USING FDTD METHOD TO THE ANALYSIS OF ELECTRIC FIELD INTENSITY INSIDE COMPLEX BUILDING CONSTRUCTIONS

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No 97 Electrical Engineering 2019 DOI 10.21008/j.1897-0737.2019.97.0004

___________________________________________________

* Białystok University of Technology

Agnieszka CHOROSZUCHO

^*

, Jacek Maciej STANKIEWICZ

^*

USING FDTD METHOD TO THE ANALYSIS OF ELECTRIC FIELD INTENSITY INSIDE COMPLEX BUILDING

CONSTRUCTIONS

The aim of this article is to make a detailed analysis of the influence of the reinforcement diameter, the number of rows of reinforcing bars and the spacing between them for the values of the electric field intensity. The subject of the research is a model containing a wall made of concrete (dielectric) and reinforcement (conductor). Four reinforcement systems commonly used in building construction have been analysed. In addition, the influence of symmetry and asymmetry in the structure of bars on the values of field intensity determined for non-homogeneous material structures (reinforced concrete) was considered. For comparison, a concrete wall, without reinforcement (homogeneous material) was also analysed. Using FDTD method, the maximum electric field values generated by the Wi-Fi operating at the f = 2.4 GHz were calculated.

KEYWORDS: finite-difference time-domain method (FDTD), wireless communications systems, electromagnetic wave propagation, building materials.

1. INTRODUCTION

Fundamental building materials are used to form constructions, which internal structure, its complexity reflected in its construction and electrical properties. The materials discussed in this publication are complex in nature, being a combination of materials of various properties. The discussion of such materials allows includ- ing construction technologies used in a Europe [1, 2, 3, 7, 8, 10, 11, 12, 14].

Single-family units consist of single- and multi-layered walls of various types of brick, silicate blocks or gas aerated clay. Reinforcement is used only in ceilings, posts and load-bearing walls. In large-panel constructions, the supporting elements are walls made of reinforced concrete.

In recent years the most commonly used technology is masonry. Strain is transferred through reinforced ceilings, which allows to freely shape the space inside the building. The main building materials are ceramic, for example: brick, hollow brick and blocks. The walls, depending on the material in use and their function may also be multi-layered. Due to electromagnetic phenomenon the

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40 Agnieszka Choroszucho, Jacek Maciej Stankiewicz

description of the material structure is very significant. In the other publications the dimensions of reinforcement in analysed models are random and not occurring in building technology [1, 2, 7, 8, 10]. In this article real models were taken into account. The complexity of the structure of the reinforced walls requires to be investigated on a case-by-case basis. Due to the construction of walls, models of walls with and without reinforcement require a separate discussion. This also influences the assumptions made while choosing the calculation method.

2. REINFORCEMENT INSIDE BUILDING CONSTRUCTIONS

Analysis of building elements with reinforcement is more interesting due to the occurring field phenomenon. The introduction of metal inlays in the construction causes distortion in the propagating electromagnetic wave (EM), which leads to changes in field distribution and as a consequence influences the quality of wireless communication system among other things.

Commonly used material like concrete is a material which moving compres- sion strain well, but its resistance to stretching is very little. Due to, steel reinforcement is used to transfer the stretching strain. The reinforcement is in the form of steel bars, strings or nets. Due to the creation process and the coopera- tion of steel elements and concrete we can distinguish: reinforced concrete, ferro-cement and prestressed concrete. A more rare form of building material is fibrobeton, which contains dispersed micro-reinforcement of steel fibres (which is added to the cement mixture) [1, 2, 3, 7, 8].

The location of reinforcement within the construction elements depends mainly on the construction aims with the usage of the proper concrete ingredi- ents. The spacing between the bars (L) depends chiefly on calculations and strains on the construction. The nominal diameter of reinforcement bars is d=0.0050.04 m. In order to improve the strain resistance of the construction, hooks and anchoring loops are used, running perpendicularly to the rods. The mounting of reinforcement and the space between the bars are strictly determined for individual construction elements [1, 2, 7]. In case of ferro-cement the hole of the reinforcement mesh is 0.0060.012 m.

The dispersion of EM field by the steel mesh placed in a lossless dielectric is presented in [1, 2, 3, 7, 8]. In literature also authors presented an analysis of a single-dimension periodic row of transferring bars placed inside a plate with dielectric properties, discussing various angles of the electromagnetic wave. An individual issue is modeling the walls as layered structures.

The determining of electrical parameters is relatively difficult in many cases.

For this reason in publication [8] the analysis of the influence of reinforced concrete on radio communication, despite the wide range of frequencies (f = 0.16 GHz), assumed constant material parameters, often used for f = 1 GHz.

Even for reinforced concrete constructions, concrete parameters are used [8].

