INTRODUCTION
It is well known that the nominal strength of specimens made of quasibrittle
materials such as mortar, concrete, rock, ice, ceramic and composite materials
are affected by the specimen size (Bazant, 1984; Bazant
et al., 1991), more specifically, the nominal strength of laboratory
size specimens differ from that of structural members used in construction sites
of real structure. The difference in the nominal strength is a direct consequence
of energy release into a finitesize fracture process zone (damaged localized
zone). Gonnerman (1925) has experimentally showed that
for concrete the ratio of the compressive failure stress to the compressive
strength decreases as the specimen size increases. This phenomenon of reduction
in strength due to specimen size increase is called the reduction phenomenon
and this is due to the fracture mechanicsbased derivation of size effect law
(Gonnerman, 1925). Earlier researches have focused on
pure tension and shear loading conditions rather than compressive, splitting
and flexural loading conditions. Recent studies, based on size effect on the
compressive strength, became a focus of interest among researchers (Cotterell,
1972; Bazant and Xiang, 1994; Jen
and Shah, 1991; Bazant et al., 1997). Most
design codes for structures do not consider the effect of size which is an important
phenomenon. Since, quasibrittle materials fail by formation of cracks and initiation
of these cracks in materials like mortar and concrete are affected by microcracks
which depends upon so many factors, in which coarse aggregate size is one of
them. Therefore; for such materials, size effect has to be considered in estimating
their strength characteristics. In this field there is a lack of work for cement
mortar, therefore, in the present study the effect of specimen size on the compressive,
splitting strength and modulus of rupture of cement mortar are investigated.
The importance of knowing and estimating mechanical properties of mortar is
based on the facts that mortar at present is widely used in restoration and
rehabilitation of defected concrete and masonry structures and its application
in ferrocement structures as well, therefore it is necessary to precisely estimate
its strength.
MATERIALS AND METHODS
Materials for cement mortar: Essentially_ cement mortar is composed of cement, sand and water. In the present study only a single mix proportion of cement: sand ratio equal to 1:2 by weight is used with a water cement ratio equal to 0.45. The properties of each material used in this study are presented below:
• 
Cement: Normal portland cement (I) produced locally
that comply the Iraqi Specification (IQS, No.5, 1984)
was used for all the mixes of mortar 
Table 1: 
Details of tested samples 

• 
Sand: Graded river sand at Mosul city was used for
preparing the test specimens and passing from sieve No. 20 (850 μm)
and retaining on sieve No. 30 (600 μm), complying the requirements
of (ASTM C33, 1978) 
• 
Mixing water: drinking tap water was used for both
mixing and curing. The temperature of the used water throughout the experimental
period ranged between (2027°C) 
Cement, sand and water are all measured by weight according to the required
proportion and the specified water cement ratio in all the mixes.
Test program: To study the effects of specimen size on the compressive, modulus of rupture and splitting strength of cement mortar, it was proposed to prepare (45) mortar specimens having different sizes and with cement/sand ratio equal to 1:2 and water cement ratio equal to (0.45) as explained below:
• 
Six samples of cement mortar are casted in a cube molds for
each of the sizes (150, 100, 50 mm). For each size three samples are tested
for compressive strength and the other three samples for splitting strength
(Table 1). The procedure of casting and testing is carried
out for size (50x50x50 mm) cube as per the (ASTM C10902,
2002) for compressive strength. Similar procedures are followed for
the other cube sizes 
• 
Three samples of cement mortar are casted in prism molds of
sizes (100x100x500, 50x50x300 and 25x25x300 mm) with three samples for each
size (Table 1). The (ASTM C78 2002,
specification) for modulus of rupture strength of mortar has specified a
sample size (40x40x160 mm) and to be tested under central Point loads. In
the present study all the specimen sizes are different from that specification
and tested under two point loads to maintain a zone of pure moment 
• 
Six samples of cement mortar are cast in cylindrical molds
for each of the sizes (150x300, 100x200 and 50x100 mm). For each size three
samples are tested for compressive strength and the other three samples
for splitting strength (Table 1). The procedure of casting
are carried out for size (150x300 mm) as per the ASTM
C3901 (2001)specification for compressive strength of concrete and
ASTM C 496 (1996) specification for splitting strength of concrete. Similar
procedure is used for preparing and testing the other specimen sizes 
The casting are took place under laboratory conditions at a temperature of
(2027°C) and a relative humidity ranged between (5060%).
Procedure for preparing and testing specimens: To prepare the specimens, the required amount of cement is weighted and the corresponding quantity of saturated surface dry sand according to the mix proportion of cement/sand ratio and also the require weight of water for mixing is weighted according to the water cement ratio stated before. The mixing is carried out using mechanical mixing powel.
The rate of loading for all the tests was applied according to the ASTM specifications (ASTM C10902, 2002) by either maintaining the specified rate of loading or the specified applied stress throughout the loading period. All specimens were tested at the age of 28 days using (ELE) compression machine. All the samples are tested immediately after being removed from the curing water tank.
Figure 1af show some of the tested cement
mortar samples with different sizes used for compression, splitting and flexural
tests.
Curing: Specimens were covered with wetted cloths and kept in the mold for 24 h after casting, thereafter, the specimens were removed from the mold and immersed in the water tank for 28 days at a temperature of 2027°C.
RESULTS AND DISCUSSION
The test results presented in terms of compressive strength, modulus of rupture and splitting strength are listed in Table 2. Each value is the average of three specimens.
The variation of compressive strength of mortar with the specimen’s size
of both cubes and cylinders is shown in Fig. 2. In this Fig.
2 and the subsequent figures, the size of cylinder refers to its diameter.
The Fig. 2 shows a similar trend in compressive strength reduction
with the increase in the specimen’s size of both cubes and cylinders.

