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Steel-concrete interfaces: Experimental aspects
Mechanics of Geomaterial Interfaces A.P.S. Selvadurai and M.J. Boulon (Editors) 9 1995 Elsevier Science B.V. All fights reserved.
S t e e l - C o n c r e t e Interfaces:
255
Experimental Aspects
H.W. Reinhardt and G.L. Balhzs Stuttgart University, Institute 70550 Stuttgart, Germany
of
Civil
Engineering
Materials,
Pfaffenwaldring
4,
1. INTRODUCTION Cementitious materials such as c o n c r e t e - similarly to natural s t o n e s - are rather brittle and have an inherent weakness in resisting tension. Reinforcement is applied to provide equilibrium and control of deformation after cracking. The interaction, which is often refered to as bond, between concrete matrix and reinforcement is an essential property influencing the behaviour of the material. Without interaction it would not be able to perform as a composite material. In early studies, a perfect bond between steel and concrete without any relative displacement was assumed. Test results from the fifties [ 1] indicated, however, that the bond forces on the interfaces are basically governed by the relative displacement (slip) of the initially coincident steel and concrete cross-sections. Furthermore, several parameters, such as geometry of the interface (pattem, inclination, height and distance of ribs), mechanical characteristics of both materials and type of applied load (monotonic, repeated or sustained), etc. also have an influence. Within this chapter the behaviour of steel-concrete interfaces together with the influencing parameters are discussed based on experimental data providing a possibility for comparison with the behaviour of those geomaterial interfaces such as different rock layers subjected to shear or soil and pile interaction where the interfacial characteristics have principle influence on the overall behaviour. Those parts of the behaviour of steel-concrete interfaces will be discussed in more details which may correlate with those of geomaterial interfaces. Specific questions of steel-concrete interaction concerning technological aspects of steel or concrete production (e.g. influence of additives) or special circumstances (e.g. fire or cryogenic conditions) will not be discussed herein.
2. BASIC BEHAVIOUR OF STEEL-CONCRETE INTERFACES A tensile or a compressive force on an embedded steel bar induces interactive forces in the surrounding concrete (Fig. 1). 2.1 Basics The component of the interaction force parallel to the bar is to be in equilibrium with the
256 applied force. Its value related to a unit of the interactional surface is referred to as bond stress (Tb) (in some literature as local bond stress). Its highest value is the bond strength (Zbu), and its average value over a given length (which is often used in design) is the average bond stress. The differences in local bond stress and average bond stress obtained on a bond length (gb) not greater than five bar diameters (50) are generally neglected owing to experimental difficulies with very short lengths.
interaction I force
applied force
steel bar concrete
hoop tensile stresses
Fig.1 Steel-concrete interaction (based on Tepfers [2])
The radial component of the interactional force induces hoop tensile stresses in the surrounding concrete which may lead to cracking parallel to the bar in case of inadequate concrete cover. Since the bond stress is a function of slip, the bond behaviour is generally characterized by the bond stress-slip (rb-S) relationship. 2.2 Phases of steel-concrete interaction
Relatively low loads may be transmitted by adhesion based on a physico-chemical contact of the two materials (Fig.2). Deformed reinforcing bars transfer, however, higher loads by mechanical interlock producing micro-cracking [3-5] and micro-crushing [6] in the close vicinity of bar deformations which lead to a measurable relative displacement of the concrete and the steel cross-sections. An increase in the applied force or deformation produces progressive micro-cracking and micro-crushing. (Cracks are considered to be micro-cracks which do not reach the concrete surface.) Based on slip measurements by the Moir6 technique, Gambarova and Giuriani [7] observed a higher contribution of micro-crushing than that of micro-cracking to the actual slip. For higher relative displacement than that at the bond strength, the concrete between the bar lugs will be sheared off producing strain softening. When the relative displacement becomes equal to the clear distance of bar lugs, a practically constant bond resistance remains. This resistance is often called as residual bond strength and is provided by friction over the cylindrical concrete surface at the tip of the bar lugs. Bond failure is theoretically possible due to failure of the ribs, however, this is not the normal situation for usual steel reinforcing bars in concrete.
257 B o n d stress
~eformed bar'~ bond strength
mechanical ,
shearing
.,
interlock
off
micro-cracking micro-crushing f~iction
residual bond strength
friction
r
.
.
.
.
[plain
.
-
.
barsl .
.
~ .
.
.
~ . .
friction - ~ . . friction
pull-out failure
_
adhesion J 9
|
slip at bond strength
r
slip
Fig.2 Phases of steel-concrete interaction for plain and deformed bars
Plain reinforcing bars develop much lower bond stresses than deformed bars because the mechanical interlock, which is the most important contribution in case of the bond of deformed bars, is provided only by surface irregularities rather than by pronotmced surface deformations (ribs). A very small slip, approximately 0.01 mm, is enough to reach the bond strength of plain bars. Then remains a frictional contact providing a constant bond stress which is the bond strength of plain bars. This bond strength is, however, only slightly higher than the adhesional bond stress. The adhesional bond stresses of plain and deformed bars are practically the same because it is only a function of the surface if otherwise equal conditions are considered (Fig.2). The ratio of bond strengths of deformed and plain bars depends mainly on the rib pattern, the concrete strength and the confining effects, and may even reach a factor of 10. Owing to the relatively poor bond properties, plain reinforcing bars are rarely used in construction. 2.3 Failure modes of steel-concrete interaction Two types of bond failures are distinguished considering the two different failure mechanisms of the concrete matrix (Fig.2). Pull-outfailure, where the concrete between the bar lugs is sheared off without a complete loss of the bond resistance (Fig.2). Visible cracks on the concrete surface are not necessarily produced. Splitting failure, where the hoop tensile stresses reach the tensile resistance of the surrounding concrete producing a longitudinal crack. In absence of transverse reinforcement or transverse pressure, it may lead to a complete loss of bond resistance.
258
2.4 Measurment technique The main concern of experimental bond studies is to detemine the bond stress-slip relationship that may be used for comparison of bond characteristics or for analytical studies. Slip over a length e b is the integral of the steel strains (esx) reduced by the concrete strains
(~x): eb
s = ~0 (esx'Ccx)dx
(1)
There are two different ways to determine slip: either to measure it directly e.g. with an LVDT on the bar end or by magnetic sensors in the interior of the concrete [39], or to measure the strains by resistance strain gauges [8-9] and to integrate them according to Eq.(1). If unloaded end slip also occurs, it is to be added to the result. Owing to the considerable work in preparing the steel bars for strain measurements and the difficulties in evaluating the results, simple specimens, the so called pull-out specimens [ 10] and beam specimens [11] were developed for direct measurement of slip. The slip is measured at the unloaded end of the specimen in both cases. The proposed bond length is 50 for pull-out tests and 100 for beam tests, respectively. Even if the shape of a beam specimen is more realistic, pull-out specimens provide the simplest way of testing and are more often used. The reinforcing bar is centrically embedded in a concrete prism of 100 (but maximum 200 mm) sides over the 50 bond length having an other 50 debonded length at the loaded end to eliminate stress concentrations. The bond stress-slip relationship is then determined from the registered tensile force-slip relationship/F(s)/relating the force to the steel-concrete interface:
% ( 0 - F(s) ~oe b
where s is the slip measured at the unloaded end of the specimen. The disadvantages of this method are that it neglects the changes of bond stress over the 50 bond length that may be considerable in case of larger diameters and uses a boundary condition for concrete (supporting block at the applied load) which is not typical. There are several proposals to improve the specimen or the evaluation method of measurements [12]. The bond stress is a function of the relative dispalcement, however, there are several parameters that influence the actual value of bond stress. The influence of rib pattern, concrete strength, confining effects, loading rate, long term loading and repeated loading are discussed in the following Sections. 3. INFLUENCE OF RIB PATTERN ON STEEL-CONCRETE INTERACTION The important parameter influencing the steel-concrete interaction is the shape of the interactional surface, i.e., the rib or deformation pattern of reinforcing bar. It consists of the shape, the heights, the inclination and distance of ribs. Different countries use different rib patterns. The rib pattern is not only intended to improve the bond characteristics but to distinguish bars of different strengths and manufacturers.
259 3.1 Influence of related rib area
To provide a possible comparison of bond characteristics of different bars, Rehm [1] introduced the related rib area (t~sb) meaning the axially projected front surface of transverse ribs related to the nominal interactional surface between two ribs. The deformation pattern not only influences the bond strength but also the failure mode. High ribs do not necessarily mean a more adequate bond behaviour because higher interactional stress increases the probability of longitudinal cracking.
rb/feU
0401
_ o.o
7#/
---
l/
0.10 .d'N.
0
0.25
0.50
0.75
1.00
1.25
slip [mm] Fig.3 Influence of the related rib area on the bond stress-slip relationship Rehm, Martin and Noakowski [13]
Fig.3 indicates experimentally derived bond stress-slip relationships as a function of the related rib area increasing from 0 (i.e. plain bars) up to 0.4. The increase in bond stress is less than proportional with the increase in related rib area. Twice of related rib area leads to less than twice of bond stress at a given slip. There should be an optimum in deformation pattern that is enough to transmit and anchor forces but still does not necessarily lead to longitudinal cracking. The optimal related rib area seems to be in the range of 0.05 < Otsb< 0.08 [ 14] which is less than that of some deformed bars used earlier. The related rib area is a practical tool for comparing bars of different rib patterns but the following analysis of single parameters of the rib pattern contributes to the characterization of bond properties.
260
3.2 Influence
of rib geometry
The experiments of Soretz und H61zenbein [15] have shown the increasing probability of splitting failure with increasing rib height on three series of reinforcing bars having the same relative rib area but different rib heights (0.10, 0.050 and 0.0250) and spacings (1.20, 0.60 and 0.30), respectively. With bars of different inclinations (30 to 90 ~ to the longitudinal axis, Soretz and HSlzenbein observed a slight improvement of bond characteristics (Fig.4). Varying the rib cross-section from a rectangle to a 45 ~ trapezoidal had no influence, and changing to a very flat triangle had only minor influence on the bond characteristics [15].
Rib patterns
Code
of rib pattern [] n
!Vl v w I
II ..... ! ......
III
1
EE
r if '~~
~_
,
e
!
IV
........ i:':/- ........,,-S;~ / --,
" tt
z'~ 2
,o I
,
V ...~~
w~
't
I
I
, / I
l
I I(~176176176
slip
J I J ~(~bu) ~ / i/~ t ]-~
J~ r---~, i j I ,
I
o., m
',/'I i ~
i
~
0.01ram
VI
21
il
I
40 50 60 70 80 90(90E) r ' Rib inclination [~ Fig.4 Influence of rib inclination on bond stresses Soretz and H61zenbein [15]
Tepfers and Olsson [ 16] conducted pull-out tests on bars of 16 mm nominal diameter with 48 mm bond length of different rib heights and spacings providing different related rib areas. The radial component of the interactional force was determined by measuring the circumferential strain in a steel ring surrounding the concrete of the pull-out specimen. The force component which is parallel to the bar was obtained by supporting the specimen with a teflon covered circular support close to the bar. Tepfers and Olsson [ 16] observed that: - Increasing rib height improves the bond stress at a given slip. - There is an optimum rib spacing. If the spacing becomes too short, the bar starts to act as a plain bar with a diameter including the bar ribs. - The slip at maximum load decreases, when the related rib area increases.
