

Shear factor Estimated self-weight

10 cm 52 cm 10 cm 0.90 0.61 18 kN/m3

Table 3.13: U-Boot void parameter



43

The void parameters have been obtained using the online design software provided by Daliform. This online software provides, among other results, the characteristic of the input slab. Besides, it gives to the user a representation of the section.

Figure 3.15: Section of the U-Boot Slab from the design software Daliform

Equivalent solid slab (*) U-Boot slab

Shear resistance VRd,c = 88 kN

VRd,c voided = VRd,c . 0.61

VRd,c voided = 54 kN Bending stiffness EI EI voided = EI . 0.90

Self -Weight γ = 25 kN/m3 γ voided = 18 kN/m 3 (*): solid slab of same thickness and same concrete grade

Table 3.14: U-Boot slab design parameters

III.6.3.3 Results Bending

reinforcement Top x-direction Top y-direction

Bottom x-direction

Bottom y-direction

Main Ø8/13 Ø8/13 Ø8/13 Ø8/13

Additional Ø8/10, Ø8/25,

Ø12/10, Ø20/15 Ø8/20, Ø8/25, Ø 12/10, Ø20/15

- -


The plan view of the slab with the position of the bending reinforcement is available at the end of the annex G.

The element section is available in annex H. The layout showing the location of the voided area within the slab is available in Annex I.

III.6.4 Conclusion The design of the voided slab isn’t a lot more binding than the conventional procedure since aside from the shear resistance criteria to distinguish solid and voided areas, the procedure is not different.



44

For the Bubbledeck slab, the reinforcement detailing is more tedious, because the mesh has to guarantee the position of the bubbles. In order to avoid that issue, another solution consists of implementing a mesh on top and bottom of the bubbles that is not resisting in the slab and whose sole purpose is to maintain the mesh in the appropriate location. A second top and bottom mesh would be implemented to resist in the section. Such a solution would ease the design, but increase the reinforcement quantity. Thus, it has not been chosen since the study aims to evaluate the material consumption.

IV. Comparative study The aim of this part is to evaluate the efficiency of the voided system in the situation of a residential high-rise building. The comparison with the conventional reinforced concrete slab will be based on the material consumption, the installation, the structural behavior and most importantly the cost. Since this study is exclusively focused on slab, only the direct consequences of the implementation of a voided slab will be quantified.

IV.1 Structural behavior

IV.1.1 Deflection The deflections have been obtained by running a non-linear analysis on Infocad with consideration of the concrete creeping.

Deflection at t = 70 years

• Load case combination = 1.0 * DL + 0.3 * LL (Quasi-continuous)

• t0 = 10 days (load start) tE = 25 550 days (concrete age at tE)

• Air humidity = 50 %

• Creep coefficient φ(t,t0) calculated by the software

Table 4.1: Non-linear analysis parameters

For consideration of the tensile strength of concrete between the appeared cracks, the stiffness of uncracked concrete is taken into account by applying a reduced tensile strength.

Fct,eff,t=70 = c x fctm = 0.1 x fctm

Figure 4.1: Concrete tensile strength



45

Since the layout is the same for the three solutions, the location of the maximum deflection is the same.

Figure 4.2: Location of the maximum deflection for all three slabs

According to Eurocode 2, the deformation shall be limited to the value l/250 to ensure that the deformation does not affect its proper functioning and appearance. Besides, in case of two-way spanning, the check is carried on the basis of the short span of the most unfavourable bays (Article 7.4.2 de l’Eurocode 2 1-1, Note 2).

Art. 7.4.1 (4) fmax � 0.U'V, � 34mm

For the deflection after construction (after the installation of the inside division walls), the value should be limited to the value l/500.

Art. 7.4.1 (5) fmax � 0.U'V,, � 18mm

Conventional RC

Voided slab Bubbledeck U – Boot

Slab thickness 20 cm 23 cm 20 cm Deflection (t=70 years) 11.84 mm 6.67 mm 10.15 mm

Table 4.2: Deflection comparison

As it has already been explained in part II.4, in the case of a residential building, the deflection for a voided slab is expected to be smaller than for a solid slab of same thickness. The results



46

from the nonlinear analysis of the deflection of the three slabs are confirming this statement, particularly when comparing the conventional slab and the U-Boot slab, which presents the same thickness.

