Prediction of the rheological properties of mortar compounded with desert sand and Pisha sandstone ceramic sand based on density-form coupling

Abstract

Ordos, China has a large amount of environmentally hazardous Pisha sandstone and desert sand. Pisha sandstone ceramic sand and desert sand can be compounded to prepare light and fine aggregates, which are often used in construction mortar. However, it is unknown how the density and particle shapes of light and fine aggregates affect their rheological properties. In this study, we establish a predictive model for the rheological properties of light and fine aggregate mortar, using the Krieger-Dougherty and Chateau-Ovarlez-Trung models as a basis. First, density and particle morphology parameters are introduced and modified for light and fine aggregate mortars. Then, the morphological parameters of different types of fine aggregate particles were measured using image analysis techniques. This showed that the roundness of the particles decreases with decreasing density, and both the roughness and the aspect ratio increase. A regression model between the particle morphology parameters and characteristic viscosity was accordingly developed. The rheological properties of different types of mortars were examined. We find that as the particle density decreases, the yield stress and plastic viscosity decrease continuously, showing shear thickening behavior. Based on the coupled density-form effect, a modified Krieger-Dougherty model and Chateau-Ovarlez-Trung model are proposed. These proposed models result in more accurate predictions of plastic viscosity and yield stress for light and fine aggregate mortars.

Introduction

With the rapid development of the global economy and the acceleration of urbanization, there is increasing demand for natural river sand as a building material¹. The total amount of sand and gravel consumed globally exceeds 5 billion tons per year, and the vast majority of this is from river sand resources. Over-exploitation of river sand can lead to the destruction of river ecosystems and deterioration of water quality, and also exacerbates the potential for river bed siltation and diversion of river channels². This therefore poses a major challenges to ecosystems as well as to sustainable development. In order to respond effectively to this global challenge, alternatives to river sand resources that are green and sustainable are being explored. Currently, the main alternative resources for river sand are mechanism sand³, waste construction recycled aggregates⁴, mine tailings⁵, sea sand⁶, and others. However, each of these alternatives has certain limitations. For example, mechanism sand has a high content of stone dust, waste construction recycled aggregates are high in impurities, mine tailings contain chemically hazardous substances, and sea sand has higher salinity.

The Ordos region of China’s Inner Mongolia Autonomous Region has impressive reserves of coal, natural gas, natural alkali, kaolin, and other mineral resources⁷. It also has a desert area of about 54,000 square kilometers⁸, and the largest area of Pisha sandstone in China. Pisha sandstone is a loosely packed rock formation, which is highly susceptible to weathering and erosion⁹. These high levels of soil erosion cause damage to the regional ecosystem, and the situation been called an "ecological cancer of the Earth" by experts. This widespread soil erosion and resulting large desert areas pose a great challenge to the local economic construction and the sustainable energy development⁸. In recent years, the Chinese government and scientists have studied soil erosion and desertification control in Pisha sandstone areas^10,11. However, this has high costs in terms of human, material, and financial resources. For this massive unused and environmentally harmful resource, it is important to achieve its ecological governance, and find ways for it to be utilized; in this way there will be greater economic benefits than environmental alone¹². One idea in this line of thought has been adding biomass straw to Pisha sandstone. Another is to include Pisha sandstone in porous lightweight ceramic sand. Such sand can be prepared by ball milling, granulation, and calcination, and for smaller particle size intervals, it can be filled with desert sand. Pisha sandstone porous lightweight ceramic sand compounded with desert sand to forms an all-solid waste lightweight fine aggregate. This aggregate can then be used in a variety of building applications.

Lightweight aggregate mortar has the advantages of light weight, heat preservation, sound absorption, fire resistance, and others. It can be used for building roof insulation layers, wall insulation layers, and in filling materials¹³. With the goals of global energy conservation and emission reductions in mind, lightweight aggregate mortar has a wide range of applications prospects due to its multifunctionality and environmental friendliness. In engineering applications, it is usually used in construction pumping operations. Therefore, the flow characteristics of this freshly mixed aggregate cement mortar are important to understand for engineering applications. Flow characteristics of cement mortars can be accurately quantified using rheological concepts¹⁴. Rheological theory, first proposed in 1920, describes the flow and deformation of materials under stress¹⁵. But it was not until 1983 that Tattersall et al. proposed the Bingham model to characterize the rheological properties of cementitious materials, which is mainly used for describing rheological behavior in low-speed shear¹⁶. Afterwards, various models have been proposed from further research. One example is the Herschel-Bulkley model, which is used to describe the rheological behavior of cementitious materials with reduced water or other admixtures¹⁷. Another is the Casson model, which is used for describing suspensions at lower concentrations¹⁸. There is also the Cell model, which describes the rheological behavior of concrete with high aggregate content¹⁹. In cement mortars, the particles are considered to be rigid and suspended in a Newtonian fluid. Based on this assumption, scholars have proposed an improved Krieger-Dougherty model for the prediction of plastic viscosity²⁰, and an improved Chateau-Ovarlez-Trung model for predicting yield stresses²¹. In this model, the maximum volume fraction of aggregate and the characteristic viscosity are presented as two key indicators.