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In analysis indicated cases there are two possible approaches:

‒ a complete unification of material properties values with no regard to fre- quency,

‒ a proper choice of electrical properties with regard to the material and fre- quency.

A separate issue is concrete posts or columns reinforced with rods, which form the basic skeleton of the building and are often separate constructions.

Such cases are discussed rarely and are included in analysis of entire buildings [1, 2, 3, 7, 8]. The diameter of reinforcement used in posts is d = 0.0080.02 m, the distance from exterior edges of the post is 0.020.03 m. In their construction, in order to increase their strain resistance, stirrups joining the rods are often used. The examples of the geometry and construction requirements for columns are presented (fig. 1) [3, 8].

Fig. 1. Example cross sections of posts and placement of the reinforcement

The showed dependencies determining the reinforcement parameters were referred to the wavelength in concrete marked by c=0.05103 m, for electrical parameters of concrete described by: εr=6 and σ=0.00195 S/m [8] with a fre- quency of f=2.4 GHz.

The dimensions of typical parts are approximately equivalent to the wavelength of the wave given by

r r

0





 c

λ f  . (1)

where: v – the phase speed (magnitude of the phase velocity) of the wave, c0 – the speed of the light in vacuum, εr – relatively electric permittivity, r – relatively permeability.

3. FDTD METHOD

To determine the distribution of EM field in analysed models, the finite difference time domain method (FDTD) was used [4, 5, 6, 9, 13]. The method is based on Maxwell’s curl equations in time and space:

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t E H



 







 

 (2)

t E E

H 

 







 

   (3)

Due to the simple formulation of the FDTD method and easy imaging of the geometry of the analysed model, it is especially useful in calculating electromagnetic fields changing in time, in the range of high frequencies and broadband sig- nals. Equations (1)–(2) are then transformed into their differentia form. The equations are solved simultaneously in time and space. The FDTD method allows the analysis of complex structures, in which every material has a corresponding material property, which directly influences the correctness of the results.

In order to obtain a simultaneous scalar equation describing the individual components of the field, the equations (1)-(2) are subjected to decomposition in the Cartesian coordinate system. As an example, the equation for the EM field intensity component (E_z) in its scalar form is:



 



 







 



x z

z y E

y H x H t

E 



1 (4)

With three dimensional issues, in a classic formulation of the method, the Yee cell is used (fig. 2) [4, 5, 6, 8, 9]. A cell contains six appropriately placed component vectors of field intensity: electrical (Ex, Ey, Ez) and magnetic (Hx, Hy, Hz). The use of the FDTD method is based on the division of the whole analysed area into an appropriate number of cells. The difference schematic in the area is realised through the proper distribution of component vectors of intensity of the electrical E and magnetic field H within each cell (fig. 1). The components of the electromagnetic field are calculated in a different point in space. The vectors Ex, Ey, Ez associated with the Yee cell are anchored in mid-points of appropriate edges, and the Hx, Hy, Hz vectors – in the middle of the planes forming the sides of the cell. Appropriate component intensity vectors of the magnetic field circu- lating around it surround each component intensity vector of the electrical field.

In the case of component intensity vectors of the magnetic field the presentation is analogical.

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F

The in schematic cal field i netic field compound prior calc H_z in the p H_x, H_y, H termined E The ad is determi that the Y priate inte pending o modificat As a r well equa





 

t i n z

k j i_, _,¹E _,

Equati ue along

Fig. 2. Example

ntegration of c. In selected is determined d are moved

d intensity v ulation of th previous tim H_z, the next v

E_x, E_y, E_z. dvantage of t

ined by grow Yee cell is a c ensity comp on the calcul ion of differe result of the ation in a diff













 n

j i k j i n z k

j E

2, 1 , , , ,

1



ion (5) after the Ox axis

e crosses section

Maxwell’s e d moments in

d, the compo d in time by

vectors of the he compound me step of the values of the the algorithm wth in the Δ

cube then Δ=

pounds of th lation require

ence equatio approximati ference form



 ^





x n

k j y i

kH ²H

1 , 2, 2 1

1 ,

the transform of the elect

ns of posts and

equations in t n time, in wh ound vector v Δ_t/2 in relev e electrical f d intensity ve e algorithm. U

compound v m is the assum space. In a t

=Δx=Δy=Δz.

he electrical ements, the e ons may be cu ion of partia m. Therefore t





 n

k j y i

H ²

1 2, , 1

mations allow tric field int

placement of th

time is based hich the dist values of the vance to them field E_x, E_y, E ectors of the Using the alr vectors of th mption, that t three dimens . The distanc and magnet elementary Y uboid in shap al derivatives

the equation



 ^

 y

n k j

x i H

H ²

1 2, , 1

ws determini tensity at the

he reinforcemen

d on using th tribution of t e intensity o m. The deter

E_z is possibl magnetic fie ready calcula he electric fie the size of th sional case, i ces between ic field are Yee cell afte pe, where Δx s we acquire (3) takes for

 _i _j_k _iⁿ_j^ Hx

, , ,

 ,

ing the comp e point of o

nt

he two-step the electri-

f the mag- rmining of le with the eld H_x, H_y, ated values eld are de- he Yee cell

if assumed the appro- 0.5Δ. De- er previous

xΔyΔz.

e the Max- rm:









z k²E

1 ,

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pound val- observation

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(i, j, k) in time (n+1) basing on the calculated compounds of the EM field in the previous moments n, in appropriate points in space [5, 9, 13].

