Evaluation of transient stresses in concrete with electromagnetic gages

CEMENT and CONCRETE RESEARCH. Vol. 6, pp. 659-666, 1976. Printed in the United States.

Pergamon Press, Inc

EVALUATION OF TRANSIENT STRESSES IN CONCRETE WITH ELECTROMAGNETICGAGES

J. Bhargava and A. Rehnstr~m Inst. for Structural Engineering & Bridge Building, KTH S-IO0 44 Stockholm 70, Sweden

(Communicated by Z. P. Bazant) (Received June 23, 1976) ABSTRACT Electromagnetic velocity gages were used to study the dynamic strength of concrete. The p r i n c i p l e of e.m. gages and t h e i r application for measuring the transient stresses produced in concrete prisms by detonation of an explosive charge are described. The dynamic strength of ordinary concrete was 20 % higher than the s t a t i c strength, whereas in case of polymer-impregnated concrete, the difference was only 5 %.

Zum Studium der dynamischen Festigkeit von Beton wurden elektromagnetische Partikelgeschwindigkeitsgeber benutzt. Das Prinzip der elektromagnetischen Geber und ihre Anwendung zur Messung von Spannungswellen, hervorgerufen in Betonprismen durch Detonation von Sprengk~rper, werden beschrieben. Die dynamische Festigkeit gew~hnlichen Betons war 20 % gr~sser als die statische, bei polymergetr~nktem Beton war der Unterschied dagegen nur 5 %.

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659

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VoI. 6, No. 5 J. Bhargava, X. Rehnstr~m

Introduction In many types of structures', cement concrete is subjected to dynamic stresses of short duration, caused by shock or impact loading. Such stresses can be produced as a r e s u l t of thermonuclear blast loading or an accidental release of energy in a prestressed concrete reactor pressure vessel, by impacting p r o j e c t i l e s or by d r i v i n g mechanism in case of foundation p i l e s . The material response of concrete to dynamic loading can be studied by methods which provide the c a p a b i l i t y f o r measurement of stresses normal to wavefronts, or the p a r t i c l e or surface v e l o c i t i e s . These methods can be c l a s s i f i e d as follows: I . Methods for recording the stress-time p r o f i l e . In-material stress measurements can be made with x-cut quartz gages [ ~ and Manganin Gages [ 2 ] . These gages are e f f e c t i v e but require laborious c a l i b r a t i o n . 2. Methods for recording the ~urface or p a r t i c l e v e l o c i t y . The p a r t i c l e v e l o c i t y is evaluated from the v e l o c i t y of a f l y i n g p e l l e t , l i g h t l y attached to the surface of the shocked specimen [ 3 ] ; electromagnetic v e l o c i t y gages [4_7 can also be employed f o r t h i s purpose. The use of e.m. gages provides a simple and v e r s a t i l e method f o r i n -material p a r t i c l e - v e l o c i t y measurements in a non-conducting material. The range of v e l o c i t i e s over which the gage can be used is l i m i t e d at the lower end by e l e c t r i c a l noise and at the higher end by gage d i s i n t e g r a t i o n . The only c o n s t r a i n t that need be made i n v o l v e s i n t e r a c t i o n of the gage and the concrete during shock loading. The e f f e c t s due to impedance mismatches can be minimized by making the gage element as small as possible, using a thin foil. This a r t i c l e describes the p r i n c i p l e and a p p l i c a t i o n of such a gage f o r measuring the t r a n s i e n t stresses induced in cement concrete prisms by detonation of an explosive charge in contact with t h e i r surface. Theory The p r i n c i p l e of the electromagnetic gage is i l l u s t r a t e d in FIG.I. The gage consists of a conducting loop of t h i n copper f o i l s t r i p 30-35 ~m t h i c k , cemented w i t h i n the specimen. I t is oriented with i t s sensing length parallel to the plane of shock f r o n t , and located in a plane parallel to the superimposed magnetic f i e l d . The pickup leads remain p a r a l l e l to the f i e l d . A f i n i t e displacement of the conducting loop r e s u l t s in a v a r i a t i o n of the enclosed magnetic f l u x . When the motion of the conductor is perpendicular to the f i e l d , a voltage E is induced around the loop, given by: E = -

~--~

(1)

~t

when @ is the magnetic f l u x enclosed by the loop. For a constant f i e l d B and gage length c, the e m f induced by a d i s placement u w i l l be E=B.