Fig. 1: 
(af) Samples of tested mortar having different specimen’s
sizes 
Table 2: 
Test results of compressive, flexural and splitting strength 

The average ratio of cylinder compression strength to the cube strength (having
cube side equal to cylinder diameter) is equal to 0.67.
The variation of mortar splitting strength with the specimen’s size of
both cubes and cylinders is shown in Fig. 3. It is worth to
mention that the width of the indenter that is used for testing the splitting
strength of each cube size is equal to 10% of the cube side, while for cylinder
splitting test the ASTM C 496 (1996) are applied.
Figure 3 shows that for cubes the variation of splitting
strength with specimen’s size is only marginal compared with that of the
cylinders.

Fig. 3: 
Variation of mortar splitting strength with specimen’s
size 

Fig. 4: 
Variation of modulus of rupture with the prism’s size 
The splitting strength of cube 50x50x50 mm is almost equal to that of cylinder
50x100 mm, while the reduction in splitting strength in cylinder 100x200 mm
compared with that of cube 100x100x100 mm is 13% and for cylinder 150x300 mm
the reduction in splitting strength compared with cube 150x150x150 mm is about
24%. This indicates that increasing the cylinder specimen’s size cause
to increase the reduction in the splitting strength of cylinders compared with
that of cube specimens.
The variation of the modulus of rupture with the dimensions of prism’s cross section is shown in Fig. 4. It can be noticed that the modulus of rupture is drastically reduced from 7.05 MPa for prism cross section 25x25 mm to 6.4 for prism with cross section 50x50 mm and it is almost came to a stationary value (6.3 MPa for the present mix proportion) when the cross section of the prism is greater than 50x50 mm.
Figure 5 depicts the variation of splitting strength with
the counterpart compressive strength of the same specimen size for both cubes
and cylinders.

Fig. 5: 
Variation of splitting strength with the compressive strength
of cubes and cylinders specimens 
It can be notice that the splitting strength for cubes is almost linearly
increased with the compressive strength (with the reduction in sample size)
and are related by the best fit equation:
With R^{2} = 0.96, where, f_{tcub} is splitting strength of cube specimen and fcu copmressive strength of mortar using cube specimen in MPa.
While, for cylinder specimens the best fit to relate splitting and compressive strength can be expressed by the power relation as:
With R^{2} = 0.97, where f_{tcyl} is splitting strength of cylinder specimen and f'c is copmressive strength of mortar using cylinder specimen in MPa.
Figure 6 shows the relation between splitting strength of mortar using cubes and that using cylinder spacimens, the sizes of the specimens are shown in the same figure. The relation is nonlinear and the best fit that relate splitting strength of cylinder with that of cube can be expressed as:
With R^{2} = 0.97.
The relation between copmressive strength of cylinderecal mortar specimens with that of cube specimens is shown in Fig. 7. The corresponding specimen sizes are shown in the same figure. These relation can be expressed with best fit by a linear equation as:

Fig. 6: 
Variation of splitting strength of cylinders with that of
cubes 
With R^{2} = 0.94.
CONCLUSIONS
From the test results and discusion of the obtained mechanical properties of cement mortar using different specimen sizes, the following may be stated:
• 
Generally the compressive, modulus of rupture and splitting
strength of the mortar is increased by reducing the size of the specimen 
• 
The compressive strength of mortar using either cubes or cylinders
specimens is drastically affected by the specimen’s size 
• 
For cubes the variation of splitting strength with specimen’s
size is only marginal compared with that of the cylinders 
• 
Some best fit relationships that relate mechanical properties
of mortar are presented in this study. Although, it cannot be generalized
due to the fact that the presented results are based on limited number of
tested specimens, nevertheless; it can gives an amble ideas about the variation
of these properties with each other 