The rheological properties of cement mortars are influenced by the cement paste matrix, air bubbles, admixtures, and aggregates. Higher water-cement ratios increase the rheology of cement mortars. The addition of different types of admixtures can also significantly affect the rheological properties of cement mortars²². Investigating the effect of aggregate properties on the rheological properties of mortars is an important task; these properties typically include particle gradation, particle shape, water absorption, and particle density^23,24. Mahmoud studied the effect of different sand volume fractions on the rheological properties of mortar²⁵. It was shown that the flow behavior becomes non-Newtonian when the sand volume fraction exceeds 0.3. Moreover, the increase in sand volume fraction leads to an increase in rheological properties, plastic viscosity, and yield stress. The grading of the aggregate particles directly affects the volume fraction of the particles, thus changing the rheological properties of the mortar²⁶. The shape of the aggregate particles also affects the rheological properties of the mortar, which is expressed in the volume fraction as well as in the interaction forces between particles. The hydrodynamic interaction between aggregate particles and the slurry was considered by Tian et al. By studying the content and shape parameters of 12 fine aggregates, they developed a semi-quantitative modelling method for the relative plastic viscosity of mortars²⁷. The morphological parameters of different particles were evaluated using image processing techniques by Hafid et al., and the effect of these parameters on rheological properties was analyzed²⁸. However, most studies of particle shape parameters have focused on the effect on volume fraction. Few scholars have performed quantitative modelling of the relationship between characteristic viscosity and aggregate particle shape. When recycled fine aggregate is used in place of natural fine aggregate, water absorption is the main factor affecting its rheological properties. Ma et al. modified recycled aggregates with Na₂SiO₃ to reduce the water absorption of recycled fine aggregates²⁹.

The rheological properties of cement mortar with mechanism sand and recycled construction waste as recycled fine aggregate have also been studied. However, the densities of mechanism sand and natural river sand are relatively close to each other, and the effect of particle density can be neglected. This study addresses ceramic and desert sands as light and fine aggregates, and investigates the rheological properties of fresh mortar under the characteristics of low particle density and large pores. The effect of particle shape on rheological properties is also analyzed as influenced by artificial aggregates, based on the Krieger-Dougherty and Chateau-Ovarlez-Trung models. Accordingly, we establish a predictive model for the rheological properties of light and fine aggregate mortars under the coupled density-form effect.

Materials and test methods

Materials

Pisha sandstone samples were obtained from Xuejiawan, Jungar Banner, Ordos City, in the Inner Mongolia Autonomous Region of China. Pisha sandstone vitrified sand was then prepared in the laboratory. The preparation method is as follows: first, the Pisha sandstone is dried and ball-milled to an average particle size of 5.46 μm. Then the Pisha sandstone powder is doped with 32 mesh corn kernel stover powder with mass fractions of 5%, 10%, 15%, and 20%. Then it is put into a circular pot granulator for granulation, and Pisha sandstone ceramic sand embryos with different particle sizes are prepared. The prepared Pisha sandstone ceramic sand embryos were dried in an oven until they reached a constant weight. Then we put them into a KR-16C high temperature resistance furnace produced by the Luoyang Kere Company. The calcination temperature was set to 1125 °C. The rate of temperature increase was 20 °C/min, the constant temperature time was 30 min, and the rate of temperature decrease was 10 °C/min. After the temperature of the furnace body is lower than 800 °C, we turn off the muffle furnace to enable it to cool. A vibrating sieving machine is then used to screen ceramic sand particles of different grain sizes.