261 The splitting tendency increases with increasing angle between the interactional force and the axis of the bar. This angle increases if the slip at maximum load increases otherwise it decreases if the related rib area increases. Kimura and Jirsa [17] compared experimentally various rib pattems of commercial and machined bars of 36 mm nominal diameter by pull-out tests on 150 mm bond length and using concretes with compressive strengths 40, 80 and 120 N/mm 2 and specimens which contained spiral reinforcement of 6 mm diameter and 40 mm pitch. They concluded that: - The average bond stress and the initial stiffness of the bond stress-slip curve increased as the rib spacing decreased for concrete strengths of 40 and 80 N/mm 2. - The average bond stress and the initial stiffness of the bond stress-slip curve increased as rib height increased. The increase was larger for higher strength concrete. - The bond stress at splitting was not strongly influenced by rib spacing or rib height, regardless of the concrete strength. - As the ratio of rib height to rib spacing increased, the average bond stress and the initial stiffness of bond stress-slip curve increased, regardless of concrete strength. However, for rib height to rib spacing ratios greater than 0.2, these values seemed to be constant. - The bond stress to splitting tended to decrease up to a rib height to rib spacing of 0.2. - Bars with rib face angles greater than or equal to 45 ~ exhibited almost the same behaviour. However, bars with a rib face angle of 30 ~ were initially less stiff.
4. I N F L U E N C E OF C O N C R E T E S T R E N G T H AND C O M P O S I T I O N ON S T E E L CONCRETE INTERACTION Not only the strength but also the composition and the consistence (i.e. cement content, water content, etc.) of concrete influences the bond characteristics.
4.1 Influence of concrete strength To develop bond stresses, contributions are derived from properties of concrete both in tension and in compression. Micro-cracking is controlled by tensile resistance, however, bearing stresses induce high compressive stresses in front of the ribs. Design equations generally relate the bond strength either directly or indirectly to the tensile strength of concrete. Considering the relationship of tensile and compressive strength of concrete as a known property, experimental studies were intended to determine the relationship between the bond stresses or the bond strength and the concrete compressive strength. The higher the concrete strength, the higher the bond stress, however, test results disagree in the actual ratios. Based on pull-out test results with concrete mixes of 16 to 50 N/mm 2 strength measured on cubes of 200 mm sides, Martin [18] concluded the following: - For the slip range of 0.01 to I. 0 ram, the bond stress of deformed bars is proportional to the concrete cube strength (Fig.5.b). - For very small slips, s < 0.01 ram, and for slips close to the bond strength, s > 1.0 ram,
262 the influence of concrete compressive strength is less important and proportional to the ~a power of the concrete cube strength (Fig.5.a). rb(s=O. 01 ) ['N/mm2] 2.5
1
1
1
rb(0.01)-~. 163 fc2P
a)
1.5
_ z ~ y w/c = 0.50 + 0.90 uu~ 9 grading curve B 7 days 28 days CI 0 9
0.5
C2 C3 0
10
20
A B
A 9
i
i
3O
4O
5O
fen ['N/mm~]
10
~(s~.Ol) t'N/mm~] consisl~ency
[~
c1.,~(01)-0.222 f~z
cl~'J
C2: %(0,1) = 0.197 fc_~ / C 2 : C3:xb(0,1)=0.145 f c ~ / /
/ ,,
C3/
b)
/////
(/y ~er legend see Fig. a)
f" 0
10
20
t
!
30
40
50
fed [N/mrn2] Fig.5 Influence of concrete strength on bond stresses; Martin [ 18] a) at 0.01 mm slip b) at 0.10 mm slip
Janovic [19] and Noakowski [20] also proposed a proportionality to the ~a power of the concrete strength. Based on pull-out test results with up to 0.25 mm slip with concrete mixes of 40, 80 and 120 N/mm 2 strength, Kimura and Jirsa [ 17] concluded that the bond stresses are proportional to the square root of the concrete strength.
263
4.2 I n f l u e n c e o f c o n c r e t e c o m p o s i t i o n
Applying various cement contents, grading curves of aggregates, water-cement ratios and consistencies, Martin [18] concluded from his test results the following" - The effect of water-cement ratio is eliminated if the bond stress is related to the concrete strength. - The grading curve of the aggregate and the consistency of fresh mix strongly influence the bond properties. The observed greatest difference was 1 to 5. - The highest bond stress belongs to the grading curve with the lowest amount of fine particles (A - Fig.6.a) and the lowest bond stress to the grading curve with considerably 100 80
a)
,~/ /I V" / / /
60
e~ o
=
40
~
20
fl,/. ~t,"1
0 0.25 0.5
1.0 2.0 4.0 8.0 16.0 31.5 sieve size [ram]
b) ~fc~
i IIII11
iw/e=0.75
0.8 -
0.5
I I
- consistencygrading c u r v e B IIII C I I 1 " 28 days ....
0.6
'
0.4
'-_/,,i,, " J~C2
/ ,/l!
rb(S = 0.2)/fc-~
~
,,"
""
0.4
/ N, . ~ . I r - ,
TM
_j
0.3
]
r
C3
9
i
f
0.2
J
0.2
/
0.1
/
I ,O 18 mm
def. bars 0 0.01
0 0.1
1
2
5
1
1.1
1.2
1.3
slip [mm]
1.4
1.5
consistency
Fig.6 Influence of concrete composition on the bond behaviour; Martin [18] a) grading of aggregates b) influence of grading curve on the bond stress at 0.2 mm slip c) influence of consistency (as degree of compaction acc. to Walz, DIN 1048)
264 higher amount of fine particles (C - Fig.6.c). The difference produced in bond stresses is more than 100 %. It means that coarser aggregates improve the bond capacity of embedded deformed bars (Fig.6.a and b). - The highest bond stress belongs to the stiff (C1) consistency and the lowest to the semifluid (C3) consistency. The produced difference in bond stresses is up to 100 % (Fig. 6. c). The reason for the influence of consistency is the composition of concrete since variation of consistency has been achieved by varying the cement content by about 30%.
5. INFLUENCE OF CONFINEMENT ON STEEL-CONCRETE INTERACTION Confinement concerns all kind of effects that control transverse deformations of concrete matrix surrounding the reinforcing bar induced by the interactional forces before or after splitting of the concrete cover. Confinement may be provided by transverse reinforcement, by transverse pressure or by improving the strength or thickness of concrete cover. By onset of longitudinal cracking, the interaction may completely vanish. The confinement provided by the reinforcement (Fig. 7.a) or by the transverse pressure (Fig. 7.b), however, controls the opening of the crack. 5.1 I n f l u e n c e o f t r a n s v e r s e r e i n f o r c e m e n t
Pull-out test results by Eligehausen, Popov and Bertero [23] (Fig. 7.a) indicate different bond stress-slip behaviours with and without transverse reinforcement. The specimen without transverse reinforcement (designated 1.4) failed by splitting of the concrete cover at rather small bond stress of 6 N/mm 2, then the bond resistance dropped rapidly. Specimens with transverse reinforcement failed by bar pull-out. The crack developed in the plane of the longitudinal axis of the bar. Therefore, transverse bars (called vertical bars) crossing the crack were effective in restraining the concrete, while the influence of bars parallel to the axis (called stirrups) was negligible. This can be seen comparing series 1.2 to 1.5 in Fig.7.a. The influence of the area of vertical bars was rather small in the applied range. The initial stiffness o f the bond stress-slip curves was almost identical for all test series, which indicate that there exists an upper limit for an effective restraining reinforcement beyond which the bond behaviour cannot be further improved, because the main role of this reinforcement is to prevent the opening of splitting cracks [23]. 5.2 I n f l u e n c e o f t r a n s v e r s e p r e s s u r e
Untrauer and Henry [21 ] studied experimentally the influence of transverse pressure on the bond behaviour on pull-out specimens. The normal pressure was applied to two parallel faces of the specimens up to 16.3 N/mm:. Slip was measured at the loaded end using a dial micrometer gauge system. Untrauer and Henry [21 ] concluded that:
- The bond strength increases with increased normal pressure. The increase is approximately proportional to the product of the square root of the normal pressure and the square root of the compressive strength of concrete. - The incerase in bond strength is higher than the increase of bond stress at lower slip values.
265 The bond strength is larger for a 28.6 mm bar than for a 19.0 mm bar when normal pressure is applied. They interpreted the larger increase in bond stresses at larger slips with the increasing contribution of the friction and bearing on the lugs which are influenced by the transverse pressure.
16 ,,
E
1
,,.
,
,~
a)
~
I//OJ
'N
)
@ l
It
r ~ , , , , ~ , ~ , , r s , .... o, r_
I
~,,
I 2~,
I
il J.2 I
|
~
~5"-~1
A,31
I~z,
! ,o
12 7
I tZ't
I
i.O
63~
I,z~
!
o z5
~
.~
0 L_
1
l
0
2
4
~E
~
1
I
6
8
Longitudinal
,
1
_--
10 12 Slip [ram]
p 0 : 0 N/mm ~ pl" 6 9 N/ram~ p2:13 8 N/rnm:
15
b)
.
)IS.,..,} Otm~} IO[~}! zA'*/As!
o~ o~ I-i
10
5
1
\
0 ,~
o
[
2.s
iii
/t
A
so
7.s
~oo
Slip [mm] Fig.7 Bond stress-slip behaviour with or without confinement leading to complete splitting failure or pull-out failure after splitting of the cover a) Confinement by transverse reinforcement; Eligehausen, Popov and Bertero [23] b) Confinement by transverse pressure; Malvar [29]
266 D/Srr [22] carried out tensile tests on cylindrical specimens with a centrally embedded steel bar of 16 mm diameter in order to obtain the bond stress-slip relationship for four different values of transverse pressure (0, 5, 10 and 15 N/minE). The specimen was 600 mm long with an embedment length of 500 mm. The specimens were notched at the middle section to localize transverse cracking. The concrete cube strength varied between 29 and 42.5 N / r a m 2 with an average of 35.9 N/ram 2. Test results by D6rr (Fig. 8) gave a 100 % increase in bond stress at 0.1 mm slip when the transverse pressure increases from 0 to 15 N/ram 2. Slip was derived from the sum of measured strain differences of steel and concrete and the bond stress was derived from the change of forces from section to section.
