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COMPRESSIVE STRENGTH FOR CONCRETE BLOCK MASONRY BASED ON THE PROPERTIES OF CONSTITUENT MATERIALS

Robert G. Drysdale Professor Dept. ofCivil Engineering and

Engineering Mechanics McMaster University, Hamilton Ontario, Canada, L8S 4L 7

ABSTRACT

PingGuo Post-Doctoral FelJow Dept. ofCiviJ Engineering and

Engineering Mechanics McMaster University, Hamilton Ontario, Canada, L8S 4L 7

For design, masonry compressive strength is based either on tests of fulJy capped 2 block high prisms or from code tables according to the mortar type and block strength. However, standard prism strengths do not closely represent the true masonry strength. To solve this problem, a set of new test methods have been developed to provide a better measure of the mechanical properties of both masonry prisms and constituent materiais. An elastoplastic constitutive model and a finite element analysis have also been utilized to study the relationships between the prism strength and the properties of the constituent materiais. Finally, a simple equation is proposed to determine masonry prism strengths from mortar and block strengths. This equation closely predicted the measured strengths of more than one thousand concrete block prisms reported in 27 references.

INTRODUCTION

For design of masonry, the compressive strength is current1y based on standard prism strengths, determined ei ther from testing of fully capped 2 block high prisms or from code vai ues tabulated according to the mortar type and block strength. However, standard prism strengths do not closely represent the true compressive strength of face shell mortared block masonry. This is because prism strengths determined from tests of fully capped standard 2 block high prisms are influenced by the significant loading platen restraint, non-representative full capping and an inadequate number of mortar joints to reproduce the mode of failure observed in structural elements. The compressive strengths tabulated on the basis ofblock strength and morta r type are influenced by the same factors beca use of being based on previous similar prism tests. An added facto r is that current standard methods of measuring the material properties do not accurately quantify the properties relevant to compressive strength of face shell mortared masonry. This leads to uncertainty regarding the relationships between prism strengths and the strengths of the constituent materiais.

It has been shown that representative masonry strengths can be obtained by carefully testing either 4 or 5 block high prisms provided that the mortar bedding, the thickness and tooling of the joints, the proportions and mixing of the mortar, the block properties, and the curing condition are the same as those used in the masonry structure. However, beca use of the test height, manpower and time requirements, it is impractical to perform such prism tests for most masonry structures. Therefore it is highly desirable to have some means such as a simple equation which can be used to closely predict prism strengths based on the block and mortar strengths.

To develop an equation to relate the prism compressive strength to the strengths of the constituent materiais, the properties of both the prisms and the constituent masonry materiais must be correct1y measured which in turn requires reliable test methods. The approach adopted1

was first to develop a set of new test methods and then to use them to systematically investigate the properties ofindividual masonry materiais and masonry prisms. Based on the test results and

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principies of mechanics, a general elastoplastic constitutive model was developed and verified for the individual masonry materiais. This constitutive model was then incorporated into a finite element program to analyze the influences of various material properties on the behaviour of concrete block prisms. After verification of the ability of the finite element program to model various masonry prisms, the prism strengths predicted by this program were used to define the prism failure surface for various combinations of the block and mortar strengths. FinalIy, a simple equation was developed and verified to calculate the prism strength from block and mortar strengths.

EXPERIMENTAL INVESTIGATIONS

Concrete Blocks

The major problem with the block strengths determined according to ASTM Standard C1402 is the significant loading platen restraint effect. In this experimental investigation, steel brush platens were used to avoid this problem. In addition, 320 coupons of ull,Íform cross sections were cut or drilIed from blocks to investigate the uniaxial and triaxial compression properties of the basic material. A total of 335 concrete blocks of different strengths and shapes were capped on different areas and tested using different loading platens.

The test results from concrete blocks hard capped on the equivalent mortar bedded face shelI area and tested using the steel brush platens were regarded as being most representative of the block strength in terms of the use of blocks in masonry structures. The ratios of the block strengths from the above tests based on the equivalent mortar bedded face shelI area to the ASTM standard block strength and to the block coupon strength were 0.84 and 1.08, respectively. Compared to the ASTM method, the lower strengths due to removal of the end platen restraint would be somewhat counteracted by the influence of the unaccounted for web areas. Conversely, in addition to the size effect, the strengths higher than from the coupon tests can be attributed to the unaccounted for web area ofthe block.