The desert sand was taken from the Kubuqi Desert in Inner Mongolia Autonomous Region, China. The cement used in this test was P.O42.5 ordinary silicate cement produced by Jidong Cement & Concrete Company. The chemical and physical properties are shown in Tables 1 and 2.The standard sand was China ISO standard sand (SS) produced by Xiamen Aisio Standard Sand Company. The water was tap water supplied by the laboratory.

Table1 Main ingredients and content of ordinary silicate cement.

Table2 Performance indicators of ordinary silicate cement.

To avoid the influence of the fine aggregate grade pair, the standard sand (SS) was sieved before the test. Its gradation interval sub-component sieve balance is shown in Table 3. Then the fine aggregate was mixed according to the standard sand gradation, to ensure that all the fine aggregates had the same gradation. Due to the small particle size of desert sand, it is mainly concentrated in the 0.1 mm to 0.5 mm interval. Pisha sandstone ceramic sand is made through artificial preparation of fine aggregate, and a particle size of less than 0.3 mm is not easy to prepare, resulting in a complex process. So in order to minimize the production cost, we made full use of the desert sand resources. Therefore, desert sand was used in the interval of 0.07 to 0.315 mm grain size, and Pisha sandstone ceramic sand was used in the interval of 0.315 to 5 mm. The compounded light and fine aggregates of Pisha sandstone ceramic sand and desert sand prepared with different straw admixtures were denoted by LS5, LS10, LS15, and LS20. The standard sand and compounded light and fine aggregates used in this test (with dry state packing density) are shown in Table 4. Before the test, the fine aggregate was moistened with water according to the water absorption rate to eliminate the effect of aggregate water absorption. The soaked aggregate was then used for mortar proportioning. In this test, the volume ratio of cement to fine aggregate was fixed at 1:3, and the water-cement ratio was 0.65. The mortar mixing ratio is shown in Table 5. The specimen preparation and testing process is shown in Fig. 1.

Table 3 Standard sand particle grading.

Table 4 Dry bulk density of fine aggregates.

Table 5 Mortar mixing ratios.

Fig. 1

Sample preparation and testing process.

Test methods

Rheological properties of mortar

The rheological properties were tested with an LBY-II cement mortar rheometer produced by Shanghai Rongji Da Instrument Technology Company. The shear stress and shear rate curves of each group of cement mortar were tested. The inner diameter of the rheometer container is 100 mm and its height is 110 mm. We choose a frame rotor with a rotor length of 70 mm and a height of 60 mm. The test procedure is shown in Fig. 2, and follows ASTM-D-2196-05. The rotor rotation speed is increased in steps from 0 to 100 rotations/min and then is reduced in steps from 100 rotations/min until stoppage. The procedure is the same for up and down ramping. The duration of each rotational process was 20 s. The data were collected at an interval of 1 s. The shear stress at each rotational speed was taken as the steady shear stress for that rotational speed. The stable shear stress at each rotational speed was taken as the shear stress for that shear rate.

Fig. 2

Procedure for testing rheological properties of cement mortar.

The Bingham model is the classic model for describing the rheological properties of cementitious materials. It assumes that the cement mortar needs to overcome an initial yield stress before it can flow. When the applied stress exceeds this yield stress, there is a linear relationship between the shear stress of the fluid and the shear rate. However, in their study it was found that as the shear rate increased, the shear stress and shear rate of some cementitious materials doped with efficient water reducing agents and nano-active substances gradually deviated from the linear relationship. The Herschel-Bulkley model was also proposed to characterize the rheological properties of cementitious materials³⁰. It has become one of the main models for studying the rheological properties of mortar and concrete materials.

In this study, the Bingham and Herschel-Bulkley models are used to fit the shear rate-shear stress curves for the descending phase of the rheometer loading procedure. The Bingham model expression is given below:

$$\tau = \tau_{0} + \eta \dot{\gamma }$$

(1)

where $\tau$ is the shear stress (Pa), $\tau_{0}$ is the yield stress of the mortar (Pa), $\eta$ is the plastic viscosity (Pa s), $\dot{\gamma }$ is the shear rate (s^-1).