Besides, we can observe that the deflection will be higher for the U-Boot slab than for the Bubbledeck slab. It can be explained for several reasons: - The thickness is smaller in the case of the U-boot slab comparing to the Bubbledeck slab - The input self-weight of the U-Boot is higher comparing to the Bubbledeck (increase of 7%).

Note: Because the solid areas around the core wall haven’t been implemented for the determination of the deflection, this result may appear underestimated for the voided slab. After the establishment of the voids distribution for both voided slab, the exact self-weight reduction could have been obtained. The resulted deflections are still below the deflection of the conventional reinforced concrete slab and far below the maximum admissible deflection.

Voided slab Bubbledeck U – Boot

Deflection 7.28 mm 11.05 mm Table 4.3: Deflections after establishment of the void layout



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IV.1.2 Bending behavior

Figure 4.3: Two-way behavior illustration with the bending moment mx from Infocad for a voided slab

As expected, the bending behavior between the solid slab and the voided slab is not different. As both systems are two-way spanning, the slab will bend in two directions.

Bending moments (value range)

Conventional RC slab Bubbledeck U-Boot

Mx [kNm/m] - 46 / 25 kNm/m - 44 / 21 kNm/m - 42 / 21 kNm/m My [kNm/m] - 49 / 27 kNm/m - 48 / 24 kNm/m - 45 /23 kNm/m

Table 4.4: Bending moment

The values of the bending moments are of the same magnitude for all three slabs.

IV.1.3 Shear resistance Using the formulas described in III.5.1.1 (Determination of the reduced shear resistance), the following values have been obtained.

Conventional RC slab Bubbledeck U-Boot VRd,c [kN] 88 99 88

VRd,c voided [kN] - 59 54 Table 4.5: Shear resistance

Since the shear factor is roughly the same for the U-boot slab and the Bubbledeck slab, the difference of resistance lies in the difference of statical height between the two slabs.

The reduced shear resistance of the voided slab is lower than the shear acting in the slab around around the supports (punching shear).



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Figure 4.4: Bubbledeck slab - Isoline of the shear acting in the slab equals to Vrd,c voided for the Bubbledeck slab (Infocad)

IV.2 Installation For the Bubbledeck slab, thanks to the reinforcement module, the installation is simplified in comparison with a traditional concrete slab. The main reinforcement is indeed already included in the module. Less crane lifts are needed, despite the lift of the modules, since less reinforcement and most of all less concrete are needed.

Figure 4.5: Bubbledeck construction method [20]

In terms of construction procedure, the main difference between the Bubbledeck slab and the U-Boot slab is that the U-Boot void arrived on the formwork stacked. It greatly reduces the crane work but, since they are manually placed on the formwork, increase the construction speed. The spacing between the voids is controlled by lateral spacer joints.

The installation benefits for the voided slab are difficult to quantify. However, in accordance with the documentation at our disposal and with the feedback from reference projects, the following statements can be assumed. [16] [17] [18]



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- The voided slab needs less labor work - The installation of the void is simple and does not require highly skilled workers - The number of crane lift will be reduced - The potential elimination of downstand beams and some bearing allow fast construction time.

To conclude, it can be safely assumed that the voided slab will allow to speed up the construction time without increasing the difficulty of execution. This last point represents a great advantage, especially regarding some other alternative systems for slab such as pre-stressed or waffle slab.

IV.3 Material consumption

IV.3.1 Concrete and self-weight reduction The reduction of the consumption of concrete will be discussed in this part, as long as its impact on the self-weight. The detailed bill of quantities can be consulted in Annex J.