r
--'15 E E
~10
B
g.a
o
m:l
t/)
D
Q
5
D
rNmml
[31 p = 10 [N/mrn ~] p = 15 [N/mm 2] 0.1
t).3
0.2 Slip [ram]
Fig.8 Influence of transverse pressure on the bond stress-slip relationship, fc[]--36 N / m m 2 D6rr [22]
From a comparison of the experimental results [21-26] relating to the influence of transverse pressure on bond strength, Eligehausen, Popov and Bertero [23] have shown a 2.5 to 8.5 N/mm 2 increase for a pressure of 10 N/mm. This large scatter is partly a consequence of the different failure modes. Twelve specimens consisting of 19 mm reinforcing bar embedded in a 76 mm diameter concrete cylinder were tested by Malvar [28, 29] under controlled confinement. The bond length was a 5 lug spacing of approximately 70 mm. Concrete cylinder strength varied between 38.4 and 44.2 N/mm 2. The support of the specimen was provided by shear stresses on the surface of the specimen. Concerning the bond stress-slip behaviour he concluded that: Preceding the onset of longitudinal cracking, the influence of confinement stress could not be properly established. - After longitudinal cracking, bond stress increased significantly with applied confining -
267
20
El5 E o
10
0 m
5
o'
TEST TEST TEST TEST TEST
1:3.4 N/mm 2:10.3 " 3:17.2 " 4:24.1 " 5:31.0 "
~
16
Slip [mm] Fig.9 Bond stress-slip diagrams with various levels of transverse pressure; Malvar [29]
stress. The maximum bond stress was increased by almost 200 % by increasing the confinement stress from 3.4 to 31 N/mm 2 at the bar level (Fig.9 and Fig. 7.b). The effect of confinement on bond behaviour appeared less pronounced for the higher confining stresses. - After longitudinal cracking, radial deformation measured on the concrete surface showed an increase up to a limit value dependent on the confinement level, then a decrease due to interface deterioration. - Bars with normal ribs (at 90 ~ to the longitudinal axis) exhibited better bond characteristics than bars with inclined ribs. Bars with normal ribs also produced more severe radial cracking. - Increasing radial pressure generated more severe radial cracking. Pull-out tests on modified specimens were carried out by Nagatomo and Kaku [27] in order to investigate the influence of transverse compressive and tensile stresses on the bond behaviour of deformed bars. The major parameters were the transverse stress and the concrete cover. The following transverse compressive stress as: 0, 3.92, 7.85, 9.81 and 11.77 N/mm 2 and transverse tensile stress as: 0, 0.49, 0.98 and 1.47 N/mm 2, were applied. Different covers were intended to influence the type of bond failure (side splitting, V-notch splitting, comer splitting or pull-out). The bond length was 70=154 mm using a bar of 22 mm diamter. The concrete compressive strength varied between 15.5 and 18.8 N/mm 2. Nagatomo and Kaku [27] concluded the following:
- The bond strength increases linearly with increasing transverse compressive stress up to approximately 30 % of the concrete compressive strength, and tends to level off for the transverse compressive stress beyond that value (Fig. 10). The relative increase rate with transverse compressive stress decreases linearly with increasing concrete cover up to 2.5 times the test
268
2.0f[~~
2.0[
~b.(p~) Xb.(P=0)
l:bu(pr ~:bo(P=O)
"tb.(Pr Tb,,(p=O)
2.0-
o
~.~%o
~.o
o'.s
9
I
1 .o
ol
o'.s
p/f~
I
1 .o
o
I
0.5
p/fr
I
1.0
p/fr
Fig.10 Influence of transverse compressive strength on bond strength Nagatomo and Kaku [27] a) Cb/O:l.08 %/O=1.98 C) %/0=3.10
b)
bar diameter and becomes zero for the concrete cover beyond that value (Fig. 10). - The effect of transverse compressive stress on bond strength is less for the failure modes by a side splitting crack parallel to the direction of transverse compressive and by shearing of concrete passing through the top of bar ribs. - The bond strength decreases rapidly and parabolically with increasing transverse tensile stress and becomes zero at the transverse tensile stress equal to the tensile strength of concrete (Fig. 11). Based on their own experimental results and those of others' experimental results, Nagatomo and Kaku [27] developed a linear and a parabolic relationship to take into account transverse stresses. The normalized bond strength in case of transverse compression (p):
Xb"(P/fCvO) = %.(p/fr
k'p + 1
(2)
and the normalized bond strength in case of transverse tension (Pt, Fig. 1 I):
Xbu(Pt/ft~0) -- Xbu(Pe/ft=0)'(9 0"755"Pt - 1)'( Pt _ 1) fc where l:bu(P/fcr
ft
) and factor k are functions of the concrete cover [27].
(3)
269
%.(p=O)~
O : %/0=1.08 A : cb/0=-1.98 !"1 : %/0=3.10
1.0~.~,, F"I ~,~ ~ , , ~
0.5- ~ 0
/Eq.(3) 0.5
1.0 P/fc
Fig.11 Influence of transverse tensile stress on bond strength; Nagatomo and Kaku [27]
6. INFLUENCE OF LOADING RATE ON STEEL-CONCRETE INTERACTION Vos and Reinhardt [30-31 ] studied experimentally the influence of loading rate on pull-out specimens of 30 bond length using concrete mixes with average cube strength of 22, 45 and 55 N/ram 2. 10 mm diameter plain and deformed bars of 0.076 related rib area were tested in addition to 3/8" diameter prestressing strands of 1730 N/mm 2 0.1% proof stress. Test results indicated that the bond resistance of plain bars and strands is hardly influenced by the loading rate (even increasing the loading rate by 100 000 times). It appears that the adhesion, the friction and the lack of fit (by prestressing strands) are insensitive to a variation in loading rate [30]. In case of deformed bars, the bond resistance increases with increasing loading rate, however, the concrete grade also has an influence. The higher the concrete strength, the less insensitive is the bond resistance to variations in loading rate (Fig.12). The influence of the loading rate and concrete strength is most pronounced for a small slip of the order of 0.01 mm. Vos and Reinhardt [30] developed the following relationship for the rate dependent bond stresses valid up to a slip (s) of 0.2 mm: Tb Tb0
_( X.b )q Tb0
0
(4)
where Tb and Tb0 are average bond stresses to a given slip and '~b and Xb0 are the respective loading rates. %o and Zb0 can be regarded as "static" reference values [30]. The power q of Eq.(4) was determined using the method of least squares for all results with deformed bars as a function of the concrete cube strength (fcc in N/mm 2) and the slip (s in ram):
270 rb/rbO 2.6 2.4 2.2 2.0
]fcz= 20 N / m m 2 [ / ~ /
1.8 1.6
/ "
./"
40.~
1.4 1.2
10
102
103
104
10'
106
,V;bO
2.0 1.8
[fc.=:O./mm
1.6 1.4 1.2 1
1
10
102
10'
104
10'
10~
fiCr
Fig.12 Influence of the loading rate on the bond resistance of deformed bars Vos and Reinhardt [30] a) 0.01 mm slip b) 0.20 mm slip 0.7(1-2.5s) fctJ 8 Eq.(4) is plotted in Fig.12 for three concrete strengths and two slip values 0.01 and 0.02 mm in double logarithmic scale. Fig.8 indicates that for a small slip as 0.01 mm, the influence of loading rate and concrete strength is more pronounced than for a higher slip as 0.2 mm. The bond resistance associated with impact loading can be twice the bond resistance of static loading. For a higher strength concrete (here 60 N/mm 2) this ratio is only 1.5. For higher displacement, the influence of the loading rate decreases to about 1.4 and 1.2, respectively.
271 7. INFLUENCE OF REPEATED LOAD ON STEEL-CONCRETE INTERACTION Repeated load produces an increase of slip as a result of progressive micro-cracking and micro-crushing [23,32-38] and can lead to failure at a cyclic stress level lower than the ultimate stress under monotonic loading. Repeated loading may be subdivided into low-cycle and high-cycle loading according to the number of load cycles up to failure. Low-cycle loading usually contains only a few cycles but at a high stress level. Low-cycle loading generally arise under seismic conditions. Highcycle loading contains (thousands or millions), but on a relatively low stress level. Bridge elements, offshore structures and supporting members of vibrating machinery are typically subjected to high-cycle loads. Another subdivision of cyclic loading, which is followed also herein, is to consider the type of applied stress as either having or not having stress alternations. Cyclic load will imply load cycles without change of sign of the applied load, and reversed cyclic load implies load reversals including both tension and compression in one cycle. 7.1 Influence of cyclic loads Test results with constant and variable amplitudes are discussed separately. 7.1.1 Constant amplitude cyclic loads According to pull-out test resuls by Rehm and Eligehausen [34] with constant amplitude cyclic loading, the slip versus number of load cycles diagram can be approximated by straight lines in double logarithmic scale. For loads below the fatigue bond strength these results give straight lines which are parallel to each other (Fig. 13). The gradient of lines were higher for specimens which failed by fatigue. 1.0 E
& 05 g:
t~ d~
O
o.o
._~ r,~
0.01 |.0
101
10 2
10 3
1r
10 5
]0 6
number of load cycles, n Fig. 13 Increase of slip at the free bar end as a function of the number of load cycles fc~=23,5 N/mm 2, O=14 mm, eb=30 Rehm and Eligehausen [34]
272 Rehm and Eligehausen [34] proposed a relationship to predict the slip after n load cycles (s,) as a function of the initial slip before applying the cyclic load (So) and the number of load cycles: sn -- s0(1+k.) where k. = (1 +n) 0"107-1 The slip coefficient, 1%, was not greatly infuenced by parameter variations of loads below the fatigue bond strength. Considering the total bond faitigue process, Baldzs [36] distinguished between three different phases in case of constant amplitude cyclic loads producing slip over the entire bond length (Fig. 14). Phase 1 Phase 2 Phase 3
: slip increase with decreasing rate : slip increase with a constant rate : slip increase with an increasing rate
Nevertheless, the slip versus number of load cycles diagram in linear scale contains, in turn, concave downwards, linear and concave upwards portions. The length (i.e. the corresponding number of load cycles) of all three portions are functions of the bond parameters and the cyclic load level. The slip rate during the secondary linear phase was also found to be dependent on the load level. In case of a relatively high load level, the second linear portion of the slip versus number of load cycles diagram can transform into a point of inflexion. To predict fatigue failure, the initial point of the failure branch (Phase 3) is of particular inter-est. It was found [36] to be equal to the slip, S(Zbu) at the monotonic bond strength (Fig. 14.b and c). Once the slip exceeds S('~bu), a pull-out failure occurs after additional load cycles.
7.1.2 Cyclic loads with variable amplitude Pull-out test results [37] with variable amplitude cyclic loading indicated that the development of slip is strongly dependent on the load history. Based on the load spectrum analyses of bridges and cranes, parabolically and logarithmically varying load histories were applied in addition to linear ones both with increasing and decreasing tendencies. These load histories were set up in stepwise fashion using shorter sub-blocks of constant amplitude loadings. Six typical test results obtained by using these load histories with a maximum cyclic load level of 40 % of the average bond strength applied in two blocks till 2.106 load cycles are presented in Fig. 15. The highest slip values of Fig. 15 are in the serviceability range far below the slip at bond strength. With increasing sequence of amplitudes, the first complete block of loading (here up to 1 million of load cycles) produces a pronounced slip increase with decreasing slip rate. Cycling in the next block at lower load levels, however, does not contribute to the slip increase (Fig.15.a, c and e).
273
a) -
I
I
I
I
!