The Herschel-Bulkley model expression is given below:

$$\tau = \tau_{0} + K\dot{\gamma }^{n}$$

(2)

where $\tau$ is the shear stress (Pa), $\tau_{0}$ is the yield stress of the mortar (Pa), $K$ is the consistency factor (Pa sⁿ), $\dot{\gamma }$ is the shear rate (s^-1), and n is the rheological index. For n = 1, the Herschel-Bulkley model evolves into the Bingham model. n > 1 is a shear-thickening fluid. n < 1 is a shear-thinning fluid³¹. The following formula was used to calculate the plastic viscosity of the mortar³²:

$$\eta = \frac{3K}{{n + 2}}\dot{\gamma }_{\max }^{n - 1}$$

(3)

Particle morphology measurement

Fifty samples each of various types of fine aggregates of different particle size intervals were randomly selected. In order to reduce the error, the mean value of the representative sample was used as the morphological parameter of the particles. In batches, they were randomly placed under a Leica Z16OPOA super depth of field 3D microscope for optical microscopy. The resulting images were processed and analysed using a LAMOS Series image analysis system. Binarization was performed by adjusting the image threshold range. In this way, different morphologies of sand particles were screened. Then, counting statistics were performed. The morphological parameters of different types of particles were obtained by computer processing.The particle images as well as the analytical processing are shown in Fig. 3. Particle roundness, roughness,and aspect ratio are the main factors affecting the rheological properties of mortar³³. The aspect ratio (L/D) is used to capture the overall shape of the particles,And Roundness (R_c) is used to capture how much the particles deviate from a perfect circle, and Roughness (R_a) is used to capture the degree of surface undulation or concavity of the particle. The particle characterization parameters are calculated as follows:

$$R_{{\text{c}}} = \frac{{R_{S}^{2} }}{4\pi A}$$

(4)

$$R_{a} = \frac{{R_{S} }}{{R_{{\text{o}}} }}$$

(5)

where R_s is the perimeter of the outer contour of the particle, R_o is the convex perimeter of the particle, and A is the area of the particle. Morphological parameters were evaluated for all particles in the single imaging range. The average values were taken as the characteristic parameters for different grain size intervals of the sand samples of the given type. The characteristics of the sand samples in different size intervals were weighted and averaged according to the grading curves of the fine aggregates. The results obtained are the characteristic parameters of the given type of sand samples.

Fig. 3

Schematic diagram of particle image and image processing.

Measurement of particle density and maximum volume fraction

In this study, the Chinese standard GB/T 14684-2022 "Sand for Construction" was used to determine the compact packing density ($\rho_{{\text{m}}}$). One specimen was taken and loaded into a volumetric cylinder in two times. After loading the first layer (about counting slightly higher than 1/2). At the bottom of the cylinder, place a 10 mm diameter round steel, press the cylinder, the left and right alternately hit the ground 25 times. Then loaded with the second layer, the second layer is filled with the same method of upturned, the bottom of the cylinder was padded steel direction perpendicular to the direction of the first layer. Then add the specimen until it exceeds the mouth of the cylinder. Then use a ruler to scrape along the cylinder mouth centre line to both sides. Weigh out the total mass of the sample and capacity (m₁), accurate to 1 g. Calculate the density of sand samples compacted according to the following equation:

$$\rho_{{\text{m}}} = \frac{{{\text{m}}_{1} - {\text{m}}_{{\text{j}}} }}{{V_{{\text{j}}} }}$$

(6)

where m_j is the mass of the cylinder, V_j is the volume of the cylinder.

The true density of fine aggregate was determined according to ASTM C128. A representative sand specimen of 500 g was taken and the specimen was dried in an oven at 110 °C until reaching a constant weight, then cooled to room temperature and set aside. The sand specimen was added to a specific gravity bottle filled with a mass of sand specimen m_s. Distilled water was then added to the specific gravity bottle using a funnel to ensure that the sand was completely wetted with water. We also use a degassing device to remove air bubbles. The specific gravity flask is placed in a thermostatic water bath, we maintain the temperature at 23 °C, and then we allow it to stand at a constant temperature for 24 h. Next, we remove the flask from the thermostatic bath, replenish it to the mark with distilled water, and dry the outside of the flask. The specific gravity bottle is then dried and weighed, and the total weight is recorded m₂. The true density of sand was calculated according to the following equation:

$$\rho_{{\text{t}}} = \frac{{{\text{m}}_{{\text{s}}} \times \rho_{{\text{w}}} }}{{{\text{m}}_{2} - {\text{m}}_{{\text{s}}} }}$$

(7)

where $\rho_{{\text{w}}}$ is the density of water at 23 °C, 0.99754 g/cm³. The maximum volume fraction of particles ($\varphi_{{\text{m}}}$) is the ratio of the compact packing density ($\rho_{{\text{m}}}$) to the true density ($\rho_{{\text{t}}}$).