Conventional RC slab

Bubbledeck U-Boot

Gross concrete volume [m3] 136 156 136

Void volume / piece [m3] - 0.0031 0.0213

Total void volume [m3] - 35 23

Final concrete volume per floor [m3] 136 122 113

Table 4.6: Concrete consumption per floor in cubic meter

Concrete Reduction in % Bubbledeck U-Boot

Comparing to the conventional RC slab 10 17

Comparing to a solid slab of same thickness 22 17

Table 4.7: Reduction in consumption of concrete per floor (in %)

The volume reduction due to the void is larger for the Bubbledeck comparing to the U-Boot slab, although the same distribution of void is applied for the two voided slabs solution (Annex I). The solid areas are indeed located at the same place and their sizes are roughly equal. The difference is due to the fact that the U-Boot module is larger than the Bubbbledeck module, but its number of occurrences are also greatly reduced.



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Figure 4.6: Local coordinates of the slab

By imagining an invisible line through the centroids of the sphere in x and y direction, 90 % of that line will be inside void for the Bubbledeck against 84% for the U-Boot slab. Similarly, by considering a line along the z axis, 78% of that line will be inside void for the Bubbledeck against only 50% for the U-Boot. This explains that the concrete reduction is less in the case of the U-Boot slab comparing to the Bubbledeck slab.

Despite this fact, the volume consumption of the Bubbledeck slab is still higher because of the higher thickness (3 cm). The U-Boot slab will allows more concrete savings since it presents the samevthicknessvthanvthevreferencevslab. The announced concrete volume reduction for the Bubbledeck is around 30 %. In this study, we got 10% reduction comparing to the conventional reinforced concrete slab. The reduction goes up to 22 % if we compare to a solid slab of same thickness, which is still far lower than what have been announced.

It should be noted that the studied layout includes a lot of shear wall (see Annex B), along which the areas have to be set solid. This concern about 30 % of the area left solid. In most cases, the voided slab is implemented on a flat slab layout, which is a solid slab that relies on columns. In that case, the walls are limited to the core or to some edges, which reduces the need of solid areas. Thus, the concrete volume reduction is greatly dependent on the type of layout of the slab.

Self-weight reduction

The reduction of the concrete volume will induce an overall load reduction, and will especially impact the foundation. The layout of the pile and its number is likely to remain unchanged, because the grid has to stay the same to maintain the stability of the slab, so the load reduction would not allow to delete piles. But it could reduce their size or reinforcement ratio. The foundation work is a particularly complex matter in Ho Chi Minh, see part V.2



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Self-weight of concrete Number of typical floors 25 kN/m3 20

Unit Bubbledeck slab U-Bboot Saved Concrete per floor m3 13.6 22.8 Load reduction per floor kN 339 571

Total load reduction kN 6 778 11 417 Reduction of load comparing to the conventional slab

%

10

17

Table 4.8: Load reduction due to the implementation of the voided slab comparing to the conventional slab (Annex J)

We logically find the same percentages than in table 4.7.

IV.3.2 Steel Note: - The spacers are not taken into account. - The detailed bill of quantities can be consulted in Annex J.

Bending reinforcement Shear Edge pin

Transition steel

Sum Reinf. ratio

mm Ø7 Ø8 Ø12 Ø20 Sum Ø7

kg kg kg kg kg kg/m2

Conv. 927 324 9651 25 1102 10779 15.9

BBD 8474 55 166 8695 17 1181 181 10073 14.9

U-Boot 8493 22 173 8689 18 1017 9724 14.3

Table 4.9: Steel consumption

Total reinforcement BBD 7 %

U-Boot 10 % Table 4.10: Steel consumption reduction compared to the conventional reinforced concrete slab

in %

Regarding only bending reinforcement, the reduction in comparison with the conventional reinforced concrete slab is off 10 % for both solutions of voided slab. The total reinforcement reduction is only off 7 % for the Bubbledeck slab mainly because of the required transition steel between the prefabricate module.



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IV.4 Cost Estimation

IV.4.1 Cost estimation per floor The same cost has been chosen for the voids both voided solutions. The cost is indeed subject to negotiation and values are not communicated by companies for obvious competitive reasons. The unit cost of 150 000 VNĐ/m2 has been estimated from a proposal issued by the company HASOP that sells the void New-Nautilus void in Vietnam (see table 2.3). Since the unit price is equal, the only point of comparison between the two voided slabs is the price difference induced by the material reduction.

