## 1 Introduction  
Chemically inert quartz filler, a byproduct of the stone industry, has been increasingly utilized in the production of high-performance and ultra-high-performance concrete in recent years. Replacing a portion of cement with chemically inert quartz filler offers several advantages, such as reduced hydration heat and lower autogenous shrinkage.  
Additionally, it provides environmental benefits by decreasing the amount of cement needed for production.  
Recently, numerous experimental studies have explored the properties of concrete mixed with chemically inert quartz filler. [PERSON] et al. found that the fluidity of ultra-high-performance concrete could be improved by replacing silica fume with quartz powder [1]. [PERSON] and [PERSON] reported that increasing the quartz content from 20% to 30% resulted in minimal toughness improvement [2]. [PERSON] et al. found that the mechanical strength of ultra-high-performance concrete first increased and then decreased as the dosage of ultrafine quartz powder increased [3]. [PERSON] et al. observed that quartz filler could lower the hydration heat in cement and concrete [4]. [PERSON] et al. discovered that partially substituting cement with quartz filler caused only a slight reduction in strength in concrete with a low water-to-binder ratio [5].  
Compared to the numerous experimental studies described in the above paragraph, the theoretical research on hydration models is relatively limited. A hydration model is a fundamental tool for evaluating the properties of cement and concrete. Many hydration models have been developed for Portland cement [6]; these models calculate the reaction level and predict properties such as strength development, hydration heat, and hydration product formation. However, research on hydration models for blended cement is less common. Some models have been developed for other additives, such as fly ash [7], slag [8], epoxy latex blended cement [9], concrete affected by high temperatures [10], and silica fume [11].  
However, these models have limitations. Firstly, although experiments have demonstrated that adding chemically inert quartz filler primarily affects cement hydration through nucleation and dilution, no quantitative methods currently exist to model these effects. Additionally, existing models fail to separate the nucleation and dilution effects of quartz filler [12]. Secondly, most models focus on high-strength or ordinary-strength concrete, where the water-to-binder ratio typically exceeds 0.30. However, newer concrete technologies are developing materials with much lower water-to-binder ratios of around 20%, which are not adequately covered by most of the previous models. Finally, with the growing emphasis on reducing carbon emissions in the cement and concrete industry [13], most studies on low-carbon concrete have concentrated on how the cement substitution rate affects CO2 reduction. Other factors, such as the impact of the water-to-binder ratio on CO2 reduction, have been less studied [14].  
To address these gaps, this study presents a new model to predict the hydration heat, combined water, portlandite, and strength development in cement and concrete blended with chemically inert quartz filler. This new hydration model applies to a wide range of water-to-binder ratios and varying quartz contents; it separates the nucleation and dilution effects of the quartz filler and emphasizes the influence of the water-to-binder ratio on the design of low-carbon concrete. The author believes that this comprehensive study will support the use of chemically inert quartz filler in the concrete industry, thereby enhancing sustainable development and waste management in society.