Granular water absorption

Referring to ASTM C128 for requirements on the determination of water absorption of fine aggregates, approximately 500 g of fine aggregate was removed from a representative specimen. The specimen was dried in an oven at 110 °C until reaching a constant weight, cooled to room temperature, and set aside. The dry mass W_d was then weighed. Subsequently, the dried fine aggregate was immersed in water for 24 h to allow the aggregate to absorb water completely. The soaked fine aggregate was then drained of excess water and placed on a levelled surface. The free water on the surface of the aggregate was wiped off with a damp cloth to bring it to a saturated surface dry condition. We weigh the mass after water absorption and call it W_h. The water absorption of the aggregate is termed W_a and is calculated by the following equation:

$$W_{{\text{a}}} = \frac{{W_{{\text{d}}} - W_{{\text{h}}} }}{{W_{{\text{d}}} }}$$

(8)

Predictive modelling

• (1) Plastic viscosity

Prediction of the relative viscosity of mortar can be achieved by the Krieger-Dougherty model, where the slurry portion of the mortar is considered as the suspended phase and the sand particles are considered as rigid inclusions. The model is defined as follows:

$$\eta = \eta_{0} \left( {1 - \frac{\phi }{{\phi_{{\text{m}}} }}} \right)^{{ - \left[ \eta \right]\phi_{{\text{m}}} }}$$

(9)

where $\eta$ is the plastic viscosity of the mortar. $\eta_{0}$ is the plastic viscosity of the net mortar portion of the mortar, which was measured using a cement mortar rheometer. $\phi$ is the solid phase volume concentration of sand particles in the mortar. $\phi_{{\text{m}}}$ is the maximum volume concentration of solid phase particles.$\left[ \eta \right]$ is the intrinsic viscosity, a measure of the effect of individual particles on viscosity. For spherical particles it is usually taken as 2.5, for irregular particles such as non-spherical particles, the characteristic viscosity is usually influenced by particle shape parameters such as L/D ratio and sphericity³⁴.

• (2) Static yield stress

Recently, a theoretical model developed by Chateau-Ovarlez-Trung has been used to predict the evolution of the relative static yield stress. The distribution of particles in the suspended phase is assumed to be isotropic. This model is given below:

$$\frac{\tau }{{\tau_{0} }} = \sqrt {\frac{1 - \phi }{{\left( {1 - \phi /\phi_{{\text{m}}} } \right)^{{\left[ \eta \right]\phi_{{\text{m}}} }} }}}$$

(10)

where $\tau$ is the yield stress of the mortar. $\tau_{0}$ is the yield stress of the net mortar portion of the mortar.

In order to apply this model to Pisha sandstone ceramic sand and desert sand compound mortars containing different types of particles, the constant 2.5 is replaced by a fitting coefficient related to the characteristics of the particles $\left[ \eta \right]^{\prime }$. In this paper, this coefficient is referred to as the modified characteristic viscosity. Our modified version of the Chateau-Ovarlez-Trung model can be expressed as:

$$\frac{\tau }{{\tau_{0} }} = \sqrt {\frac{1 - \phi }{{\left( {1 - \phi /\phi_{{\text{m}}} } \right)^{{\left[ \eta \right]^{\prime } \phi_{{\text{m}}} }} }}}$$

(11)

Similarly, the modified characteristic viscosity was used in the Krieger-Dougherty model. The modified characteristic viscosity can be determined by nonlinear regression.

Results and discussion

Aggregate characteristics

Figure 4 shows the variation of water absorption of particles for different aggregate types. It can be seen that the water absorption rate shows a gradual increase as the particle type changes from SS to LS20. Standard sand particles have the lowest water absorption rate at 3.69%. In contrast, the LS20 sand particles had the highest water absorption rate at 21.63%. This represents an increase of 17.94% relative to standard sand. This indicates that the lower the density of light and fine aggregates, the higher the water absorption.

Fig. 4

Relationship between the variation of water absorption of particles with different aggregate types.