!
y
T
r
i
7N
2 Slip I . i t i x~. t I. l pull-out ] [N/ram ] --.--...~decreasmg4.. i constant .L..4 lncreaslng..~failure ir - " ">0 1 60 [ 1 rate ' n = 10r~- - 20 i. 30 40,,', 8c,,cles
I(-' r~r4 - tittiHJ,litttilttli#i"rhititttttttti:..~ ..... ~" i-t-
-"7
'oj. i ~ i f
,t
' ,llttttttttltl;1t!ttt,Itlllttl'ltttt I.-i~ : '~ltlttttNitttllt Itt/ltltN..... r,___~
.
L1.0cycles.'
~
-u-~ _
~
I
I
t 0__
i
+
0
!l]lJtl:l[ttt '-:i" ]ttiItt}]/tt]]tlt]tttttttt i ]l~t i ' i , I Slip i
p I 1o.2,5 I o.5o i
F I<%
! t
i I l:OOl
}0.75
Load history
t 1.25
I 1.50
[mm]
.
S"
1,, r,"l!lIIl!!!111111l lilii!lili!lll~llll'llil!Sll'Jlilllilllillllli !W,ti i t~~l /. ~%,~NNttil~lll[llllllllllJtliilli]lJ. , llJ~lli,,llllt,lJlillll,Ii~illtll,/ "15~0 0 N10u~b2e0o?~oad40yclSe~ 6~0 n;
Slip [mm]# . . 2 5-[
,
.
.
b ) /2/.!0 ~!.I ~ ,- l V! l /
I
a st
I
, ~/ 1 "U
'
I
!
: !
M~e~176176
Pull-out t fa!lure ]]
3.0 ~ /
-t / ~
20~
I/
~
)
|
"/
! ' !~;-~,i.~,,,._J
/
!
I I '
+tl+lll
10 20
:
4.01
i
;~~----~,f C " i!
i jt"Pt%uJl---] I! l 10
30 40 50 60 70 n Number of load cycles
c~
5
;
10
Bond stress [N/mm 2]
Fig.14 Bond fatigue process under cyclic loads,fern=20 N/mm 2, 0=8 mm, eb=120; Balhzs [36] a) bond stress-slip diagram b) slip vs. number of load cycles diagram c) monotonic bond stress vs. slip diagram
274
With decreasing sequence of amplitudes, significant slip increase is produced only by the highest cyclic load levels both in the first and in the later blocks (Fig. 15.b, d and J). Low cyclic load levels after higher load levels have hardly any influence on the slip increase. Slip
a)
Tb
[mm] t'N/mm~]
Slip
~~ 0 10 ~ 0
Slip ~ % [ram] [N/ram 2]
c) .., Shp
"t 0
~
Load
0.5 1.0 1.5 2.0 Number of load cycles [million]
Slip
Tb
e)
[mm]~tWmm~1 ,
0.5 1.0 1.5 2.0 Number of load cycles [million]
d) Slip
0 - 1 ~ ' - - ' ~ o a _ _ d 06
Slip
0.5 1'.0 1".5 2'.0 = Number of load cycles [million] xb
f)
0.2tlO '
!
[mm] I [N/mm:]
0.2+ 10
0
' r--W"-'-~- L~_ooad
Slip xb [mm]! [N/mm2]
[mm]l t'N/mm~] 0.1~5___ ~
0
---
c
0.2~ 0.1 ~ ~ ~
0.5 1.0 1.5 2.0 Number of load cycles [million]
0 2 10
Slip
-
~iLoad_~___ .__ _ ~ `
Slip. Tb
b)
'
i
~
015 1.0 115 2.0 Number of load cycles [million]
0
Slip Load!
015
~.0
~15
2.0
Number of load cycles [million]
Fig.15 Slip increase as a functon of the load history, fr N/ram 2, O=16 mm, eb=50 a)-b) parabolically c)-d) linearly e)-f) logarithmically variable amplitude Balfizs and Koch [37] 7.2 Reversed cyclic loads
The most common case of reversed cyclic loading is seismic loading. Cycles with reversed loading produce a more severe degradation of bond strength and bond stiffness than the same number of load cycles with cyclic loading without change of sign. Degradation primiraly depends on the number of load cycles and the peak slip in either direction between the bar is cyclically loaded [34, 36]. Under otherwise constant conditions the largest deterioration will occur for full reversals of slip. Whenever the load cycles are limited to produce slip only in one direction, there is no significant degradation of the bond strength [38].
275 Slip controlled load reversals produce deterioration both of the peak bond stress at the applied maximum slips and that of the frictional bond stress which is the necessary bond stress from the other direction to withdraw the previous slip (Fig. 16)[36]. Five cycles between +0.2 mm slip caused the peak bond stress to decrease by 35 percent (Fig.16).
Load history Decrease of peak bond stress
Ivvvvr I 2 3 ~ 5-
----q ---i
Xb(n) 100l -
i
--~-~.,....~
i
9
i
9
1
] ' ] 2"23+ "
Slip i [mm]_~
"
9
3
.
,
1
4" 5" 4
n
5
Decrease of frictional bond stress
15 ~ ~bf(n))
-
!
"l:bf(n-89 10 ~
[%] 5 ~ - -
_+__,_ 1+ 1. 2§
4 +
4
5+
5
n
Fig.16 Bond behaviour under slip controlled load reversals, fen=20 N/ram 2, O=16 mm, eb=20 (The ordinate axis of loaded side curves is skew to correct the elongation of reinforcing bar between the loaded end section and the point of attachment of the LVDT) Bal~s [36]
Force controlled load reversals produce a remarkable slip increase which indicates an increasing damage in the concrete matrix around the steel bar (Fig.17) [36]. The higher the
276 load, the higher the slip increment. The slip rate during force controlled load reversals was approximately four times higher in comparison to that of a repeated loading.
Load history FI "l:b
,,!j, !pJll!JJ!llJ!l!lI .,
:
.,..,
. . . . . . .
9
p
_ _ Slip at peak stress
0.4+~
. ~
[N/xb2]mm 13.3 11.2
.... 9.4 9 | 2 345-n
Fig.17 Bond behaviour under force controlled load reversals, fen=30 N/mm 2, O=16 mm, eb=20; Balfizs [36]
8. S U M M A R Y
The behaviour of steel-concrete interfaces is discussed in reference to experimental data. Tensile or compressive forces on an embedded steel bar induce interactional forces in the surrounding concrete matrix. Only relatively low loads can be transmitted by physicochemical adhesion, however, higher loads are transmitted by mechanical interlock and friction leading to relative displacement of the sections. Bond failure may be reached by pull out of the bar or by splitting of the concrete cover. Shape and dimension of ribs, strength and composition of concrete, confinement provided by transverse reinforcement or by transverse pressure, type and rate of loading all have a strong influence on the bond behaviour.
277 NOTATIONS Cb fc[] fc ft n p p, s So Sn S(Xbu) eb
C~sb ~cx ~s• zb Zbu "l~bx %-s 0
bottom concrete cover average concrete strength measured on cubes of 200 mm sides average concrete cylinder strength tensile strength of concrete number of load cycles transverse pressure transverse tension slip (relative displacement) initial slip before cyclic or sustained loading slip after n load cycles slip at bond strength bond length related rib area concrete strain distribution steel strain distribution bond stress bond strength bond stress distribution bond stress-slip relationship nominal bar diameter
mm N/mm 2 N/mm 2 N/rnrn 2 N/mrn 2
N/mm: mm mm mm mm mm % % N/mm 2 N/mm 2 N/mm 2
N/mm2-mm mm
REFERENCES 1. G. Rehm, 13ber die Grundlagen des Verbundes zwischen Stahl und Beton, Deutscher Ausschuss f'tir Stahlbeton, Heft 138 (1961) 2. R. Tepfers, Cracking of concrete cover along anchored deformed reinforcing bars, Magazine of Concrete Research, Vol.31, N-~ (1979) 3. 3. B.B. Broms, Technique for investigation of internal cracks in reinforced concrete members, ACI Joumal, Vol.62, N~ (1965) 35. 4. Y. Goto, Cracks formed in concrete around deformed tension bars, ACI Journal, Vol.68. (1971) N-~ 244. 5. Y. Goto and K. Otsuka, Studies on internal cracks formed in concrete around deformed tension bars, Transaction of of the Japan Concrete Institute 1980, 159. 6. E. Giuriani, Experimental investigation on the bond-slip law of deformed bars in concrete", IABSE Colloquium Delft 1981, IABSE Proceedings, Zfirich 1981, 121. 7. P. Gambarova and E. Giuriani, Fracture mechanics of bond in reinforced concrete, Discussion, Journal of Structural Engineering ASCE, Vol. 111. N~ (1985) 1161. 8. R.H. Scott and R.A. Gill, Short-term distributions of strain and bond stress along tension reinforcement, The Structural Engineer, Vol.65B/N~ (1987) 39. 9. S.M. Mirza and J. Houde, Study of bond stress-slip relationships in reinforced concrete", ACI Journal Vol.76. (1979) N~ 19.
