In this study, we used ordinary Portland cement (OPC) meeting the specifications of MS522 part 1:2003 (16), with compressive strengths of 36 MPa at 7 days and 48 MPa at 28 days. The specific gravity and specific surface area of the OPC used were 3.14 and 3510 cm²/g, respectively. The chemical properties of the OPC are shown in Table 1. For all mixtures, we used local mining sand with a fineness modulus of 2.6, saturated-surface-dry (SSD) specific gravity of 2.55, water absorption of 1.5% and maximum particle size of 4.75 mm. The grading of the sand used is shown in Figure 1.

Seven different mixes were prepared, each with a different cement-to-sand (C/S) ratio (1:2, 1:3, 1:4, 1:5, 1:6, 1:7 and 1:8) and good workability (flow of 190 ± 5 mm). This range of C/S ratios was selected as these are the most commonly found in mortars used in practice and other research. The proportions for all mixes are shown in Table 2. As can be seen from the table, the W/C ratio of mortars with a lower cement content was higher. This is due to the need to ensure equivalent workability for all mixes.

A cylinder with a diameter of 100 mm and a height of 200 mm was cast for the thermal conductivity, specific heat capacity and porosity tests. A cube with dimensions 100 mm × 100 mm × 100 mm was prepared for use in the density, compressive strength and water absorption tests. The samples were removed from the moulds after 24 h. The specimens were cured in normal water with a temperature of 23 ± 3 °C until reaching testing age. All properties were evaluated at 28 days of curing, except compressive strength which was measured at both 7 and 28 days.

In this study, we tried to prepare the mixtures with an approximate fixed workability. For this reason, the W/C ratio varied depending on the cement-to-sand ratio (from 1:2 to 1:8). The workability of fresh mortar was evaluated using the flow table test according to ASTM C 1437-1 (17). The truncated cone was filled with fresh mortar in three layers, each tamped 20 times with a tamping rod. Next, the mould was lifted away and 25 strokes were applied to the table over 15 seconds (Figure 2). Finally, the change in mortar diameter was measured in three directions. The average diameter was reported as mortar flow in Table 2.

At 28 days, three cylindrical specimens (100 mm x 200 mm) were selected to measure thermal conductivity. The samples were dried in an oven at 105 °C for 24 h to remove all moisture. The k-value of the specimens was determined with a KD2-PRO analyser using a TR1 needle. A TR1 sensor (2.4 mm in diameter and 100 mm in length) is capable of measuring thermal conductivity in the range of 0.1 W/(m·K) to 4 W/(m·K) (18). A pilot pin was inserted to the uncured specimens to produce a hole matching the size of the TR1 sensor. The sensor’s relatively long read times (10 minutes for each reading at 15-minute intervals) help minimise errors associated with the large-diameter needle. The contact between needle and specimen was guaranteed by applying thermal grease to the hole (Figure 3).

The KD2-PRO analyser works by heating the needle for a certain period of time (t_h) and monitoring the temperature during heating and cooling. The temperature during heating and cooling is calculated using Equation [1] and Equation [2], respectively (18):

Where m₀ and m₁ are the initial temperature, m₂ is the rate of background temperature drift and m₃ is the gradient of a line relating temperature rise to logarithm of temperature.

Consequently, thermal conductivity can be calculated using the following Equation [3] based on heat flux (q):

The influence of ambient temperature and humidity on the samples should be kept to a minimum, in order to achieve a more accurate value while using the KD2-PRO. Therefore, the specimens were wrapped in a plastic sheet to minimise the effect of ambient moisture and keep the sample in a dry condition.

The specific heat capacity of cement mortar in dry conditions can be calculated using the law of mixtures. Given a well-hydrated sample, the law of mixtures is a reasonable predictor for the heat capacity of mortar, and accounts for both the ‘bound water’ and ‘physical water’ heat capacity (19). This Equation [4] is based on the specific heat capacity of a mixture as a function of its composition (20):

Where C_p is the specific heat of mixture (kJ/kg.K), C_pi is the specific heat of each component and F_i is the weight fraction of each component.

Differential scanning calorimetry (DSC) at a heating rate of 10 °C/min was used to measure the specific heat of cement and sand. The specific heat capacity of water is 4.18 (kJ/kg·K) in 23 °C. The measured specific heat capacity of cement and sand in the range of 20°C to 50 °C is shown in Figure 4. However, the specific heat capacity of bounded water for hydration as a gel product is 2.2 (kJ/kg·K) (21). The total amount of chemical and physical bound water for the hydration of cement is 0.42 grams per gram of cement. The remainder is solely to improve the workability of the mortar and is vaporised when the mortar is dried (22).