Mortars

The major differences between the mortar strength determined according to ASTM Standard C1093 and the strength of mortar in masonry structures are due to the effects of non­representative water/cement ratio, curing condition and due to end confinement by rigid loading platens. To simulate the actual water/cement ratios of morta r in masonry joints, mortar specimens were cast using mortar taken from the joints of 2 block high prisms which had been aIlowed to sit for 10 minutes. These mortar specimens were air cured in the laboratory with the block prisms. The effect of lateral restraint on the mortar, such as might occur due to restraint by the blocks, was investigated by providing different leveis of confining pressures in triaxial compressive tests. Steel brush platens were again used to elimina te the loading platen restraint effect. A total of 183 mortar specimens of various strengths and curing conditions were tested under different loading combinations.

The test results from the air cured mortar joint mortar specimens tested using the steel brush platens were regarded as being most representative of the mortar strength in the masonry. The average ratios of compressive strength between these air cured mortar joint mortars and the unabsorbed and water cured mortars tested using solid platens were 0.63, 0.47 and 0.49 for the Types N, S and M mortars, respectively. Similar strength ratios between the air cured mortar joint mortars and air cured unabsorbed mortars were 1.25, 1.03 and 0.83 where again the latter tests were between solid steel platens as per ASTM specifications.

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Concrete 8lock Prisms

As mentioned above, the major weaknesses of the ASTM tests of fully capped 2 block high stacked prism are the strong efTect of loading platen restraints and the nonrepresentative bond and capping pattern. In this study, steel brush platens, running bond, face shell mortar bedding and equivalent mortar bedded face shell area capping were used to avoid these weaknesses . A total of 356 concrete block prisms were tested to investigate the failure mechanisms and influences ofvarious material and geometrical parameters.

The results either from prisms tested between the steel brush platens or 5 block high prisms tested according to ASTM were found to be most representative of the strength. The correction factors for 2, 3, 4 and 5 block high prisms tested between solid loading platens were found to be 0.85, 0.95, 0.99 and 1.00, respectively.

ELASTOPLASTIC ANALYSIS

Constitutive Model

8ased on the experimental evidence and principIes of mechanics, a general constitutive model was developed for concrete block materiaIs and mortars within the rate-independent theory ofplasticity l . The proposed failure surface is convex and smooth in the three dimensional stress space. Its cross section in the deviatoric plane gradually changes from a curvilinear triangular shape to a nearly circular form with increasing hydrostatic pressure . Loading surfaces were defined using an evolution function to scale down the above failure surface . This evolution function is in the same function form as a stress-strain relationship previously suggested for hollow concrete blocks in compression4. Plastic potential surfaces were obtained by modifying an existing function according to the above loading surfaces. The nonassociated flow rule was used to defined the plastic strain increment tensor. The 9 material parameters involved in this model were determined using the results of tests under some sim pie loading conditions.

The performance of the proposed constitutive model was first checked by comparing the predicted responses under dilTerent confining pressures to the measured responses for various concrete block coupons and mortars. These comparisons indicated that the proposed model did realistically predict the ultimate strengths and deformations throughout the whole loading stage including the smooth transition from the strain hardening region to the strain softening region . The smooth brittle-ductile transition with increasing confining pressures was also closely reproduced. The typical performance of the proposed mode) is illustrated in Figure 1 for Type N mortar under dilTerent confining pressures.

Elastoplastic Finite Element Program

The above constitutive model was incorporated into an elastoplastic finite element program1 to analyze block prisms in both two- and three-dimensional space. The performance of this program was verified first by comparing the predicted responses with the corresponding test results. The input block properties were based on the test of block coupons. The input mortar properties were based on tests of the air cured mortar joint mortar specimens tested between steel brush platens. The comparisons indicated that this program could successfully model the influences of block strength, block flare and taper, block webs for face shell mortaring, morta r strength, and mortar joint thickness on the compressive strength. In addition, the behaviour in both the strain hardening and strain softening stages was closely reproduced. The analytical results were found to be relatively insensitive to the mesh size.