Note: - Prices in euro have been included to ease the understanding (25 000 Viet Nam Đồng = 1€) - Prices are including the labor work - Prices of steel, formwork and concrete are following the Price of Ministry of Construction - The detailed bill of quantities can be consulted in Annex J.

Conventional reinforced concrete slab

Quantity Unit Unit cost Total cost

VNĐ € k VNĐ € Rebars

fy =500 Mpa 15.90 kg/m2 15 846 0.63 252 10

Concrete B25 0.20 m3/m2 2 596 650 104 519.3 20.8 Formwork 1.05 m2/m2 136 931 5.5 143.8 5.8

Total cost / m 2 915 36.6 Table 4.11: Material costs per floor for the conventional reinforced concrete slab

Bubbledeck slab



fy =500 Mpa 14.86 kg/m2 15 846 0.63 235.4 9.4

Concrete B25 0.18 m3/m2 2 596 650 104 467.4 18.7 Formwork 1.05 m2/m2 136 931 5.5 143.8 5.8 BBD el. 0.66 m2/m2 150 000 4 99 4

Total cost / m 2 946 37.8 Table 4.12: Material costs per floor for the Bubbledeck slab

U-Boot slab



fy =500 Mpa 14.86 kg/m2 15 846 0.63 227.3 9

Concrete B25 0.18 m3/m2 2 596 650 104 432 17.3 Formwork 1.05 m2/m2 136 931 5.5 143.8 5.8 U-Boot el. 0.66 m2/m2 150 000 4 99 4

Total cost / m 2 902 36.1 Table 4.13: Material costs per floor for the U-Boot slab



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Bubbledeck slab

U-Boot slab

Cost increase + 3.35 %

Cost reduction -1.43 %

Table 4.14: Difference in costs per floor for the voided slab comparing to the conventional reinforced concrete slab

It is clear from the previous tables that no substantial cost reduction should be expected when considering one floor. It is due to the fact that the cost reduction induced by the material savings is covering the cost of the voids, therefore resulting in a cost per square meter roughly equals to thevonevofvthevconventionalvslab. The cost per square meter of the U-Boot slab is sighly lower since it induces more material savings than the Bubbledeck slab, which is 3 cm thicker than the two other slabs. Because of this increase in thickness, the savings resulting from the material reduction are not enough to cover the cost of the void makers.

IV.4.2 Summary comparison of economic efficiency If the voided slab will not generate any savings within the slab, it will surely induce saving in the overall building. As we already saw, the voids will greatly reduce the dead load that has to be supported by the structural supports: beams, columns and foundation.

Besides, since the voided slab is dedicated to be implemented in a high-rise building, the scale effect should not be underestimated. A very slight difference in price for the slab can end up having an impact on the overall costs.

Content Unit Result Note Typical floor area m2 13 560 20 floors of 678 m2

Podium area m2 2 034 3 floors of 678 m2 Total floor area m2 15 594

Investment cost 1000 VNĐ/m2 68 000 ≈ 3000 $/m2 following the estimated market price. It includes all the structural elements (beams, columns, facade etc)

Construction cost Million VNĐ 10 603 400

Million € 42 Table 4.15: Estimated construction cost of the building



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Bubbledeck slab Content Unit Result Note

Bubbledeck slab 1000 VNĐ - 415 163 See Annex J Columns and concrete

walls 1000 VNĐ 18 441 600 Estimated at 2 % of the construction cost due to

the load reduction (*)

Foundation 1000 VNĐ 22 129 920 Estimated at 2.4 % of the construction cost due

to the load reduction (*) Economic efficiency of the Bubbledeck slab

Million VNĐ 40 156 Million € 1.85

% Economic efficiency comparing to reference

slab % 4.36

Table 4.16 : Estimated savings resulting from the implemtation of the Bubbledeck slab

U-Boot slab Content Unit Result Note

U-Boot slab 1000 VNĐ 177 462 See Annex J Columns and concrete

walls 1000 VNĐ 18 441 600 Estimated at 2 % of the construction cost due to

the load reduction (*)

Foundation 1000 VNĐ 22 129 920 Estimated at 2.4 % of the construction cost due

to the load reduction (*) Economic efficiency of

the U-Boot slab Million VNĐ 40 749

Million € 1.87 % Economic eficiency compring to reference

slab % 4.42

Table 4.17: Estimated savings resulting from the implemtation of the U-Boot slab

(*): The estimated percentages have been calculated by the company HASOP (see part III.7.4.1). It has been determined for another project based in Ho Chi Minh City, The Sun Avenue (see Figure 1.1). This project is larger than the Waterbay but is of the same nature: it consists of 8 residential towers with 28 to 30 floors with around 1 200 m2 per floors.