Table 6 shows the morphological parameters of different sand sample particles in different particle size intervals. The morphological parameters of different particles were weighted according to the mass share of each particle size interval. Figure 5 shows the trends of sphericity, roughness, and aspect ratio for five different standard sand particle types and compounded lightweight sand. The results show that the standard sand particles have higher sphericity and lower roughness than the compounded lightweight sand. This indicates that their shapes are close to spherical and have smooth surfaces. As the particle type of compounded lightweight sand gradually changes from LS5 to LS20, the roundness decreases significantly and the roughness increases gradually. This indicates that the particles become more irregular in shape and rougher on the surface, which is due to the increase in surface porosity. Meanwhile, the aspect ratio of LS5 particles is smaller, which is due to the artificial granulation process resulting in a relatively small aspect ratio. With the conversion of LS5 to LS20, the amount of surface defects on the particles increases, and the aspect ratio increases in parallel. The particle shape tends to be more elongated than uniform.

Table 6 Morphological parameters of particles of different types of sand samples.

Fig. 5

Trends of roundness, roughness and L/D ratio for different particle types.

In order to determine the characteristic viscosity of different types of mortar particles, tests were carried out using a rheometer. Existing studies have shown that when the aggregate volume fraction is low, the aggregation generated between particles can be reduced³⁵. This behavior has also been confirmed through field tests. When the water-cement ratio is less than 0.3, the net cement paste is more viscous. Moreover, the particles after rheological tests do not display the phenomenon of sinking. In order to minimize the effect of particle settling, different volume fractions of low concentration mortar suspensions ($\phi \le 0.35$) were selected for the test. Also, a higher concentration of cementitious net mortar was selected as the matrix (with a water-cement ratio of 0.3). According to previous studies, lower volume fractions of mortar suspensions are more consistent with the Bingham rheological model³⁶. We use the Bingham model to fit the experimental data and obtain the experimental yield stress. The Chateau-Ovarlez-Trung model was then used to predict the yield stress. The calculated characteristic viscosities for different volume fractions were averaged to obtain the characteristic viscosities of varying types of mortar particles.

To further analyse the relationship between the characteristic viscosity of particles and particle shape parameters, particle sphericity, roughness and aspect ratio were used as independent variables. The characteristic viscosity of the particles was used as the dependent variable. Multiple regression analysis was performed and the following model was established.

$$\left[ \eta \right]^{\prime } = \alpha + \beta_{1} R_{{\text{c}}} + \beta_{2} R_{{\text{a}}} + \beta_{3} \frac{L}{D}$$

(12)

where $\alpha$ is the intercept. $\beta_{1} ,\beta_{2} ,\beta_{3}$ is the correlation coefficient of particle roundness (R_c), roughness (R_a) and length to diameter ratio (L/D).

The regression results show that the model has a strong correlation, with a coefficient of determination R² of 0.9997. The regression coefficient of R_c was 123.57. Furthermroe, the p-value was 0.02694 (p < 0.05), indicating that roundness has a significant effect on characteristic viscosity. In addition, the regression coefficient of Ra was 153.85, with a p-value of 0.02558 (p < 0.05), indicating that roughness had a significant effect on the characteristic viscosity. The regression coefficient of L/D was -35.24, with a p-value of 0.03717 (p < 0.05), suggesting that the aspect ratio had a significant effect on the characteristic viscosity. The relationship between the characteristic viscosity of the particles and the particle shape parameters is thus derived as follows:

$$\left[ \eta \right]^{\prime } = - 210.05 + 123.57R_{{\text{c}}} + 153.85R_{{\text{a}}} - 35.24\frac{L}{D}$$

(13)

Rheological profile of cement mortar

Figure 6 shows the relationship between shear stress and shear rate for different tested mortar rheological properties. The Bingham model and Herschel-Bulkley model were used to fit the data. As can be seen from the figure, for the standard sand mortar samples, the experimental values follow the fitted curves of both models. In terms of R² values, the fits of both models are high, being 0.9985 (BingHam model) and 0.9971 (Herschel-Bulkley model). This demonstrates that both models describe the experimental data well.

Fig. 6

Rheological curves of different types of mortar.

The Herschel-Bulkley model fits better than the BingHam model for different types of lightweight aggregate mortars. This is especially noticable as the particle density decreases. The Herschel-Bulkley model therefore more accurately reflects the rheological properties of light and fine aggregate cement mortars.

The static yield stress and plastic viscosity derived from the fitted model decreased gradually as the density of the particles decreased. This may be due to the decrease in density of the light aggregate particles, which leads to a reduction in the mutual gravitational interaction between the low density particles. Accordingly, the material starts yielding and flowing at lower shear stresses, and shear yield stress and plastic viscosity both decrease.

