2.1 Objective

The objective of this study is to propose reference compressive strength and diagonal compressive strength design values based on historical experimental information in accordance with the compressive strength of the mortar and components used.

2.2 Standardization of historical experimental data

A total of 13 experimental researches conducted between 2000 and 2016 were analyzed. Table 1 and Figure 6 show both a listing and the type of information obtained, as well as the origin of the units. The materials and dosages used in the preparation of the specimens were those commonly used in masonry construction in the different cities of the state (^{Caballero, 2016}).

Table 1 List of Experimental Researches (^{Caballero, 2016}) 

SCB: Solid Clay Brick, SCU: Solid Concrete Unit, HCB: Hollow Concrete Block

Figure 6 Origin of the masonry units (^{Caballero, 2016}) 

The data were standardized using the specially developed index card shown in Figure 7, where the physical-mechanical characteristics of the components (sand, mortar and units) and masonry (compressive strength in prisms and diagonal compression strength in masonry wallets) are shown. From the 13 consulted studies, 43 index cards similar to that in Figure 7 were prepared.MFrefers to the fineness module of sand,PVSS is the volumetric weight of loose dry sand,C _vr is the experimental coefficient of variation, C _vn is the standard coefficient of variation, f _j is the average compressive strength of mortar, f _j ^* is the compressive strength design value of the mortar, f _p is the average compressive strength of the unit, f _p ^* is the compressive strength design value of the unit, f _m is the average compressive strength of the masonry, and v _m is the average diagonal compressive strength of the masonry. The header of each index card has a serial number, the type of unit analyzed, the author and the year of the study.

In Figure 7, the first subscript of the coefficients indicates the type of specimen - mortar (j), unit (p), prism (m) and wallet (v) - and the second subscript indicates if it is experimental (r) or standard (n).

According to the information obtained, in most cases, the mortar was made with cement and sand, but it sometimes also contained lime. Thus, the volumetric mix ratio of mortar indicated in the index card has three parts, which correspond to the amounts of cement, lime and sand.

3.1 Average values of mechanical properties

According to regulations, the design strength of type I mortar is equal to or greater than 12.3 MPa. Equation 1 was used with 156 recorded data points across a variety of units to assess the compressive strength design value, which was found to be f _j ^* = 16.98 MPa. In this equation, C _j is the coefficient of variation that is greater than or equal to 0.20 (^{NTCDCM, 2004}). The average volumetric mix ratio for this strength was 1:0.05:2.82 (cement:lime:sand), and the historical experimental coefficient (C _jr ) was 21 %. Similarly, 77 data points were obtained from type II mortar, and the compressive strength design value was f _j ^* = 10.0 MPa with a coefficient of variation C _jr = 14 % (Figure 8).

Figure 8 Frequency Polygon of Compressive Strength for Mortar I and II 

Table 2 shows the design parameters of the mortar and the units obtained from a statistical analysis. The compressive strength and diagonal compressive strength design values could not be assessed due to the nature of the data, and thus, the variablesf _m1 ^** and v _m1 ^** were defined, respectively. In equation 1, the average value and the higher coefficient of variation (experimental or standard,C _p , C _j , C _m , C _v ) of the parameter under study were replaced. Because the data used here were from different test series over a 16 year period, it was necessary to use a proper evaluation criterion. For the compressive strength, a Colombian standard (NSR-98, 1998) proposes 70 % of the historical average value as the design value when there are between 10 and 30 results with a coefficient of variation lower than 30%. The parametersf _m2 ^** and v _m2 ^** shown in Table 2were obtained with this criterion.

Figures 9 and 10show the distribution of the diagonal compressive strength,v _m , of both mortars for each type of unit. The graphs also show the number of cases, the average values of the compressive strength of the joint (f _j ) and the unit (f _p ) and the mix ratio of the mortar. The experimental coefficients of variation with type I and II mortars were 23 % and 22 % in SCB, 21 % and 26 % in SCU, and 22 % and 24 % in HCB, respectively. The standard proposes a minimum value of 20 %.

Figure 9 Frequency Polygon of Diagonal Compressive Strength for Mortar I 

Figure 10 Diagonal Compressive Strength for Mortar II 

3.2 Comments

Table 3 shows the maximum diagonal compressive strength values measured. Each row was obtained by standardizing the available data, as in Figure 7. The maximum value, v _m1 ^** = 0.99 MPa, was obtained in SCB saturated for 24 hours and bonded with a type I mortar with a compressive strength f _j ^* of 14.92 MPa (case (2)). Case (3) had v _m1 ^** = 0.79 MPa, which was the maximum stress for the SCU bonded with a mortar with a compressive strength design value f _j ^* of 16.2 MPa, a compressive strength design value for the unit of f _p ^* = 3.1 MPa, and an absorption of 5 %. For HCB, the maximum value was v _m1 ^** = 0.40 MPa with a compressive strength design value of the mortar and the units of 9.34 MPa and 2.35 MPa, respectively (case (4)).