~.~

du

(2)

Now du = v d t , where v is the p a r t i c l e v e l o c i t y , hence we get E v - B~

(3)

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661 DYNAMIC STRESS, POLYMER IMPREGNATED CONCRETE

Plexigtas

E I'A Gage

/

FIG. 1 Schematic view of electromagnetic v e l o c i t y gage

I t can be seen from eq. (3) that the particle velocity is always linearly related to the voltage induced. Thus no calibration of the gage element i t s e l f is required. Only a knowledge of the applied field intensity B and the gage length ~ is necessary to deduce velocity-time profile. Propagation of Stress Wave When a uniform impulse is applied to one end of a long specimen of an e l a s t i c m a t e r i a l , a l o n g i t u d i n a l wave t r a v e l s down the length of the specimen. The rate of displacement of a point along the length of the specimen, au/at, can be used to determine the transmitted stress. At any point in the specimen the t r a n s i e n t stress o, due to the wave is given by: au

a=pc

aT

(4)

where p = mass per u n i t volume and c = longitudinal wave v e l o c i t y . In the case of concrete the assumption regarding the e l a s t i c character has been shown to be approximately v a l i d [ 5 ] . The p a r t i c l e v e l o c i t y can be obtained from e.m. gage traces. The average wave v e l o c i t y can be calculated from the time i n t e r v a l between the a p p l i c a t i o n of loading, such as by detonation, and the a r r i v a l of the wave at the gage. Energy Transmission Capacity Studies made on rock materials [6] have shown that there is a maximum energy l i m i t , which could be transmitted through a rock specimen by a stress pulse. This l i m i t is e s s e n t i a l l y a stress amplitude l i m i t , such t h a t the stresses above t h i s are not transmitted but r e s u l t in i r r e v e r s i b l e crushing of the rock. The deformational behaviour of cement concrete in compressive and t e n s i l e tests closely resembles t h a t of rocks. I t would be reasonable to conclude t h a t f o r each grade of concrete there is a c r i t i c a l or maximum l i m i t for stresses which can be transmitted by a shock wave. Thus i f a concrete specimen is subjected to load higher than the f r a c t u r e load, the magnitude of the transmitted stresses w i l l be a measure of the dynamic stress l i m i t of the material. Some studies of the impact strength on concrete using Hopkinson's s p l i t bar method support t h i s hypothesis [ 7 ] .

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o J. Bhargava, A. Rehnstr~m

Vol. 6, No. 5

Experimental Details Specimen Preparation Two types of concrete were used in these investigations: I. Ordinary concrete. Nominal 28-days cube strength 60 MPa, 2. Polymer-impregnated concrete. These specimens of cement concrete were dried at I05OC and impregnated with styrene, containing 3 % by weight of benzoylperoxide as i n i t i a t o r . The impregnated specimens were stored in an oven at 85°C for thermal polymerization. For a study of the material response to dynamic loading, i t is desirable to have specimens of very small lateral dimensions in order to minimize the effect of geometric dispersion of the wave. But at the same time concrete prisms must have a certain thickness for the material to be representative of the material in larger specimens. In view of these considerations, 20-mm thick prisms were sawn from larger cubes. The f o i l gage with a sensing length of I0 mm was f i r s t glued to the plexiglas base, using a glue of same properties as plexiglas. This assembly was then bonded to the underside of the concrete prism.

Film

Kerr- Cell Shutter

Objeclive

Glass Wind w

Charge "~,

~Display j

E M Gage

~

Magnetic Coil

Flash

Plexiglas Concre FIG. 2 Experimental set-up Experimental Set-up FIG. 2 shows the experimental arrangement used. The concrete prism, was placed v e r t i c a l l y between the two concentric electromagnetic c o i l s , so that the sensing arm of the e.m. gage was at the centre of the c o i l s . The prism was subjected to an explosive loading, by detonating a capsule of high explosive, intense enough to fracture the specimen completely. During the passage of the resultant pulse, e.m. gage sandwiched in the specimen recorded the variation of p a r t i c l e velocity with time. The maximum amplitude of this trace was used to obtain the transmitted stress.