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Predicted and Measured Stress-Strain Curves for Air Cured Mortar Joint Type N Mortar under Different Lateral Confining Pressures

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Mortar Strength

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Tensile/Compressive Strength Ratio

Material Strength/"Standard" Material Strength

Figure 2 Influences of Material Properties on Prism Strength

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The program was further verified by comparing the predicted prism strengths with the measured strengths for sets of 5 prisms built using blocks and masonry sand from 29 block plants in Ontari05 . The input block and morta r strengths were obtained by applying the corresponding correction factors reported above to the reported strengths determined using the ASTM methods2.3. Although these prisms involved many different combinations of block compressive strengths, block tensile strengths and mortar strengths, ali of the measured prism strengths were closely predicted with an average ratio of the testedlpredicted prism strengths of 0.96 and a coefficient ofvariation ofO.10.

Parametric Study

The use of the program to predict block prism strengths from different constituent material properties was discussed above. Following its verification, it was utilized in a parametric study to document the influences of block compressive strength, mortar strength and the ratio of block tensile/compressive strengths on the block prism strength.

The "standard" input compressive strength, corresponding compressive strain, ratio of tensile/compression strengths, and Poisson's ratio for the "standard prism" were, respectively , 20 MPa, 0.002, 0.10 and 0.2 for the blocks and 10 MPa, 0.003, 0.15 and 0.2 for the mortar. The predicted "standard prism strength" was 18.4 MPa for face shell mortared 20 em blocks. To investigate the influence ofblock compressive strength, it was changed from 4 to 40 MPa at 4 MPa increments, while other input data was kept constant. The predicted prism strengths ranged from 4.0 to 30.1 MPa. Similarly, to study the influence of mortar compressive strength, this parameter was changed from 2 to 20 MPa in 2 MPa increments . The corresponding predicted prism strengths ranged from 16.3 to 19.7 MPa. The input block tensile strength was also changed from 1.2 to 4 MPa in increments ofO.2 MPa to investigate the influence ofthe ratio ofblock tensile/compressive strength changing from 0.06 to 0.20. The predicted prism strengths ranged from 15.4 to 19.0 MPa.

To compare the ·relative significance of the influences of the above three parameters, the predicted results are plotted in nondimensional form in Figure 2. As shown in Figure 2, the compressive strength of concrete block prisms is dominated by the block compressive strength but is not directly proportional to it especially when the block is much stronger than the mortar. Figure 2 also indicates that the mortar strength is the second most significant influencing parameter on the prism strength, while the block tensile/compressive strength ratio has only a minor influence for block tensile strengths higher than 7% ofthe block compressive strength.

Before developing an equation to relate the prism strength to the block and mortar strengths, it is necessary to first investigate whether there is any interaction between the block and mortar strengths. The above analyses regarding the influence of mortar strength were repeated with the block compressive strength increased to 40 MPa. The computed prism strengths now ranged from 21.6 to 35.0 MPa. Therefore, there is some interaction between the mortar and block strengths with the influence ofmortar strength being more significant for stronger blocks.

PRISM STRENGTH EQUATION

Prism Strengths from Elastoplastic Analyses

Using the results of above analyses, Equation 1 was developed to approximate the predicted prism failure surface:

Dl

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where f 'm, fbc, and fma represent the compressive strengths of the prism, block coupon, and air cured mortar joint mortar ali tested between steel brush platens. The average ratio of the prism strengths computed using Equation 1 and the computer program predictions was 1.00 with a coefficient of variation of 5.0%. The good fit between the predicted prism strengths and those computed using Equation 1 is also shown in Figure 3.

Prism Strengths from the Literature

Equation 1 has been shown to closely approximate the prism strengths predicted by the elastoplastic finite element program for block compressive strengths ranging from 4 to 40 MPa and for mortar strengths ranging from 2 to 20 MPa. However, a more direct examination is to compare the calculated prism strengths from Equation 1 to the measured prism strengths reported in the literature.

Prism, block and mortar strengths for more than one thousand ungrouted concrete block prisms tested under concentric compression were collected from 27 published papers, theses and reports. Because many different specimen configurations and test conditions had been used, ali of the reported data were first converted to the more representative prism, block and mortar strengths using the corresponding ratios reported earlier in this paper. Then Equation 1 was used to calculate the adjusted prism strengths from the adjusted block and mortar strengths.