IV.5 Conclusion of the comparison The structural behavior of the voided slab was following the theoretical expectations already exposed in part II.4. With respect to theses results and except for the shear resistance which is a slightly more complex matter, the voided slab is providing equivalent or better performance for a same thickness.

Its implementation will induce a significant material reduction for the slab for both voided solutions, up to 10 % for the steel and 17 % for the concrete of the U-Boot slab comparing to the conventional reinforced concrete slab. This will greatly impact the overall structure by reducing the load transmitted to the supports.

If it only will induce modest cost saving or slight increase in cost for the slab itself, the important subsequent load reduction will allow materials savings for other structural element such as the beams, the columns and the foundations. As a result, a reduction of around 4% is obtained for the estimated cost of the building for both voided solutions.



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In the present study, the U-Boot slab is giving better results in term of savings than the Bubbledeck slab. It is mainly due to the fact that it presents the same thickness than the reference slab (the conventional slab). On the other hand, since the Bubbledeck slab is a semi-precast solution, significant saving can be expected from its installation. Besides, if the Bubbledeck solution is compared to a solid slab of same thickness, the concrete volume reduction is higher than with the U-Boot slab.

To conclude, both voided solutions allow material and cost savings while achieving the structural capacity required.

V. Additional research

V.1 Beams consideration The previous work did not include the study of the beams. However, the removal of the downstand beams is one of the advantages of the implementation of the voided slab according to the providers. Thus, at a later stage of the study, the option of removing downstand beams has been considered, through the example of the U-Boot slab. As a reminder, the downstand beams (25 cm wide and 50 cm height) are initially located at the edges (See Annex B).

Since the self-weight of the slab is reduced with the voided slab, this part aimed to know if the beams can be removed. The U-Boot slab has been selected over the Bubbledeck slab since it presents the same thickness than the conventional reinforced concrete slab and its deflection is higher than the Bubbledeck slab. The critical point is expected to be the deflection, since the removal of the beams will induce a loss of stiffness.

The deflection has been calculated following the same procedure than previously (see Part IV.1.1), at t=70 years and taking into consideration the solid area at the edge.

U-Boot slab With downstand beam Without

Deflection 11.05 mm 11.26 mm Table 5.1: Deflection in the slab with and without downstand beams

As it can be seen, the consequence on the deflection is very limited. Besides, slightly higher bending moments are obtained from the solution without beam, but this small augmentation does not induce any important increase in the quantity of reinforcement required.

We can conclude that the downstand beams in the layout do not fulfill any important structural function. Their occurrence in the layout is more for practical and constructive approach, for example in order to fix the facade. This statement has been confirmed by the study of the conventional reinforced concrete slab without downstand beams. The deflection only increase of 2.5 % without impacting the overall stability of the slab.

The removal of the beams would allow to achieve savings for all three slab systems, as shown in the following table.



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Reduction per floor Concrete section Reinforcement Total length Concrete Steel

m2 kg/m m m3 kg 0.125 11.5 65.5 8.2 752

Table 5.2: Beam parameters and material reduction per floor due to its removal

The quantity of steel has been estimated by conducting a preliminary design on the software Frilo.

Figure 5.1: Beam reinforcement

Note: These quantities have not been included in the bills of quantities discussed in part III.7.3.

V.2 Foundation work in Ho Chi Minh City For a high-rise building, the foundation can account for up to 30 % of the total cost of the building. It is all the more true in Ho Chi Minh City. The city is indeed located along the banks of the Saigon river and close to the Mekong Delta, which induced complex condition of ground. The soil of the area is mainly composed of alluvial soil with clay major focus (low bearing capacity and high compressibility subsidence) and presents a high humidity rate. [27]

Therefore, foundations in Ho Chi Minh City have to be carefully designed and constitute an important cost parameter of the project. The load reduction resulting from the implementation of the voided slab is thus highly appreciated and constitute a real benefit in term of cost saving and difficulty of execution.