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663

DYNAMIC STRESS, POLYMER IMPREGNATED CONCRETE The specimens were illuminated from behind by a synchronized flash and were photographed using a m u l t i p l e Kerr-cell camera. The sequence of detonation and exposures was programmed to allow a recording of the shock wave f r o n t during i t s passage through the p l e x i g l a s base. The sequence of detonation, flash i g n i t i o n and exposures for plain concrete was as follows (KC = Kerr-cell exposure). Flash

Detonation

Oscilloscope

KCI

KC2

KC3

KC4 pS

For polymer-impregnated concrete the following sequence was used. Detonation

Flash

Oscilloscope

t F-q_q

KCI

KC2

KC3

t ,FrL_L

KC4

t

its

This system of t r i g g e r i n g the oscilloscope through the programmable e l e c t r o n i c u n i t was found to be more r e l i a b l e than internal t r i g g e r mode of the oscilloscope. Another advantage of t h i s system was that knowing the exact time i n t e r v a l between the a r r i v a l of detonation signal and the wave at the gage, the average wave v e l o c i t y in the specimen could be estimated. A Hall-generator was used for c a l i b r a t i n g the magnetic f i e l d strength. A current of 118 A in the concentric electromagnetic c o i l s gave a f i e l d strength of 0.072 Wb/m2, and a uniform d i s t r i b u t i o n of f l u x over a s u f f i c i e n t l y large area. The signal from the gage was displayed on an oscilloscope screen. Results and Analysis The image of the shock f r o n t recorded during i t s passage through the p l e x i g l a s , consists of a shadow and a l i g h t s t r i p located together, since the pressure increases sharply at the shock f r o n t and then gradually decreases in the d i r e c t i o n of perturbing source. FIG. 3 shows that the shock f r o n t a f t e r i t s passage through the concrete was f a i r l y l i n e a r . Two t y p i c a l v e l o c i t y - t i m e traces recorded by the e.m. gages, during the passage of the l o n g i t u d i n a l wave are shown in FIG:s 4 (a) f o r plain

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FIG. 3 Shape of the shock wave f r o n t a f t e r passing through the concrete

_.~5~ ~ . ~ o ; ~ ° o ~ > a"~, ~-~ ]

/ Plexiglas

J

Shock-wave front

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Vol. 6, No. 5 J. Bhargava, X. Rehnstr6m

FIG. 4 Oscilloscope records of electromagnetic v e l o c i t y - g a g e Output Vert, s e n s i t i v i t y I0 mV/div. (a) Ordinary concrete, 5 u s / d i v . h o r i z o n t a l (b) Polymer-imp. concrete 2 ~ s / d i v . h o r i z . concrete and 4 (b) f o r polymer-impregnated concrete. In more homogenous P-I concrete the t r a n s m i t t e d wave had a t r a p e z o i d a l shape, whereas in p l a i n concrete the wave form was modified by a t t e n u a t i o n . The adhesive used f o r bonding of e.m. gage had the same c h a r a c t e r i s t i c s as the p l e x i g l a s . The gage can be considered to be embedded in the p l e x i glas j u s t below the c o n c r e t e - p l e x i g l a s i n t e r f a c e . In order to estimate the stresses in concrete i t is necessary to cons i d e r shock wave transmission across t h i s i n t e r f a c e . When a s t r e s s wave impinges on an i n t e r f a c e , i t is p a r t l y r e f l e c t e d and p a r t l y t r a n s m i t t e d at the surface o f d i s c o n t i n u i t y . I f the two m a t e r i a l s were e x a c t l y s i m i l a r , the wave would be w h o l l y t r a n s m i t t e d . The c o n d i t i o n s to be s a t i s f i e d at the i n t e r f a c e are: Io the forces a c t i n g on i t from concrete and p l e x i g l a s are equal at a l l times and 2. the p a r t i c l e v e l o c i t y in both the m a t e r i a l s at i n t e r f a c e i s equal. I t can be shown t h a t s t r e s s due to t r a n s m i t t e d wave is 2o

at

=

c

2 2 p ic +p c 1

• oi

(5)