4. ANALYSED MODEL

The aim of this analysis was to assess the influence of electrical properties of the walls and kind of reinforcement inside the wall on the values of the electric field intensity. Analysis of electromagnetic occurrences was performed using a three dimensional model. In the analysed area contain the wall made of concrete with various dimension and spacing between steel bars of dimensions (fig. 3).

Fig. 3. The geometry of analysed area in one of the variants of the discussed reinforced concrete wall

The field was induced by a sinusoidal changeable plane wave at f=2.4 GHz.

The analysis of the four building constructions of the walls was calculated with unchanged area geometry, where dimension of the concrete wall was 0.24 m.

Models have been marked:

‒ d5: wall with the reinforcement in the form of a singular mesh consisting of one horizontal and vertical bars d = 0.005 m in diameter with spacing of L = 0.2 m (fig. 4a),

‒ d10: wall with bar diameter of d = 0.01 m (fig. 4b),

‒ d5_sym: reinforced concrete wall consisting of two meshes (i.e. two horizontal bars and vertical ones placed symmetrically to each other, where d = 0.005 m, L = 0.1 m (fig. 4d),

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‒ d5_asy shift o

Fig. 4. D mesh d = 0 double

The ca was deter of the eve Nyquist c amounted boundary

In figs intensity reinforcem obtained f wall the h model wit Analys mum valu reinforcem ameter re behind the

ym: a model f the bottom

iscussed model 0.01 m (d10), c) e reinforced mes

a th

alculation of rmined by th

enly cuboida condition wa d to 3240000

conditions w

5. TH

s. 5-6 the cha

(E_z compon ment (d5, d1 for model wi highest valu thout reinfor sing the area ues of the E_z ment diamet esults in a ra

e reinforcem

l created thr bars by 0.05

ls of a wall: a) w ) a three dimens shes (d5_sym), hree dimensiona

f electric field e Finite-Diff al Yee cell w s therefore f 0. On edges were assume

HE ANALY

aracteristics o nent) were p 0, d5_sym, ithout reinfor es electric fi rcement (con a directly be component w ter of 0.01 m

apid decreas ment mesh (in

rough the as 5 m along the

with one steel m sional view of t

e) with an asym al view of the w

d intensity (o fference Time was assumed fulfilled [2, 4

of the whol d [5].

YSIS OF C

of the analys presented. Th

d5_asym) w rcement (con field intensity ncrete).

ehind the wa were observe m (d10). An se in the ele nside the wal

symmetry of e Ox axis (fig

mesh d = 0.005 the wall model mmetric double wall model d5_s

one of the co e-Domain me d at Δx = Δy 4, 9, 10]. The e area Mur’

ALCULAT

sed maximal

he results re were also com ncrete). It ca y (max(Ez)) all y1.93, 2

ed in the sing increase in ectric field in ll) (fig. 5).

f vertical ba g. 4e).

m (d5), b) with (d10), d) with a e meshes (d5_as

sym

omponent of ethod [6, 45]

y = Δz = 0.00 e total numb s first-order

TION

values of ele egarding mo mpared with an be seen tha

were obtain 2 m the low gle mesh wa

the reinforc ntensity valu

ars using a

h one steel a symmetric sym), f)

f EM field) ]. The size 05 m. The ber of cells absorbing

ectric field odels with the results at after the ned for the west maxi- all with the

cement di- ue directly

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Fig. 5. Dependence the diameter of steel bars on maximum values of Ez component (inside area near the analysed wall)

Fig. 6. Maximum values of Ez component received in symmetric and asymmetric model (inside area near the analysed wall)

Inside the wall, in the range y2.1, 2.13 m among others, partial reflections of the EM wave from the single reinforcement mesh cause a temporary increase in the max(Ez). In the observed area y2, 2.08 m, behind the reinforcement in models d5, d10 a rapid decrease of the value electric field intensity to be observed.