The thresholds of MF, fj*, fp*, absorption, and the diagonal compressive strength design (v _m ^* ) are defined in regulations. Additionally, the range of the fineness modulus of sand is between 1.75 and 2.83, in accordance with the grain size distribution (NMX-C-486-ONNCCE-2014, 2014). The orange cells indicate values below the regulatory standard, and the green cells indicate values that meet it.

The mortar and units used in case (1) and case (2) were the same, except that in case (1), the units were wetted just prior to preparing the samples instead of being saturated for 24 hours, which decreased the strength of case (2) by 50 %.

The relationship between the mixture of the components (aggregates, cement, and unit) that achieves an acceptable diagonal compressive strength is complex; there were at least four mechanical-physical variables to assess in addition to the construction quality of the wallets and controlling the tests. The first variable was the fineness modulus (MF) of the sand, the next two were the compressive strength design values of the mortar (f _j ^* ) and of the unit (f _p ^* ), and the last variable was the absorption of the unit. In the first row, the four variables were within the standardized limits, whereas in the second row, the strength of the unit was lower than the standard value; in both cases the diagonal compressive strength design value (v _m ^* ) was not met. This strength was met in the third row, but only 3 of the 4 variables were in compliance. In the sixth row, all the parameters were met, while in the last two rows, only one of four parameters met the standard; however, in both cases, the regulatory value was reached.

There were five cases using SCU. In four of them, two variables met the requirements, and in the remaining case, only one variable did not meet the requirements; for all five cases, the desired value of v _m ^* was reached. Finally, only the HCB with type II mortar met the desired strength.

According to these results, increases in the compressive strength of the mortar used with SCB did not significantly increase the diagonal compressive strength of the masonry, and consequently, a type II mortar can be used in place of a type I mortar. For the case of HCB, a higher strength is achieved with type II mortar, as shown in Table 2.

Although it was possible to obtain diagonal compressive strength design values that were higher than the regulatory values without complying with three of the four variables measured, a question remains: What is the maximum value that can be obtained with adequate quality control of materials and procedures? Furthermore, there is historical experimental evidence that the diagonal compressive strength (case (2), Table 3) increases when SCB are in water for 24 hours, yet here, it decreased by 50 % when the units were soaked before being bonded; therefore the advantages of this process are questioned. It should be mentioned that the Colombian Code specifies pre-moistening times as a function of masonry unit absorption (^{NTC 4205, 2000}).

3.3 Comparison of the results

As stated above, the information processed in this study corresponds to 43 test series conducted over the course of 16 years. For that reason, the values cannot be accepted as the compression and diagonal compression design parameters, and thus, the variablesf _j1 ^** and v _m1 ^** were defined, which are not significantly different from other tests conducted in Mexico. These tests were performed by ^{De la Cruz and Silva (2002)} on SCU from Colima, ^{De Gante et al. (2002)} on SCB From Puebla, ^{Ruiz and Carboney (2006)} on SCB from Tuxtla Gutiérrez, ^{Fernández et al. (2009)} on HCB from Merida, Mendoza-Pérez et al. (2011) on SCB from Queretaro, and ^{Tena et al. (2017)} on SCU from the Valley of Mexico. In the case of diagonal compression, the calculated values were within 0.20-0.55 MPa and were similar to those referenced. It should be noted that the highest strength was recorded in Puebla (1.4 MPa). Most compressive strength values, including the calculated ones, were lower than 3.0 MPa, and only four were higher, as shown in Figures 11a and 11b.

Figure 11 a) Diagonal Compressive Strength, b) Compressive strength 

Additionally, due to the historical nature of the data, the equation proposed in the Colombian Code was used, but the calculated variables f _m2 ^** and v _m2 ^** were slightly higher than the values off _m1 ^** and v _m1 ^** , respectively.

An additional comparison factor is the ratio of experimental coefficients of variation to the standard coefficients of the two variables studied (compression and diagonal compression). Figure 12a shows this relationship for four additional cases. For the calculated values, there are two test series with greater dispersion, while another has the same level (^{Aguilar and Alcocer, 2014}), and two have less dispersion. Two cases have similar dispersions in their compressive strengths, while in the remaining two, the dispersion is reduced (Figure 12b).

Figure 12 Ratio of experimental coefficients of variation to the standard values: a) Diagonal Compressive Strength, b) Compressive Strength