In standard sand samples, the Herschel-Bulkley fitted model yielded a rheological index that converged to 1. The rheological index increased as the density of light and fine aggregate particles decreased. The shear stress and shear rate gradually deviated from a linear relationship, and the viscosity was low at low shear rates. However, the viscosity increases at high shear rate, and shear thickening behaviour is observable. This may be due to the decrease in density of the aggregate particles. At a low shear rate, the low density particles are relatively uniformly distributed in the fluid. But as the shear rate increases, the particles tend to concentrate in certain regions. Localized areas of high concentration are then formed, leading to an increase in the viscosity of the fluid.

Based on the fitted curves in Fig. 6 and Eqs. (1) - (3), the relevant parameters of the Bingham model and Herschel-Bulkley model were calculated as shown in Table 7. From the point of view of the fit, the Herschel-Bulkley model is more suitable for describing the rheological behaviour of lightweight aggregate cement mortar. Therefore, the rheological parameters derived from the Herschel-Bulkley model are analysed below.

Table 7 Fitting parameters of rheological model for different types of mortar.

Figure 7 demonstrates the relationship between the fine aggregate packing density and the yield stress and plastic viscosity of cement mortar. The yield stress gradually decreases with the decrease of fine aggregate packing density. When the stacking density of Pisha sandstone ceramic sand decreased from 1239.75 kg/m³ to 1100.41 kg/m³, the yield stress decreased from 480.45 Pa to 324.06 Pa. This corresponds to a decrease of 48.02% with respect to the standard sand specimen. Moreover, the plastic viscosity reduced from 7.43 to 1.43 Pa s, which is a decrease of 81.99% with respect to the standard sand specimen. This indicates that mortar is more prone to plastic deformation at low density. This is because high-density particles settle more easily in the mortar, increasing the internal friction and thus making it more difficult for the mortar to flow. Conversely, low-density particles enable the mortar to flow more easily.

Fig. 7

Variation of fine aggregate packing density with yield stress and plastic viscosity of cement mortar.

Prediction of rheological parameters

The Krieger-Dougherty model was used to predict the plastic viscosity of different types of mortar with high consistency. Figure 8 shows a comparison between predicted plastic viscosity and measured data. One can see that the plastic viscosity predicted by the Krieger-Dougherty model is larger than the measured value. This is especially true for the case of low-density particles. The main reason for this is the action of the low-density particles and their lighter mass, whereby the gravity and settling effects in the mixture are weaker. The interaction forces between such particles are relatively small, and so low-density particles tend to be more easily dispersed uniformly in the matrix. This results in lower friction and chance of contact between particles. It is likely that the model does not adequately account for the easier movement and rearrangement between particles, and thus overestimates the plastic viscosity.

Fig. 8

Plastic viscosity prediction model.

The Krieger-Dougherty model does not directly consider the effect of particle density. Therefore the Krieger-Dougherty model is modified based on the perspective of particle packing density. The modified plastic viscosity is a functional expression related to particle packing density.

$$\eta^{\prime} = f\left( {\rho ,\eta } \right)$$

(14)

Assume that $\rho_{{\text{g}}}$ is the particle density of the suspension.$\rho_{{0}}$ is the matrix density. Introduce the following correction factors $f_{\eta } \left( {\rho_{{\text{g}}} ,\rho_{{0}} } \right)$. We assume that the two correction factors can be expressed as some function of the ratio of particle density to matrix density.

$$f_{\eta } \left( {\rho_{{\text{g}}} ,\rho_{{0}} } \right) = \alpha \left( {\frac{{\rho_{{\text{g}}} }}{{\rho_{{0}} }}} \right)^{\beta }$$

(15)

Then the modified Krieger-Dougherty model can be expressed as the following equation:

$$\eta^{\prime} = \alpha \left( {\frac{{\rho_{{\text{g}}} }}{{\rho_{{0}} }}} \right)^{\beta } \eta_{0} \left( {1 - \frac{\phi }{{\phi_{{\text{m}}} }}} \right)^{{ - \left[ \eta \right]^{\prime } \phi_{{\text{m}}} }}$$