Using Equation I, the average ratio for the ca\culated to measured prism strengths was found to be 1.00 with the coefficient of variation of 12% for ali of these prisms. Although the perfect match of the average strength ratio is no doubt accidental, the c\ose agreement and relatively small coefficient of variation indicate clearly that Equation 1 can closely predict the collected numerous prism strengths. Because both the function form and the coefficients of Equation 1 are totally independent of the data for these prisms and depend solely on the predictions of the compute r program, the above results further verified the accuracy of the elastoplastic constitutive model incorporated into this computer programo

In judging the above degree of agreement, not too much is made of the exact average agreement beca use it must be understood that much of the prism data and block and morta r data is flawed to some extent. Different thickness of bearing plates, different capping materiaIs and configurations, different interpretations ofthe effective areas ofblocks and prisms and incomplete documentation of material properties and curing conditions will ali lead to some expected variation from the predicted strengths. The fact that the average strength ratio is close to unity and that the scatter is not too high provides confidence for using this relationship.

Although Equation 1 has been shown to give good predictions of prism strength, it is not Iikely to be suitable for daily use beca use ofthe block strength and the strength of air cured mortar joint mortar are for tests using brush platens . However, using the ratios reported for the Experimental Investigations, Equation 1 can be easily converted into Equation 2:

[2]

where f 'm still represents the compressive strength of ungrouted concrete block prisms without the effects of loading platen restraint but fb and fm are the block and morta r strengths as determined in accordance with the appropriate ASTM Standards2,3 . Using Equation 2, the average ratio for the calculated to measured prism strength is 0.99 with a coefficient ofvariation of 13% for ali of the above prisms. (The actual comparisons are shown in Figure 4.) Therefore, Equation 2 can be used to closely predict the strengths ofungrouted concrete block masonry.

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Prism Strength Predicted by Compute r Program (MPa) Measured Prism Strength (MPa)

Figure 3 Evaluation ofPrism Strengths Computed using Figure 4 Comparison ofPredicted and Measured Prism Strengths

Equation 1 (Acijusted to 5 Block High Prismsl

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CONCLUSIONS

The major conclusions drawn from the above discussion are:

1. Equations 1 or 2 can be used to closely predict the compressive strengths of ungrouted concrete block prisms using block and mortar strengths.

2. The elastoplastic finite element program can accurately model the mechanical behaviour of ungrouted concrete masonry.

3. The elastoplastic constitutive model can realistically model the material properties of masonry blocks and mortars.

ACKNOWLEDGEMENTS

This research was funded through operating grants from the Natural Sciences and Engineering Research Council of Canada and the Ontario Concrete Block Association. Mason's time made available through the Ontario Masonry Contractors Association and the Ontario Masonry Industry Promotion Fund, plus blocks supplied by the Ontario Concrete Block Association and member companies are gratefully acknowledged.

REFERENCES

1. Guo, P., "Investigation and Modelling of the Mechanical Properties of Masonry," Ph. D. thesis, McMaster University, Ontario, Canada, Feb. 1991, 388 pages.

2. ASTM Standard C140-75 (Reapproved 1988), "Standard Method of Sampling and Testing Concrete Masonry Units," Annual Book of ASTM Standards, Vol. 04.05,1990, pp. 87-89.

3. ASTM Standard C-I09-86, "Standard Test Method for Compressive Strength of Hydraulic Cement Mortars (Using 2-in or 5.0-mm Cube Specimens)," Annual Book of ASTM Standards, Vol. 04.01, 1986, pp. 74-79.

4. Guo, P. and Drysdale, R.G., "Stress-Strain Relationship for Hollow Concrete Block in Compress;on," Proc. 5th Canadian Masonry Symp., Vancouver, Canada, June 1989, pp. 599-608.

5. Chahine, G.N., "Behaviour Characteristics of Face Shell Mortared Block Masonry under Axial Compression," M. Eng. thesis, McMaster University, Ontario, Canada, 1989, 423 pages.

6. ACI-ASCE Committee 530, "Specifications for Masonry Structures (ACI 530.1-881ASCE 6-88)," ACI, Michigan, USA, 1988.

7. Canadian Standard Association, "Masonry Design for Buildings (CAN3-S304-M84)," CSA, Ontario, Canada, 1984, 69 pages.