The following Equation [5] was used to calculate thermal diffusivity:

Where α is thermal diffusivity (m²/s), k is the thermal conductivity of a material (W/m·K), ρ is density (kg/m³) and C is specific heat (J/kg·K).

A compressive strength test was carried out on 100-mm³ cubic specimens. Like the cylindrical specimens, the cubic specimens were cured in water and tested at the ages of 7 and 28 days. A water-absorption test was also carried out on the 100-mm³ cubic samples at the age of 28 days. The specimens were dried in an oven for 24 h prior to the test. The initial and final water absorption of the specimen were determined after full immersion in water for 30 min and 72 h, respectively.

The porosity test was carried out on three cylindrical specimens, each with a diameter of 100 mm and a height of 200 mm, after 28 days of curing. One piece 5 cm thick was cut from each sample. Next, the samples were dried in an oven at 105 °C for 24 h to remove moisture. The vacuumed samples were then filled with water. The amount of water held by the sample is a measure of its porosity, as follows (23):

Where P is porosity (%), m_a is oven-dry weight (kg) and m_b is saturated surface dry weight (kg).

Figure 5 shows the compressive strength of cement mortars containing different C/S ratios at the ages of 7 and 28 days. As expected, sample M1:2 had the highest strength with values of 47.7 MPa and 60.2 MPa, and sample M1:8 had the lowest compressive strength at 4.4 MPa and 6.4 MPa. The compressive strength of the mortars was reduced by decreasing the C/S ratio in mixtures with the same workability. The 28-day compressive strength of mix M1:8 is about 89% lower than M1:2. This mix is classified as type N as per ASTM C270 (24), which shows that it can be used in external and internal load-bearing walls.

Table 3 shows the measured thermal conductivity, specific heat capacity and calculated thermal diffusivity of each cement mortar.

The k-value indicates the cement mortar’s capacity for steady-state conduction heat transfer. Low thermal conductivity results in good thermal performance, indicating that the mortar is suitable for use as a heat-resistant material. As can be seen from Table 3, with the exception of the mortar with a cement-to-sand ratio of 1:3, the k-value declines as the cement-to-sand ratio (C/S) is decreased. Moreover, M1:8 has the lowest k-value, about 45% lower than mix M1:2. However, M1:3shows the highest k-value of all the mortars.

The k-value for M1:3is greater than for M1:2despite its higher water-to-cement ratio (W/C) and its lower cement-to-sand ratio (C/S). This may be related to the different proportions of cement and sand in each mix. The larger amount of sand in M1:3 in comparison with M1:2reduces the potential porosity between cement and sand and results in homogenous slurry. In addition, Mix M1:2, with a higher cement content (about 31%) and lower W/C ratio (16%), is a stickier mixture in its fresh state compared to mix M1:3. This means that given the same vibration method and time, more trapped air will remain inside the mixture, which can be seen in the porosity test results of the hardened mortars (Table 3).

As can be seen from Table 2, mixes with a W/C ratio of M1:4to M1:8score significantly higher than mix M1:2. As mentioned in the research methodology section, extra water is required to maintain a high workability similar to mix M1:2. Consequently, this extra water creates more porosities inside the mixture, and higher porosity results in a lower k-value.

The heat capacity (C-value) of cement mortar indicates its capacity to store heat. Mortar with a high C-value is not affected by sudden changes in temperature. M1:8, with a C-value of around 0.87 kJ/kg·K, has the lowest specific heat capacity of all mortar types tested. The highest C-value was for mix M1:2,at around 20% greater than that of mix M1:8_.

The thermal diffusivity of a cement mortar indicates its transient heat conductivity. Cement mortars with low thermal diffusivity are considered heat insulators in transient heat transfer conditions. The thermal diffusivity of M1:3is greater than those of the other mortars due to its higher k-value. M1:8has the lowest thermal diffusivity, at around 30% lower than M1:3.

Knowing the thermal properties of cement mortar is essential for analysing energy consumption in buildings. To measure thermal properties, special tools are required. Preparing the samples correctly, setting up the test and the testing procedure itself take time. Therefore, using equations to predict the thermal properties of cement mortar is essential to save time and costs. The high coefficient of determination (R²) shows the strength of the correlation (25). Most relationships reported in the literature are between the thermal conductivity and density of cement-based materials, and there are very few existing equations to predict thermal conductivity based on the other physical and mechanical properties of the material. In addition, there is little information about the thermal diffusivity of cement-based materials, and very few predictive models. The following sections present the relationship between thermal conductivity and thermal diffusivity and certain physical/mechanical properties of cement mortar, such as oven-dry density, compressive strength, water absorption and porosity.