278 10. RILEM/CEB/FIP, Recommendations on reinforcement steel for reinforced concrete. Revised edition of: RC6 Bond test for reinforcement steel: (2) Pull-out test, CEB News No-73, Lausanne May 1983 11. RILEM/CEB/FIP, Recommendations on reinforcement steel for reinforced concrete. Revised edition of: RC5 Bond test for reinforcement steel: (1) Beam test. CEB News No-61, Paris April 1982 12. A. Windisch, A modified pull-out test and new evaluation methods for a more real local bond-slip relationship, RILEM Materials and Structures, Vol.18, No-105(1985) 181. 13. G. Rehm, H. Martin and P. Noakowski, Einfluss der Profilierung und des Betons auf die Verbundqualit~it von Stahl in Beton- Ausziehversuche an gefr~ten St~.hlen, Report Nr.2203/1970, Lehrstuhl und Institut far Massivbau, Technische Universit~it Mfinchen 14. CEB, Bond Action and Bond Behaviour of Reinforcement, CEB Bulletin d'Information No-151, Paris, Dec. 1981 15. S. Soretz and H. H61zenbein, Influence of rib dimensions of reinforcing bars on bond and bendability, ACI Journal, Vol.76, No-I, (1979) 111. 16. R. Tepfers and P.-A. Olsson, Ring test for evaluation of bond properties of reinforcing bars, Proceedings, Int. Conf on Bond in Concrete, Riga Oct. 1992, Vol. 1. 1-89. 17. H. Kimura and J.O. Jirsa, Effects of bar deformation and concrete strength on bond of reinforcing steel to concrete, Proceedings, Int. Conf. on Bond in Concrete, Riga Oct. 1992. Vol.1. 1-100. 18. H. Martin, Bond performace of ribbed bars (pull-out-ests): Influence of concrete composition and cosistency, Bond in Concrete, Proceedings, (Ed. P. Bartos) Applied Science Publishers London, 1982, 289. 19. K. Janovic, Bericht fiber den neuen konsolenfOrmigen Ausziehk6rper als Vorschlag far ein allgemeingfiltiges Verbundprfifverfahren, Report, Massivbau TU Mfinchen, 1979 20. P. Noakowski, Verbundorientierte, kontinuierliche Theorie zur Ermittlung der Rissbreite, Beton- und Stahlbetonbau 7(1985) 185. + 8(1985) 221. 21. R.E. Untauer and R.L Henry, Influence of normal pressure on bond strength, ACI Journal, Proceedings, Vol.62, N-~ (1965) 577. 22. K. D6rr, Bond behaviour of ribbed reinforcement under transversal pressure. Nonlinear behaviour of reinforced concrete spatial structures, Preliminary Reports, IASS Symposium 1978, Vol. 1, Werner-Verlag, Dtisseldorf, 1978 23. R. Eligehausen, E.P. Popov and V.V. Bertero, Local bond stress-slip relationships of deformed bars under generalized excitations, Report N~ UCB/EERC 82-23, Earthquake Engineering Research Center, University of California, Berkeley, California, Oct. 1983 24. T.P. Tassios, Properties of bond between concrete and steel under load cycles idealising seismic actions", CEB Bulletin d'Information No-131, Vol.1, 1979 25. S. Viwathanatepa, E.P. Popov and V.V. Bertero, Effects of generalized loadings on bond of reinforcing bars embedded in confined concrete blocks, Research Report, Earthquake Engineering Research Center, No.UCB/EERC-79/22, University of California, Berkeley, August 1979 26. A.D. Cowell, V.V. Bertero and E.P. Popov, An investigation on local bond slip under variation of specimen parameters, Research Report, Earthquake Engineering Research Center, No.UCB/EERC 82/23, University of California, Berkeley, 1982
279 27. K Nagatomo and T. Kaku, Bond behaviour of deformed bars under lateral compressive and tensile stress, Proceedings of the Bond in Concrete Conference Riga 1992, 1-69. 28. L.J. Malvar, Bond of reinforcement under controlled confinement, ACI Joumal, Vol.89, N~ 1992, 593. 29. L.J. Malvar, Confinement stress dependent behavior, Part I: Experimental Investigation, Proceedings of the Bond in Concrete Conference Riga 1992, 1-79. 30. E. Vos and H.W. Reinhardt, Bond stress-slip behaviour of deformed bars, plain bars and strands under impact loading, Bond in Concrete (Ed. P.Bartos), Proceedings, Applied Science Publishers London, 1982, 173. 31. E. Vos and H.W. Reinhardt, Influence of loading rate on bond behaviour of reinforcing steel and prestressing strands, Materiaux et Constructions, 15 (1982), N-~ 3 32. B. Bresler and V. Bertero, Behaviour of reinforced concrete under repeated load, ASCE Journal of Structural Division, Vol.94. ST6 (1968), 1567. 33. A.D. Edwards and P.J. Yannopoulos, Local bond stress-slip relationship under repeated loading, Magazine of Concrete Research, Vol.30, N~103 (1978) 62. 34. G. Rehm and R. Eligehausen, Bond of ribbed bars under high-cycle repeated loads, ACI Journal, Vol.76, N~ (1979) 297. 35. P. Plaines, T. Tassios and E. Vintz61eo,,, Bond relaxation and bond-slip creep under monotonic and cyclic actions, Proceedb:gs, Bond in Concrete (Ed. P. Bartos), Applied Science Publishers London, 1982, 193. 36. G.L. Balfizs, Fatigue of bond, ACI Materials Journal Vol.88, N% (1991) 620. 37. G.L. Balfizs and R. Koch, Influence of load history on bond behaviour, Proceedings of the Bond in Concrete Conference Riga 1992, 7-1. 38. M.N. Hawkins, I.J. Lin and F.L. Jeang, Local bond strength of conrete for cyclic reversed actions, Proceedings, Bond in Conrete, Applied Science Publishers London, 1982, 151. 39. W. Nies, Ein neues Verfahren zur Messung der 6rtlichen Relativverschiebungen zwischen Stahl und Beton. Diss. Darmstadt 1979
S t e e l - C o n c r e t e Interfaces:
255
Experimental Aspects
H.W. Reinhardt and G.L. Balhzs Stuttgart University, Institute 70550 Stuttgart, Germany
of
Civil
Engineering
Materials,
Pfaffenwaldring
4,
1. INTRODUCTION Cementitious materials such as c o n c r e t e - similarly to natural s t o n e s - are rather brittle and have an inherent weakness in resisting tension. Reinforcement is applied to provide equilibrium and control of deformation after cracking. The interaction, which is often refered to as bond, between concrete matrix and reinforcement is an essential property influencing the behaviour of the material. Without interaction it would not be able to perform as a composite material. In early studies, a perfect bond between steel and concrete without any relative displacement was assumed. Test results from the fifties [ 1] indicated, however, that the bond forces on the interfaces are basically governed by the relative displacement (slip) of the initially coincident steel and concrete cross-sections. Furthermore, several parameters, such as geometry of the interface (pattem, inclination, height and distance of ribs), mechanical characteristics of both materials and type of applied load (monotonic, repeated or sustained), etc. also have an influence. Within this chapter the behaviour of steel-concrete interfaces together with the influencing parameters are discussed based on experimental data providing a possibility for comparison with the behaviour of those geomaterial interfaces such as different rock layers subjected to shear or soil and pile interaction where the interfacial characteristics have principle influence on the overall behaviour. Those parts of the behaviour of steel-concrete interfaces will be discussed in more details which may correlate with those of geomaterial interfaces. Specific questions of steel-concrete interaction concerning technological aspects of steel or concrete production (e.g. influence of additives) or special circumstances (e.g. fire or cryogenic conditions) will not be discussed herein.
2. BASIC BEHAVIOUR OF STEEL-CONCRETE INTERFACES A tensile or a compressive force on an embedded steel bar induces interactive forces in the surrounding concrete (Fig. 1). 2.1 Basics The component of the interaction force parallel to the bar is to be in equilibrium with the
256 applied force. Its value related to a unit of the interactional surface is referred to as bond stress (Tb) (in some literature as local bond stress). Its highest value is the bond strength (Zbu), and its average value over a given length (which is often used in design) is the average bond stress. The differences in local bond stress and average bond stress obtained on a bond length (gb) not greater than five bar diameters (50) are generally neglected owing to experimental difficulies with very short lengths.
interaction I force
applied force
steel bar concrete
hoop tensile stresses
Fig.1 Steel-concrete interaction (based on Tepfers [2])
The radial component of the interactional force induces hoop tensile stresses in the surrounding concrete which may lead to cracking parallel to the bar in case of inadequate concrete cover. Since the bond stress is a function of slip, the bond behaviour is generally characterized by the bond stress-slip (rb-S) relationship. 2.2 Phases of steel-concrete interaction
Relatively low loads may be transmitted by adhesion based on a physico-chemical contact of the two materials (Fig.2). Deformed reinforcing bars transfer, however, higher loads by mechanical interlock producing micro-cracking [3-5] and micro-crushing [6] in the close vicinity of bar deformations which lead to a measurable relative displacement of the concrete and the steel cross-sections. An increase in the applied force or deformation produces progressive micro-cracking and micro-crushing. (Cracks are considered to be micro-cracks which do not reach the concrete surface.) Based on slip measurements by the Moir6 technique, Gambarova and Giuriani [7] observed a higher contribution of micro-crushing than that of micro-cracking to the actual slip. For higher relative displacement than that at the bond strength, the concrete between the bar lugs will be sheared off producing strain softening. When the relative displacement becomes equal to the clear distance of bar lugs, a practically constant bond resistance remains. This resistance is often called as residual bond strength and is provided by friction over the cylindrical concrete surface at the tip of the bar lugs. Bond failure is theoretically possible due to failure of the ribs, however, this is not the normal situation for usual steel reinforcing bars in concrete.
257 B o n d stress
~eformed bar'~ bond strength
mechanical ,
shearing
.,
interlock
off
micro-cracking micro-crushing f~iction
residual bond strength
friction
r
.
.
.
.
[plain
.
-
.
barsl .
.
~ .
.
.
~ . .
friction - ~ . . friction
pull-out failure
_
adhesion J 9
|
slip at bond strength
r
slip
Fig.2 Phases of steel-concrete interaction for plain and deformed bars
Plain reinforcing bars develop much lower bond stresses than deformed bars because the mechanical interlock, which is the most important contribution in case of the bond of deformed bars, is provided only by surface irregularities rather than by pronotmced surface deformations (ribs). A very small slip, approximately 0.01 mm, is enough to reach the bond strength of plain bars. Then remains a frictional contact providing a constant bond stress which is the bond strength of plain bars. This bond strength is, however, only slightly higher than the adhesional bond stress. The adhesional bond stresses of plain and deformed bars are practically the same because it is only a function of the surface if otherwise equal conditions are considered (Fig.2). The ratio of bond strengths of deformed and plain bars depends mainly on the rib pattern, the concrete strength and the confining effects, and may even reach a factor of 10. Owing to the relatively poor bond properties, plain reinforcing bars are rarely used in construction. 2.3 Failure modes of steel-concrete interaction Two types of bond failures are distinguished considering the two different failure mechanisms of the concrete matrix (Fig.2). Pull-outfailure, where the concrete between the bar lugs is sheared off without a complete loss of the bond resistance (Fig.2). Visible cracks on the concrete surface are not necessarily produced. Splitting failure, where the hoop tensile stresses reach the tensile resistance of the surrounding concrete producing a longitudinal crack. In absence of transverse reinforcement or transverse pressure, it may lead to a complete loss of bond resistance.
258
2.4 Measurment technique The main concern of experimental bond studies is to detemine the bond stress-slip relationship that may be used for comparison of bond characteristics or for analytical studies. Slip over a length e b is the integral of the steel strains (esx) reduced by the concrete strains
(~x): eb
s = ~0 (esx'Ccx)dx
(1)
There are two different ways to determine slip: either to measure it directly e.g. with an LVDT on the bar end or by magnetic sensors in the interior of the concrete [39], or to measure the strains by resistance strain gauges [8-9] and to integrate them according to Eq.(1). If unloaded end slip also occurs, it is to be added to the result. Owing to the considerable work in preparing the steel bars for strain measurements and the difficulties in evaluating the results, simple specimens, the so called pull-out specimens [ 10] and beam specimens [11] were developed for direct measurement of slip. The slip is measured at the unloaded end of the specimen in both cases. The proposed bond length is 50 for pull-out tests and 100 for beam tests, respectively. Even if the shape of a beam specimen is more realistic, pull-out specimens provide the simplest way of testing and are more often used. The reinforcing bar is centrically embedded in a concrete prism of 100 (but maximum 200 mm) sides over the 50 bond length having an other 50 debonded length at the loaded end to eliminate stress concentrations. The bond stress-slip relationship is then determined from the registered tensile force-slip relationship/F(s)/relating the force to the steel-concrete interface:
% ( 0 - F(s) ~oe b
where s is the slip measured at the unloaded end of the specimen. The disadvantages of this method are that it neglects the changes of bond stress over the 50 bond length that may be considerable in case of larger diameters and uses a boundary condition for concrete (supporting block at the applied load) which is not typical. There are several proposals to improve the specimen or the evaluation method of measurements [12]. The bond stress is a function of the relative dispalcement, however, there are several parameters that influence the actual value of bond stress. The influence of rib pattern, concrete strength, confining effects, loading rate, long term loading and repeated loading are discussed in the following Sections. 3. INFLUENCE OF RIB PATTERN ON STEEL-CONCRETE INTERACTION The important parameter influencing the steel-concrete interaction is the shape of the interactional surface, i.e., the rib or deformation pattern of reinforcing bar. It consists of the shape, the heights, the inclination and distance of ribs. Different countries use different rib patterns. The rib pattern is not only intended to improve the bond characteristics but to distinguish bars of different strengths and manufacturers.