V.3 Environmental impact As it has already been mentioned in part II.5, a reduced environmental impact is one of the benefits of this system and constitutes an important point to emphasize. Nowadays, moving to more sustainable industries in order to respect the global ecosystem is a necessity. The concrete production is problematic for two main reasons. First, the production of concrete relies on non-renewable materials, such as sand or cement. Besides, the fabrication of cement is one of the primary producers of carbon dioxide (about 6% of the worldwide man-made emission). The cement is second of water as the most consumed substance on earth and 7 billion of cubic meters of concrete are used every year. [28]



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In order to manage the usage of natural resources and emissions resulting from construction, new ways must be found. Different researches are carried on, especially innovative process for the production of cement or recycled concrete. But the most obvious way is to reduce the direct consumption of concrete.

A system such as the voided allows it since it reduces of the concrete volume and is made of recycled plastic. Besides, the reduction of material consumption also allows to reduce the transportation. This aspect of this system should not be underestimated, even so it does not imply cost reduction of any kinds. It has been recognized through numerous awards and prizes including the German Sustainability Award for Cobiax in 2013 and a nomination for the European Environmental Prize for Sustainable Development for Bubbledeck.[3] [8]



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Conclusion

The present work has allowed to summarize the knowledge related to the voided slab, from its behavior to the different kinds of void makers available. From this state of the art and through the example of the Waterbay project, the design procedure of a voided slab on a finite element software has been developed.

The material savings can be evaluated at the level of the slab, between 10 and 20 % of the concrete and up to 10% of the steel.

The magnitude of the material savings actually depends on numerous parameters. In the first place, the load distribution should be favorable, which implies a small live load compared to the dead load, like for a residential building. Secondly, if the slab is excessively thin, its thickness will be increased for the implementation of the voided slab, which would minimize the benefit. At last, the layout should be suitable for such a system, given that the ideal configuration is a flat slab. These three features should be closely studied before the implementation of the voided slab and for the choice of the type of void.

The cost savings can only be appreciated on the scale of the building, since they result from the total reduction of dead load. Thus, the implementation of such a system should be limited to rather high buildings in order to maximize the scale effect. This corroborates the orientation of the subject.

Also, the cost saving for the entire building may look moderate in the present study (around 4%). This feature shows that the cost reduction should not be the only argument while choosing to implement this system. It is actually really beneficial when it solves several constraints imposed on the project, in addition to reduce the cost. The constraints can be for example a seismic weakness, a construction site in a highly urbanized area or, as it is the case in Ho Chi MinhvCity,vavsoilvwithvlowvbearingvbehavior. To conclude, the voided slab allows to save materials and to reduce the overall cost of a building while achieving the same structural capacities. When submitting this solution as part of the value engineering process, the argumentation should not rely exclusively on the cost reduction since this system implies others advantages that could, depending of the project parameters, be significant.



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References

[1] M. KAMARA, M. MUHAMID, C.NOVAK. Historical Perspective on the Evolution of Two-Way Slab Design. Special publication, American Institute of Concrete, Volume 287, 2012, 10 pages.

[2] P.E. REGAN. Behaviour of reinforced concrete flat slabs, Construction Industry Research and Information Association, Report Nr 89, 1981, 91 pages. [3] BubbleDeck Voided Flat Slab Solutions, Technical Manual & Documents, BubbleDeck UK, Issue 1, 2008, 91 pages.

[4] C.H GOODCHILD, Economic Concrete Frame Elements. British Cement Association, 1997. 133 pages.

[5] N. MARTI, Types of structural floors. Universidad Ramon Llull, Constrution II, 2nd year, 2015, 75 pages.

[6] BubbleDeck Design Guide for compliance with BCA using AS3600 and EC2, Prepared by KYNG Consulting PTY LTD. Ref. DG_v1.2, 2008, 18 pages.