1,0E-05 1,0E-04 1,0E-03 1,0E-02

1,4 1,5 1,6 1,7 1,8 1,9 2 2,1 2,2 2,3 2,4 2,5 2,6

y [m]

model d5 model d10 concrete

the wall made of concrete

k max (E_z)

[ V/mm ]

1,0E-05 1,0E-04 1,0E-03 1,0E-02

1,4 1,5 1,6 1,7 1,8 1,9 2 2,1 2,2 2,3 2,4 2,5 2,6

y [m ] m odel d5_sym

m odel d5_asym concrete

the wall m ade of concrete

k m ax (E_z)

[ V/m m ]

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The reinforcement influences the creation of local strengthening and weaken- ing of the signal. Due to a partial reflection of the electromagnetic wave and its entry into the reinforced concrete wall, where it is subjected to multiple reflections minimums and maximums are created in the area in front of the wall y2.24, 2.5 m (figs. 5, 6).

6. CONCLUSION

In all dielectric media some part of the electromagnetic wave energy is lost and is transformed into the internal energy of the substance. Due to absorption the power decreases and its attenuation depend on the properties of the medium (e.g. the concrete), the thickness of the wall. In some media the wave can be damped and distorted as a result of wave phenomena caused by complex dielectric (reinforced concrete) and untypical building constructions. The obtained results of the analysis enable to understand the wave phenomena connected with the electromagnetic wave inside the complex buildings made of heterogeneous materials used in civil engineering.

The analysis of reinforced concrete walls have shown that each wall on the way of the EM wave especially the one made of a heterogeneous material with steel bars decreases the value of the field. The attenuation coefficient is greatly influenced by the properties of the concrete and the steel bars in the wall. The reinforcement causes local fading that has influence on the quality of data transmission.

A lot of steel bars cause multiple reflections inside the wall and sometimes influence on increase of the electromagnetic field. The asymmetric reinforcement model always causes lower value of EM field than model with symmetric reinforcement.

Analysis of large and complex structures should consider an introduction, in the future, of the homogenization of building constructions and its material in order to improve wave propagation.

Acknowledgment. This work was prepared under scientific work S/WE/2/18 and supported by the Polish Ministry of Science and Higher Education.

REFERENCES

[1] Ping L., Qi-tao Y., Yun-liang L., Analysis of electromagnetic propagation into reinforced concrete walls by FEM-PML methods, IEEE International Conference on Microwave and Millimeter Wave Technology, ICMMT 2008 Proceedings, pp. 1–4, 2008.

[2] Ping L., Xuewang W., The reflection and transmission properties of reinforced concrete wall, International Conference on Microwave and Millimeter Wave Tech- nology, ICMMT’07, 2007.

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[3] Drewnowski S., Understand constructions. Principles of concrete reinforcement, Częstochowa, 2002 (in Polish).

[4] Oskooi A.F., Roundyb D., Ibanescua M., Bermelc P., Joannopoulosa J.D., John- son S.G., MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method, Computer Physics Communications, Vol. 181, pp. 687–

702, 2010.

[5] Taflove A., Hagness S.C., Computational electrodynamics, The Finite–Difference Time–Domain Method, Boston, Artech House, 2005.

[6] Piątek Z., Jabłoński P., Fundamentals of electromagnetic field theory, WNT, War- szawa, 2010 (in Polish).

[7] Yang M., Stavrou S., Three-dimensional modal transmission-line method for radio wave propagation through periodic building structures. IEEE Proceedings Micro- waves, Antennas and Propagation, pp. 597–603, 2005.

[8] Choroszucho A., An analysis of the electromagnetic waves propagation in construction elements with a complex structure in the range of wireless communication, PhD dissertation, Białystok, 2014 (in Polish).

[9] Sadiku M.N.O., Numerical techniques in electromagnetics, CRS Press LLC, edi- tion II, 2001.

[10] Dalke R.A., Holloway Ch.L., Mckenna P., Johanson M., Ali A.S., Effects of reinforced concrete structures on RF communications. IEEE Trans. Electromagnetic Compatibility, Vol 42 (4), pp. 486–496, 2000.

[11] Chiba H., Miyazaki Y., Analysis of radio wave reflection and transmission charac- teristics at reinforced concrete slab by numerical simulation and scaled model ex- periment, International Symposium on Electromagnetic Compatibility, Japan, 19P301, pp. 424–427, 1999.

[12] Boryssenko A., Boryssenko O., Lishchenko A., Prokhorenko V., Inspection of internal structure of walls by subsurface radar, IEEE Aerospace and Electronic Systems Magazine, Volume 21, Number 10, pp. 28–31, 2006.

[13] Sadiku M.N.O., Numerical techniques in electromagnetics, CRS Press LLC, edi- tion II, 2001.

[14] Van Damme S., Franchois A., Taerwe L., Comparison of two coaxial probes for the non-destructive evaluation of a steel fiber reinforced concrete layer, Proceed- ings of the 21^st IEEE Instrumentation and Measurement Technology Conference, IMTC’04, Volume 1, pp. 579–582, 2004.

(Received: 04.02.2019, revised: 07.03.2019)