(16)

where $\alpha ,\beta$ is the empirical coefficient. The above data were fitted using nonlinear least squares. The best parameters of the model were obtained. The value of $\alpha$ was obtained as 0.0826 and the value of $\beta$ was 2.425. the fitted R² was 0.8181. Combined with the fitted model of particle shape parameters and characteristic viscosity above, the modified Krieger-Dougherty model with particle shape parameters can be derived:

$$\frac{{\eta^{\prime}}}{{\eta_{0} }} = 0.0826\left( {\frac{{\rho_{{\text{g}}} }}{{\rho_{{0}} }}} \right)^{2.425} \left( {1 - \frac{\phi }{{\phi_{{\text{m}}} }}} \right)^{{\left( {210.05 - 123.57R_{{\text{c}}} - 153.85R_{{\text{a}}} + 35.24\frac{L}{D}} \right)\phi_{{\text{m}}} }}$$

(17)

The Chateau-Ovarlez-Trung model was used to predict the yield stresses of different types of mortars at high concentrations. Figure 9 shows a comparison between the predicted yield stress and the measured data. From the figure, it is clear that the yield stress predicted by the Chateau-Ovarlez-Trung model is lower than the measured values, especially for higher density particles. The main reason for this is the higher mass, causing the gravity and settling effects in the mixture to be stronger. Also, the phenomenon of particle sedimentation occurs during the measurement process using the rheometer. That is to say, there is a large volume fraction difference between the upper and lower suspensions. Moreover, the model fails to fully consider the effect of settlement between particles on the yield stress, thus underestimating the yield stress. Therefore, the Chateau-Ovarlez-Trung model was corrected based on the perspective of particle packing density. The modified yield stress is expressed as a function of particle packing density.

$$\tau^{\prime} = f\left( {\rho ,\eta } \right)$$

(18)

Fig. 9

Yield stress prediction model.

Assume that $\rho_{{\text{g}}}$ is the particle density of the suspension.$\rho_{{0}}$ is the matrix density. Introduce the following correction factors $f_{\eta } \left( {\rho_{{\text{g}}} ,\rho_{{0}} } \right)$. We assume that these two correction factors can be expressed as some functional form of the ratio of particle density to matrix density. Same as Eq. (15). Then the modified Chateau-Ovarlez-Trung model can be expressed as

$$\frac{{\tau^{\prime}}}{{\tau_{0} }} = \alpha \left( {\frac{{\rho_{{\text{g}}} }}{{\rho_{{0}} }}} \right)^{\beta } \sqrt {\frac{1 - \phi }{{\left( {1 - \phi /\phi_{{\text{m}}} } \right)^{{\left[ \eta \right]^{\prime } \phi_{{\text{m}}} }} }}}$$

(19)

where $\alpha ,\beta$ is the empirical coefficient. The above data were fitted using nonlinear least squares. The best parameters of the model were obtained. The value of $\alpha$ was obtained as 4.42 and the value of $\beta$ was 1.09. the fitted R² was 0.9681. Combined with the fitted model of particle shape parameters and characteristic viscosity above, the modified Chateau-Ovarlez-Trung model with particle shape parameters can be derived:

$$\frac{{\tau^{\prime}}}{{\tau_{0} }} = 4.42\left( {\frac{{\rho_{{\text{g}}} }}{{\rho_{{0}} }}} \right)^{1.09} \sqrt {\frac{1 - \phi }{{\left( {1 - \phi /\phi_{{\text{m}}} } \right)^{{\left( { - 210.05 + 123.57R_{{\text{c}}} + 153.85R_{{\text{a}}} - 35.24\frac{L}{D}} \right)\phi_{{\text{m}}} }} }}}$$

(20)

Conclusions

Pisha sandstone ceramic sand and desert sand compounded light and fine aggregates have lower particle density and higher water absorption relative to standard sand aggregates. As the density of these aggregates decreases, it leads to a decrease in sphericity, an increase in roughness, and an increase in aspect ratio. A characteristic viscosity model based on morphological parameters was developed to describe this behavior.

It was found that as the particle density decreases, the static yield stress and plastic viscosity of the cement mortar gradually decrease. Also, the viscosity increases at high shear rates, showing shear thickening behavior. The Herschel-Bulkley model was more suitable for describing the rheological behavior of lightweight aggregate cement mortars than the Bingham model.

At high concentrations, variations in particle density lead to different degrees of aggregate settling. The coupled particle density-form effect was therefore considered, and modified Krieger-Dougherty and Chateau-Ovarlez-Trung models were proposed. We used these models to accurately predict the plastic viscosity and yield stress of lightweight aggregate mortars. This study may act as a reference for those using lightweight aggregate mortar in engineering applications.