259 3.1 Influence of related rib area
To provide a possible comparison of bond characteristics of different bars, Rehm [1] introduced the related rib area (t~sb) meaning the axially projected front surface of transverse ribs related to the nominal interactional surface between two ribs. The deformation pattern not only influences the bond strength but also the failure mode. High ribs do not necessarily mean a more adequate bond behaviour because higher interactional stress increases the probability of longitudinal cracking.
rb/feU
0401
_ o.o
7#/
---
l/
0.10 .d'N.
0
0.25
0.50
0.75
1.00
1.25
slip [mm] Fig.3 Influence of the related rib area on the bond stress-slip relationship Rehm, Martin and Noakowski [13]
Fig.3 indicates experimentally derived bond stress-slip relationships as a function of the related rib area increasing from 0 (i.e. plain bars) up to 0.4. The increase in bond stress is less than proportional with the increase in related rib area. Twice of related rib area leads to less than twice of bond stress at a given slip. There should be an optimum in deformation pattern that is enough to transmit and anchor forces but still does not necessarily lead to longitudinal cracking. The optimal related rib area seems to be in the range of 0.05 < Otsb< 0.08 [ 14] which is less than that of some deformed bars used earlier. The related rib area is a practical tool for comparing bars of different rib patterns but the following analysis of single parameters of the rib pattern contributes to the characterization of bond properties.
260
3.2 Influence
of rib geometry
The experiments of Soretz und H61zenbein [15] have shown the increasing probability of splitting failure with increasing rib height on three series of reinforcing bars having the same relative rib area but different rib heights (0.10, 0.050 and 0.0250) and spacings (1.20, 0.60 and 0.30), respectively. With bars of different inclinations (30 to 90 ~ to the longitudinal axis, Soretz and HSlzenbein observed a slight improvement of bond characteristics (Fig.4). Varying the rib cross-section from a rectangle to a 45 ~ trapezoidal had no influence, and changing to a very flat triangle had only minor influence on the bond characteristics [15].
Rib patterns
Code
of rib pattern [] n
!Vl v w I
II ..... ! ......
III
1
EE
r if '~~
~_
,
e
!
IV
........ i:':/- ........,,-S;~ / --,
" tt
z'~ 2
,o I
,
V ...~~
w~
't
I
I
, / I
l
I I(~176176176
slip
J I J ~(~bu) ~ / i/~ t ]-~
J~ r---~, i j I ,
I
o., m
',/'I i ~
i
~
0.01ram
VI
21
il
I
40 50 60 70 80 90(90E) r ' Rib inclination [~ Fig.4 Influence of rib inclination on bond stresses Soretz and H61zenbein [15]
Tepfers and Olsson [ 16] conducted pull-out tests on bars of 16 mm nominal diameter with 48 mm bond length of different rib heights and spacings providing different related rib areas. The radial component of the interactional force was determined by measuring the circumferential strain in a steel ring surrounding the concrete of the pull-out specimen. The force component which is parallel to the bar was obtained by supporting the specimen with a teflon covered circular support close to the bar. Tepfers and Olsson [ 16] observed that: - Increasing rib height improves the bond stress at a given slip. - There is an optimum rib spacing. If the spacing becomes too short, the bar starts to act as a plain bar with a diameter including the bar ribs. - The slip at maximum load decreases, when the related rib area increases.
261 The splitting tendency increases with increasing angle between the interactional force and the axis of the bar. This angle increases if the slip at maximum load increases otherwise it decreases if the related rib area increases. Kimura and Jirsa [17] compared experimentally various rib pattems of commercial and machined bars of 36 mm nominal diameter by pull-out tests on 150 mm bond length and using concretes with compressive strengths 40, 80 and 120 N/mm 2 and specimens which contained spiral reinforcement of 6 mm diameter and 40 mm pitch. They concluded that: - The average bond stress and the initial stiffness of the bond stress-slip curve increased as the rib spacing decreased for concrete strengths of 40 and 80 N/mm 2. - The average bond stress and the initial stiffness of the bond stress-slip curve increased as rib height increased. The increase was larger for higher strength concrete. - The bond stress at splitting was not strongly influenced by rib spacing or rib height, regardless of the concrete strength. - As the ratio of rib height to rib spacing increased, the average bond stress and the initial stiffness of bond stress-slip curve increased, regardless of concrete strength. However, for rib height to rib spacing ratios greater than 0.2, these values seemed to be constant. - The bond stress to splitting tended to decrease up to a rib height to rib spacing of 0.2. - Bars with rib face angles greater than or equal to 45 ~ exhibited almost the same behaviour. However, bars with a rib face angle of 30 ~ were initially less stiff.
4. I N F L U E N C E OF C O N C R E T E S T R E N G T H AND C O M P O S I T I O N ON S T E E L CONCRETE INTERACTION Not only the strength but also the composition and the consistence (i.e. cement content, water content, etc.) of concrete influences the bond characteristics.
4.1 Influence of concrete strength To develop bond stresses, contributions are derived from properties of concrete both in tension and in compression. Micro-cracking is controlled by tensile resistance, however, bearing stresses induce high compressive stresses in front of the ribs. Design equations generally relate the bond strength either directly or indirectly to the tensile strength of concrete. Considering the relationship of tensile and compressive strength of concrete as a known property, experimental studies were intended to determine the relationship between the bond stresses or the bond strength and the concrete compressive strength. The higher the concrete strength, the higher the bond stress, however, test results disagree in the actual ratios. Based on pull-out test results with concrete mixes of 16 to 50 N/mm 2 strength measured on cubes of 200 mm sides, Martin [18] concluded the following: - For the slip range of 0.01 to I. 0 ram, the bond stress of deformed bars is proportional to the concrete cube strength (Fig.5.b). - For very small slips, s < 0.01 ram, and for slips close to the bond strength, s > 1.0 ram,
262 the influence of concrete compressive strength is less important and proportional to the ~a power of the concrete cube strength (Fig.5.a). rb(s=O. 01 ) ['N/mm2] 2.5
1
1
1
rb(0.01)-~. 163 fc2P
a)
1.5
_ z ~ y w/c = 0.50 + 0.90 uu~ 9 grading curve B 7 days 28 days CI 0 9
0.5
C2 C3 0
10
20
A B
A 9
i
i
3O
4O
5O
fen ['N/mm~]
10
~(s~.Ol) t'N/mm~] consisl~ency
[~
c1.,~(01)-0.222 f~z
cl~'J
C2: %(0,1) = 0.197 fc_~ / C 2 : C3:xb(0,1)=0.145 f c ~ / /
/ ,,
C3/
b)
/////
(/y ~er legend see Fig. a)
f" 0
10
20
t
!
30
40
50
fed [N/mrn2] Fig.5 Influence of concrete strength on bond stresses; Martin [ 18] a) at 0.01 mm slip b) at 0.10 mm slip
Janovic [19] and Noakowski [20] also proposed a proportionality to the ~a power of the concrete strength. Based on pull-out test results with up to 0.25 mm slip with concrete mixes of 40, 80 and 120 N/mm 2 strength, Kimura and Jirsa [ 17] concluded that the bond stresses are proportional to the square root of the concrete strength.
263
4.2 I n f l u e n c e o f c o n c r e t e c o m p o s i t i o n
Applying various cement contents, grading curves of aggregates, water-cement ratios and consistencies, Martin [18] concluded from his test results the following" - The effect of water-cement ratio is eliminated if the bond stress is related to the concrete strength. - The grading curve of the aggregate and the consistency of fresh mix strongly influence the bond properties. The observed greatest difference was 1 to 5. - The highest bond stress belongs to the grading curve with the lowest amount of fine particles (A - Fig.6.a) and the lowest bond stress to the grading curve with considerably 100 80
a)
,~/ /I V" / / /
60
e~ o
=
40
~
20
fl,/. ~t,"1
0 0.25 0.5
1.0 2.0 4.0 8.0 16.0 31.5 sieve size [ram]
b) ~fc~
i IIII11
iw/e=0.75
0.8 -
0.5
I I
- consistencygrading c u r v e B IIII C I I 1 " 28 days ....
0.6
'
0.4
'-_/,,i,, " J~C2
/ ,/l!
rb(S = 0.2)/fc-~
~
,,"
""
0.4
/ N, . ~ . I r - ,
TM
_j
0.3
]
r
C3
9
i
f
0.2
J
0.2
/
0.1
/
I ,O 18 mm
def. bars 0 0.01
0 0.1
1
2
5
1
1.1
1.2
1.3
slip [mm]
1.4
1.5
consistency
Fig.6 Influence of concrete composition on the bond behaviour; Martin [18] a) grading of aggregates b) influence of grading curve on the bond stress at 0.2 mm slip c) influence of consistency (as degree of compaction acc. to Walz, DIN 1048)
264 higher amount of fine particles (C - Fig.6.c). The difference produced in bond stresses is more than 100 %. It means that coarser aggregates improve the bond capacity of embedded deformed bars (Fig.6.a and b). - The highest bond stress belongs to the stiff (C1) consistency and the lowest to the semifluid (C3) consistency. The produced difference in bond stresses is up to 100 % (Fig. 6. c). The reason for the influence of consistency is the composition of concrete since variation of consistency has been achieved by varying the cement content by about 30%.
5. INFLUENCE OF CONFINEMENT ON STEEL-CONCRETE INTERACTION Confinement concerns all kind of effects that control transverse deformations of concrete matrix surrounding the reinforcing bar induced by the interactional forces before or after splitting of the concrete cover. Confinement may be provided by transverse reinforcement, by transverse pressure or by improving the strength or thickness of concrete cover. By onset of longitudinal cracking, the interaction may completely vanish. The confinement provided by the reinforcement (Fig. 7.a) or by the transverse pressure (Fig. 7.b), however, controls the opening of the crack. 5.1 I n f l u e n c e o f t r a n s v e r s e r e i n f o r c e m e n t
Pull-out test results by Eligehausen, Popov and Bertero [23] (Fig. 7.a) indicate different bond stress-slip behaviours with and without transverse reinforcement. The specimen without transverse reinforcement (designated 1.4) failed by splitting of the concrete cover at rather small bond stress of 6 N/mm 2, then the bond resistance dropped rapidly. Specimens with transverse reinforcement failed by bar pull-out. The crack developed in the plane of the longitudinal axis of the bar. Therefore, transverse bars (called vertical bars) crossing the crack were effective in restraining the concrete, while the influence of bars parallel to the axis (called stirrups) was negligible. This can be seen comparing series 1.2 to 1.5 in Fig.7.a. The influence of the area of vertical bars was rather small in the applied range. The initial stiffness o f the bond stress-slip curves was almost identical for all test series, which indicate that there exists an upper limit for an effective restraining reinforcement beyond which the bond behaviour cannot be further improved, because the main role of this reinforcement is to prevent the opening of splitting cracks [23]. 5.2 I n f l u e n c e o f t r a n s v e r s e p r e s s u r e
Untrauer and Henry [21 ] studied experimentally the influence of transverse pressure on the bond behaviour on pull-out specimens. The normal pressure was applied to two parallel faces of the specimens up to 16.3 N/mm:. Slip was measured at the loaded end using a dial micrometer gauge system. Untrauer and Henry [21 ] concluded that:
- The bond strength increases with increased normal pressure. The increase is approximately proportional to the product of the square root of the normal pressure and the square root of the compressive strength of concrete. - The incerase in bond strength is higher than the increase of bond stress at lower slip values.