[7] BubbleDeck Design Guide, The biaxial hollow deck, BubbleDeck Company. 5 pages.

[8] Cobiax Quickguide, provided by Cobiax Technologies GmbH, 2015, 2 pages.

[9] Eco-Line Technology Handbook, provided by Cobiax Technologies AG, 2017, 33 pages.

[10] U-Boot Guide, provided by Daliform, 17 pages.

[11] New Nautilus Guide, provided by Geoplast. 28 pages.

[12] Beeplate Bamtec Guide, provided by Beeplate, 2017, 25 pages

[13] C. MARAIS, Design adjustement factors and the economical application of concrete flat-slabs with internal spherical voids in South-Africa. Master of Structural Engineering. University of Pretoria, 2009, 264 pages.

[14] J.J CHUNG, J.H PARK, H.K CHOI, S.C LEE, C.S CHOI, An analytical study on the impact of hollow shapes in bi-axial hollow slabs, Fracture Mechanics of Concrete and Concrete Structures - High Performance, Fiber Reinforced Concrete, Special Loadings and Structural Applications, Korea Concrete Institute, 2010, 8 pages.

[15] T.LAI, Structural behaviour of Bubbledeck slabs and their application to lightweight bridge deck. Master thesis, Master of Engineering in Civil and Environmental Engineering, Massechysetts Institure of Technology, 2010, 42 pages.

[16] BubbleDeck Structures Solutions, provided by BubbleDeck Company, 2004, 10 pages.



60

[17] F. MOLA, L. PELLIGRINI, G.SCONNOCCHIA, MOLA.E, Recent developments in tall buildings in Italy. Council on Tall Buildings and Urban Habitat, CTBUH New York Conference, 2015, 9 pages.

[18] Cobiax brochure - Lightweight Concrete Slab, provided by Cobiax company, 2016, 8 pages.

[19] Research of Two-axis hollow body. Darmstadt Concrete, Annual journal on Concrete and Concrete Structures, 1999.

[20] Site erection & Installation Manual, type B – Reinforcement modules. Bubbledeck United Kingtom, Edition 1, Revision C: June 2008, 11 pages.

[21] M. MOTA, Concrete Reinforcing Steel Institute, Voided SLABS – New Trends, December 2014, 66 pages.

[22] EOSLAND, Dự án Waterbay Novaland quận 2 - Tập đoàn Novaland [online]. Avalaible on : http://www.eosland.com/2017/02/du-an-water-bay-novaland-quan-2.html (Visited on the 7th of July 2017)

[23] TCVN Tiêu Chuẩn Quốc Gia. Kết cấu bê tông và bê tông cốt thép - Tiêu chuẩn thiêt kê. TCVN 5574 : 2012, Ha Noi, 2012, 143 pages.

[24] TCVN Tiêu Chuẩn Quốc Gia. Thép cốt bê tông. TCVN 1651-2 : 2008, Ha Noi, 2008, 25 pages.

[25] R.D. COOK, Concepts and applications of finite element analysis. Fourth Edition. University of Wisconsin – Madison, John Wiley & Sons. Inc., 2002, 733 pages.

[26] Infocad User Manual. Infograph GmbH, Aachen, Germany, 2016, 720 pages.

[27] INATECH (International Applied Technology Company). The soft soil treatment technology in Vietnam [online]. Available on: http://www.intatech.vn/en/technology-news/297-the-soft-soil-treatment-technology-in-vietnam.html (Visited on the 6th of July 2017)

[28] World Business Council for Sustainable Development.The cement sustainability initiative, our agenda for action, July 2002, 40 pages.

[29] ExxonMobil Chemical. Product safety summary: High Density Polyethylene. September 2015, 3 pages.

[30] T. PHAN, Real estate in Vietnam: The high rise future of Ho Chi Minh City. Available on: http://vietcetera.com/real-estate-in-vietnam-the-high-rise-future-of-ho-chi-minh-city/ (Visited on the 20th of July 2017)

[31] A. ALBERT, J. SCHNELL, D. BUSCH. New void formers for biaxial voided slabs. FIB Symposium (Fédération international du béton), 2016, Cape Town, South Africa. 9 pages.