2 2

% being the i n c i d e n t s t r e s s , and 1 and 2 r e f e r to concrete and p l e x i g l a s r~spectively. The m a t e r i a l s used had the f o l l o w i n g p r o p e r t i e s : Ordinary conc. p kg/m 3 c m/s

2350 3600

Polymer-imp. conc. 2400 4330

Plexiglas 1180 1850

S u b s t i t u t i n g these values in eq. (5) we get o i = 2.44 ot f o r p l a i n concrete, and o. = 2.88 o, f o r polymer-impregnated concrete. These values have been used ~o c a l c u l a t e the stresses t r a n s m i t t e d by the concrete, given in TAB. I . I t should be noted t h a t the p a r t i c l e v e l o c i t y , v, and o t computed from i t are f o r p l e x i g l a s .

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665 DYNAMIC STRESS, POLYMER IMPREGNATEDCONCRETE

r

TABLE I Transmitted Stresses

Aver.peak Particle amplitude velocity E E/B ~ mV m/s Ordinary concrete Polymer-imp. "

I0 II

13.88 15.27

°t (plexiglas) MPa 30 33

o. concrete °stat °dyn MP°dyn'a MPa °stati c 74 96

62±3 1.20 90+_4 1.06

Discussion For ordinary concrete the dynamic strength was about 20 % higher than the s t a t i c strength. This value is much smaller than the values reported by some previous investigators [8, 9]. Though the specific fracture energy i . e the energy required to fracture a u n i t volume of material is same for dynamic and s t a t i c loads, the dynamic strength w i l l obviously depend upon the loading mechanism. The use of high i n t e n s i t y pressure pulses gives a dynamic strength lower than that obtained by other methods. No attempt was made to optimize the experimental conditions. The precision of the method, taking into account the error in i n t e r p r e t i n g oscilloscope data etc, can be estimated as ca ± 5 %. Hence the value of Odyn/~static can be taken as 1.20 ± 0.05 for ordinary concrete.

For polymer-impregnated concrete, the difference between the static and the dynamic strength was only 5 %. These observations confirm the results of a previous investigation [3]. Conclusions Transient stresses in ordinary and polymer-impregnated concrete were evaluated using electromagnetic gages. Such gages are easy to fabricate and use; no c a l i b r a t i o n is required. I t was observed that the dynamic strength of ordinary concrete was 20 ± 5 % higher than the s t a t i c strength, whereas in polymer-impregnated concrete, the difference was only 5 % between the two strengths. Acknowledgements The authors would l i k e to thank the Swedish Board for Technical Development f o r the financial support, and the Swedish Detonic Research Foundation for the permission to use the f a c i l i t i e s in t h e i r laboratories. Help of Mr Algot Persson in the experiments is thankfully acknowledged.

References

[i]

R.A. Graham, F.W. Neilson and W.B. Benedick, J. Appl. Phys., 36, 1775 (1965).

[2]

D.D. Keough, "Procedure for Fabrication and Operation of Manganin Shock Pressure Gages", Stanford Research I n s t i t u t e , AFWL-TR-68-57, NTIS No. AD 839983 (1968).

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Vol. 6, No. 5 J. Bhargava, X. Rehnstr6m

[3]

J. Bhargava and A. Rehnstr~m, Cem. and Conc. Res., 5, 239 (1975).

[41

A.N. Dremin and G.A. Adadurov, Soviet Phys.-Solid-State, 6, 1379 (1964).

[5]

W. Goldsmith, M. Polivka and T. Yang, Experimental 65 (1966).

[6]

K.O. Hakalehto, "The Behaviour of Rock under Impulse Loads", Acta Polytech. Scan., p. 31, Ch.81 (1969).

[7] [8]

J. Bhargava and A. Rehnstr~m, to be submitted to Cem. Concr. Res.

[9]

J. Takeda and H. Tachikawa, Mech. Behaviour of Materials, Int. Conf. 4, 267 (1972).

Mechanics, 6,

D. Watstein, Symp. on Impact Testing, A.S.T.M. Spec. Tech. Publ. 176, 156 (1955).