265 The bond strength is larger for a 28.6 mm bar than for a 19.0 mm bar when normal pressure is applied. They interpreted the larger increase in bond stresses at larger slips with the increasing contribution of the friction and bearing on the lugs which are influenced by the transverse pressure.
16 ,,
E
1
,,.
,
,~
a)
~
I//OJ
'N
)
@ l
It
r ~ , , , , ~ , ~ , , r s , .... o, r_
I
~,,
I 2~,
I
il J.2 I
|
~
~5"-~1
A,31
I~z,
! ,o
12 7
I tZ't
I
i.O
63~
I,z~
!
o z5
~
.~
0 L_
1
l
0
2
4
~E
~
1
I
6
8
Longitudinal
,
1
_--
10 12 Slip [ram]
p 0 : 0 N/mm ~ pl" 6 9 N/ram~ p2:13 8 N/rnm:
15
b)
.
)IS.,..,} Otm~} IO[~}! zA'*/As!
o~ o~ I-i
10
5
1
\
0 ,~
o
[
2.s
iii
/t
A
so
7.s
~oo
Slip [mm] Fig.7 Bond stress-slip behaviour with or without confinement leading to complete splitting failure or pull-out failure after splitting of the cover a) Confinement by transverse reinforcement; Eligehausen, Popov and Bertero [23] b) Confinement by transverse pressure; Malvar [29]
266 D/Srr [22] carried out tensile tests on cylindrical specimens with a centrally embedded steel bar of 16 mm diameter in order to obtain the bond stress-slip relationship for four different values of transverse pressure (0, 5, 10 and 15 N/minE). The specimen was 600 mm long with an embedment length of 500 mm. The specimens were notched at the middle section to localize transverse cracking. The concrete cube strength varied between 29 and 42.5 N / r a m 2 with an average of 35.9 N/ram 2. Test results by D6rr (Fig. 8) gave a 100 % increase in bond stress at 0.1 mm slip when the transverse pressure increases from 0 to 15 N/ram 2. Slip was derived from the sum of measured strain differences of steel and concrete and the bond stress was derived from the change of forces from section to section.
r
--'15 E E
~10
B
g.a
o
m:l
t/)
D
Q
5
D
rNmml
[31 p = 10 [N/mrn ~] p = 15 [N/mm 2] 0.1
t).3
0.2 Slip [ram]
Fig.8 Influence of transverse pressure on the bond stress-slip relationship, fc[]--36 N / m m 2 D6rr [22]
From a comparison of the experimental results [21-26] relating to the influence of transverse pressure on bond strength, Eligehausen, Popov and Bertero [23] have shown a 2.5 to 8.5 N/mm 2 increase for a pressure of 10 N/mm. This large scatter is partly a consequence of the different failure modes. Twelve specimens consisting of 19 mm reinforcing bar embedded in a 76 mm diameter concrete cylinder were tested by Malvar [28, 29] under controlled confinement. The bond length was a 5 lug spacing of approximately 70 mm. Concrete cylinder strength varied between 38.4 and 44.2 N/mm 2. The support of the specimen was provided by shear stresses on the surface of the specimen. Concerning the bond stress-slip behaviour he concluded that: Preceding the onset of longitudinal cracking, the influence of confinement stress could not be properly established. - After longitudinal cracking, bond stress increased significantly with applied confining -
267
20
El5 E o
10
0 m
5
o'
TEST TEST TEST TEST TEST
1:3.4 N/mm 2:10.3 " 3:17.2 " 4:24.1 " 5:31.0 "
~
16
Slip [mm] Fig.9 Bond stress-slip diagrams with various levels of transverse pressure; Malvar [29]
stress. The maximum bond stress was increased by almost 200 % by increasing the confinement stress from 3.4 to 31 N/mm 2 at the bar level (Fig.9 and Fig. 7.b). The effect of confinement on bond behaviour appeared less pronounced for the higher confining stresses. - After longitudinal cracking, radial deformation measured on the concrete surface showed an increase up to a limit value dependent on the confinement level, then a decrease due to interface deterioration. - Bars with normal ribs (at 90 ~ to the longitudinal axis) exhibited better bond characteristics than bars with inclined ribs. Bars with normal ribs also produced more severe radial cracking. - Increasing radial pressure generated more severe radial cracking. Pull-out tests on modified specimens were carried out by Nagatomo and Kaku [27] in order to investigate the influence of transverse compressive and tensile stresses on the bond behaviour of deformed bars. The major parameters were the transverse stress and the concrete cover. The following transverse compressive stress as: 0, 3.92, 7.85, 9.81 and 11.77 N/mm 2 and transverse tensile stress as: 0, 0.49, 0.98 and 1.47 N/mm 2, were applied. Different covers were intended to influence the type of bond failure (side splitting, V-notch splitting, comer splitting or pull-out). The bond length was 70=154 mm using a bar of 22 mm diamter. The concrete compressive strength varied between 15.5 and 18.8 N/mm 2. Nagatomo and Kaku [27] concluded the following:
- The bond strength increases linearly with increasing transverse compressive stress up to approximately 30 % of the concrete compressive strength, and tends to level off for the transverse compressive stress beyond that value (Fig. 10). The relative increase rate with transverse compressive stress decreases linearly with increasing concrete cover up to 2.5 times the test
268
2.0f[~~
2.0[
~b.(p~) Xb.(P=0)
l:bu(pr ~:bo(P=O)
"tb.(Pr Tb,,(p=O)
2.0-
o
~.~%o
~.o
o'.s
9
I
1 .o
ol
o'.s
p/f~
I
1 .o
o
I
0.5
p/fr
I
1.0
p/fr
Fig.10 Influence of transverse compressive strength on bond strength Nagatomo and Kaku [27] a) Cb/O:l.08 %/O=1.98 C) %/0=3.10
b)
bar diameter and becomes zero for the concrete cover beyond that value (Fig. 10). - The effect of transverse compressive stress on bond strength is less for the failure modes by a side splitting crack parallel to the direction of transverse compressive and by shearing of concrete passing through the top of bar ribs. - The bond strength decreases rapidly and parabolically with increasing transverse tensile stress and becomes zero at the transverse tensile stress equal to the tensile strength of concrete (Fig. 11). Based on their own experimental results and those of others' experimental results, Nagatomo and Kaku [27] developed a linear and a parabolic relationship to take into account transverse stresses. The normalized bond strength in case of transverse compression (p):
Xb"(P/fCvO) = %.(p/fr
k'p + 1
(2)
and the normalized bond strength in case of transverse tension (Pt, Fig. 1 I):
Xbu(Pt/ft~0) -- Xbu(Pe/ft=0)'(9 0"755"Pt - 1)'( Pt _ 1) fc where l:bu(P/fcr
ft
) and factor k are functions of the concrete cover [27].
(3)
269
%.(p=O)~
O : %/0=1.08 A : cb/0=-1.98 !"1 : %/0=3.10
1.0~.~,, F"I ~,~ ~ , , ~
0.5- ~ 0
/Eq.(3) 0.5
1.0 P/fc
Fig.11 Influence of transverse tensile stress on bond strength; Nagatomo and Kaku [27]
6. INFLUENCE OF LOADING RATE ON STEEL-CONCRETE INTERACTION Vos and Reinhardt [30-31 ] studied experimentally the influence of loading rate on pull-out specimens of 30 bond length using concrete mixes with average cube strength of 22, 45 and 55 N/ram 2. 10 mm diameter plain and deformed bars of 0.076 related rib area were tested in addition to 3/8" diameter prestressing strands of 1730 N/mm 2 0.1% proof stress. Test results indicated that the bond resistance of plain bars and strands is hardly influenced by the loading rate (even increasing the loading rate by 100 000 times). It appears that the adhesion, the friction and the lack of fit (by prestressing strands) are insensitive to a variation in loading rate [30]. In case of deformed bars, the bond resistance increases with increasing loading rate, however, the concrete grade also has an influence. The higher the concrete strength, the less insensitive is the bond resistance to variations in loading rate (Fig.12). The influence of the loading rate and concrete strength is most pronounced for a small slip of the order of 0.01 mm. Vos and Reinhardt [30] developed the following relationship for the rate dependent bond stresses valid up to a slip (s) of 0.2 mm: Tb Tb0
_( X.b )q Tb0
0
(4)
where Tb and Tb0 are average bond stresses to a given slip and '~b and Xb0 are the respective loading rates. %o and Zb0 can be regarded as "static" reference values [30]. The power q of Eq.(4) was determined using the method of least squares for all results with deformed bars as a function of the concrete cube strength (fcc in N/mm 2) and the slip (s in ram):
270 rb/rbO 2.6 2.4 2.2 2.0
]fcz= 20 N / m m 2 [ / ~ /
1.8 1.6
/ "
./"
40.~
1.4 1.2
10
102
103
104
10'
106
,V;bO
2.0 1.8
[fc.=:O./mm
1.6 1.4 1.2 1
1
10
102
10'
104
10'
10~
fiCr
Fig.12 Influence of the loading rate on the bond resistance of deformed bars Vos and Reinhardt [30] a) 0.01 mm slip b) 0.20 mm slip 0.7(1-2.5s) fctJ 8 Eq.(4) is plotted in Fig.12 for three concrete strengths and two slip values 0.01 and 0.02 mm in double logarithmic scale. Fig.8 indicates that for a small slip as 0.01 mm, the influence of loading rate and concrete strength is more pronounced than for a higher slip as 0.2 mm. The bond resistance associated with impact loading can be twice the bond resistance of static loading. For a higher strength concrete (here 60 N/mm 2) this ratio is only 1.5. For higher displacement, the influence of the loading rate decreases to about 1.4 and 1.2, respectively.
271 7. INFLUENCE OF REPEATED LOAD ON STEEL-CONCRETE INTERACTION Repeated load produces an increase of slip as a result of progressive micro-cracking and micro-crushing [23,32-38] and can lead to failure at a cyclic stress level lower than the ultimate stress under monotonic loading. Repeated loading may be subdivided into low-cycle and high-cycle loading according to the number of load cycles up to failure. Low-cycle loading usually contains only a few cycles but at a high stress level. Low-cycle loading generally arise under seismic conditions. Highcycle loading contains (thousands or millions), but on a relatively low stress level. Bridge elements, offshore structures and supporting members of vibrating machinery are typically subjected to high-cycle loads. Another subdivision of cyclic loading, which is followed also herein, is to consider the type of applied stress as either having or not having stress alternations. Cyclic load will imply load cycles without change of sign of the applied load, and reversed cyclic load implies load reversals including both tension and compression in one cycle. 7.1 Influence of cyclic loads Test results with constant and variable amplitudes are discussed separately. 7.1.1 Constant amplitude cyclic loads According to pull-out test resuls by Rehm and Eligehausen [34] with constant amplitude cyclic loading, the slip versus number of load cycles diagram can be approximated by straight lines in double logarithmic scale. For loads below the fatigue bond strength these results give straight lines which are parallel to each other (Fig. 13). The gradient of lines were higher for specimens which failed by fatigue. 1.0 E
& 05 g:
t~ d~
O
o.o
._~ r,~
0.01 |.0
101
10 2
10 3
1r
10 5
]0 6
number of load cycles, n Fig. 13 Increase of slip at the free bar end as a function of the number of load cycles fc~=23,5 N/mm 2, O=14 mm, eb=30 Rehm and Eligehausen [34]
272 Rehm and Eligehausen [34] proposed a relationship to predict the slip after n load cycles (s,) as a function of the initial slip before applying the cyclic load (So) and the number of load cycles: sn -- s0(1+k.) where k. = (1 +n) 0"107-1 The slip coefficient, 1%, was not greatly infuenced by parameter variations of loads below the fatigue bond strength. Considering the total bond faitigue process, Baldzs [36] distinguished between three different phases in case of constant amplitude cyclic loads producing slip over the entire bond length (Fig. 14). Phase 1 Phase 2 Phase 3
: slip increase with decreasing rate : slip increase with a constant rate : slip increase with an increasing rate
Nevertheless, the slip versus number of load cycles diagram in linear scale contains, in turn, concave downwards, linear and concave upwards portions. The length (i.e. the corresponding number of load cycles) of all three portions are functions of the bond parameters and the cyclic load level. The slip rate during the secondary linear phase was also found to be dependent on the load level. In case of a relatively high load level, the second linear portion of the slip versus number of load cycles diagram can transform into a point of inflexion. To predict fatigue failure, the initial point of the failure branch (Phase 3) is of particular inter-est. It was found [36] to be equal to the slip, S(Zbu) at the monotonic bond strength (Fig. 14.b and c). Once the slip exceeds S('~bu), a pull-out failure occurs after additional load cycles.
7.1.2 Cyclic loads with variable amplitude Pull-out test results [37] with variable amplitude cyclic loading indicated that the development of slip is strongly dependent on the load history. Based on the load spectrum analyses of bridges and cranes, parabolically and logarithmically varying load histories were applied in addition to linear ones both with increasing and decreasing tendencies. These load histories were set up in stepwise fashion using shorter sub-blocks of constant amplitude loadings. Six typical test results obtained by using these load histories with a maximum cyclic load level of 40 % of the average bond strength applied in two blocks till 2.106 load cycles are presented in Fig. 15. The highest slip values of Fig. 15 are in the serviceability range far below the slip at bond strength. With increasing sequence of amplitudes, the first complete block of loading (here up to 1 million of load cycles) produces a pronounced slip increase with decreasing slip rate. Cycling in the next block at lower load levels, however, does not contribute to the slip increase (Fig.15.a, c and e).
273
a) -
I
I
I
I
!
!
y
T
r
i
7N
2 Slip I . i t i x~. t I. l pull-out ] [N/ram ] --.--...~decreasmg4.. i constant .L..4 lncreaslng..~failure ir - " ">0 1 60 [ 1 rate ' n = 10r~- - 20 i. 30 40,,', 8c,,cles
I(-' r~r4 - tittiHJ,litttilttli#i"rhititttttttti:..~ ..... ~" i-t-
-"7
'oj. i ~ i f
,t
' ,llttttttttltl;1t!ttt,Itlllttl'ltttt I.-i~ : '~ltlttttNitttllt Itt/ltltN..... r,___~
.
L1.0cycles.'
~
-u-~ _
~
I
I
t 0__
i
+
0
!l]lJtl:l[ttt '-:i" ]ttiItt}]/tt]]tlt]tttttttt i ]l~t i ' i , I Slip i
p I 1o.2,5 I o.5o i
F I<%
! t
i I l:OOl
}0.75
Load history
t 1.25
I 1.50
[mm]
.
S"
1,, r,"l!lIIl!!!111111l lilii!lili!lll~llll'llil!Sll'Jlilllilllillllli !W,ti i t~~l /. ~%,~NNttil~lll[llllllllllJtliilli]lJ. , llJ~lli,,llllt,lJlillll,Ii~illtll,/ "15~0 0 N10u~b2e0o?~oad40yclSe~ 6~0 n;
Slip [mm]# . . 2 5-[
,
.
.
b ) /2/.!0 ~!.I ~ ,- l V! l /
I
a st
I
, ~/ 1 "U
'
I
!
: !
M~e~176176
Pull-out t fa!lure ]]
3.0 ~ /
-t / ~
20~
I/
~
)
|
"/
! ' !~;-~,i.~,,,._J
/
!
I I '
+tl+lll
10 20
:
4.01
i
;~~----~,f C " i!
i jt"Pt%uJl---] I! l 10
30 40 50 60 70 n Number of load cycles
c~
5
;
10
Bond stress [N/mm 2]
Fig.14 Bond fatigue process under cyclic loads,fern=20 N/mm 2, 0=8 mm, eb=120; Balhzs [36] a) bond stress-slip diagram b) slip vs. number of load cycles diagram c) monotonic bond stress vs. slip diagram
274
With decreasing sequence of amplitudes, significant slip increase is produced only by the highest cyclic load levels both in the first and in the later blocks (Fig. 15.b, d and J). Low cyclic load levels after higher load levels have hardly any influence on the slip increase. Slip
a)
Tb
[mm] t'N/mm~]
Slip
~~ 0 10 ~ 0
Slip ~ % [ram] [N/ram 2]
c) .., Shp
"t 0
~
Load
0.5 1.0 1.5 2.0 Number of load cycles [million]
Slip
Tb
e)
[mm]~tWmm~1 ,
0.5 1.0 1.5 2.0 Number of load cycles [million]
d) Slip
0 - 1 ~ ' - - ' ~ o a _ _ d 06
Slip
0.5 1'.0 1".5 2'.0 = Number of load cycles [million] xb
f)
0.2tlO '
!
[mm] I [N/mm:]
0.2+ 10
0
' r--W"-'-~- L~_ooad
Slip xb [mm]! [N/mm2]
[mm]l t'N/mm~] 0.1~5___ ~
0
---
c
0.2~ 0.1 ~ ~ ~
0.5 1.0 1.5 2.0 Number of load cycles [million]
0 2 10
Slip
-
~iLoad_~___ .__ _ ~ `
Slip. Tb
b)
'
i
~
015 1.0 115 2.0 Number of load cycles [million]
0
Slip Load!
015
~.0
~15
2.0
Number of load cycles [million]
Fig.15 Slip increase as a functon of the load history, fr N/ram 2, O=16 mm, eb=50 a)-b) parabolically c)-d) linearly e)-f) logarithmically variable amplitude Balfizs and Koch [37] 7.2 Reversed cyclic loads
The most common case of reversed cyclic loading is seismic loading. Cycles with reversed loading produce a more severe degradation of bond strength and bond stiffness than the same number of load cycles with cyclic loading without change of sign. Degradation primiraly depends on the number of load cycles and the peak slip in either direction between the bar is cyclically loaded [34, 36]. Under otherwise constant conditions the largest deterioration will occur for full reversals of slip. Whenever the load cycles are limited to produce slip only in one direction, there is no significant degradation of the bond strength [38].
275 Slip controlled load reversals produce deterioration both of the peak bond stress at the applied maximum slips and that of the frictional bond stress which is the necessary bond stress from the other direction to withdraw the previous slip (Fig. 16)[36]. Five cycles between +0.2 mm slip caused the peak bond stress to decrease by 35 percent (Fig.16).
Load history Decrease of peak bond stress
Ivvvvr I 2 3 ~ 5-
----q ---i
Xb(n) 100l -
i
--~-~.,....~
i
9
i
9
1
] ' ] 2"23+ "
Slip i [mm]_~
"
9
3
.
,
1
4" 5" 4
n
5
Decrease of frictional bond stress
15 ~ ~bf(n))
-
!
"l:bf(n-89 10 ~
[%] 5 ~ - -
_+__,_ 1+ 1. 2§
4 +
4
5+
5
n
Fig.16 Bond behaviour under slip controlled load reversals, fen=20 N/ram 2, O=16 mm, eb=20 (The ordinate axis of loaded side curves is skew to correct the elongation of reinforcing bar between the loaded end section and the point of attachment of the LVDT) Bal~s [36]
Force controlled load reversals produce a remarkable slip increase which indicates an increasing damage in the concrete matrix around the steel bar (Fig.17) [36]. The higher the
276 load, the higher the slip increment. The slip rate during force controlled load reversals was approximately four times higher in comparison to that of a repeated loading.
Load history FI "l:b
,,!j, !pJll!JJ!llJ!l!lI .,
:
.,..,
. . . . . . .
9
p
_ _ Slip at peak stress
0.4+~
. ~
[N/xb2]mm 13.3 11.2
.... 9.4 9 | 2 345-n
Fig.17 Bond behaviour under force controlled load reversals, fen=30 N/mm 2, O=16 mm, eb=20; Balfizs [36]
8. S U M M A R Y
The behaviour of steel-concrete interfaces is discussed in reference to experimental data. Tensile or compressive forces on an embedded steel bar induce interactional forces in the surrounding concrete matrix. Only relatively low loads can be transmitted by physicochemical adhesion, however, higher loads are transmitted by mechanical interlock and friction leading to relative displacement of the sections. Bond failure may be reached by pull out of the bar or by splitting of the concrete cover. Shape and dimension of ribs, strength and composition of concrete, confinement provided by transverse reinforcement or by transverse pressure, type and rate of loading all have a strong influence on the bond behaviour.
277 NOTATIONS Cb fc[] fc ft n p p, s So Sn S(Xbu) eb
C~sb ~cx ~s• zb Zbu "l~bx %-s 0
bottom concrete cover average concrete strength measured on cubes of 200 mm sides average concrete cylinder strength tensile strength of concrete number of load cycles transverse pressure transverse tension slip (relative displacement) initial slip before cyclic or sustained loading slip after n load cycles slip at bond strength bond length related rib area concrete strain distribution steel strain distribution bond stress bond strength bond stress distribution bond stress-slip relationship nominal bar diameter
mm N/mm 2 N/mm 2 N/rnrn 2 N/mrn 2
N/mm: mm mm mm mm mm % % N/mm 2 N/mm 2 N/mm 2
N/mm2-mm mm
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