Fluidity and strength are two important performance indicators of concrete. The fluidity of concrete is not only directly related to the efficiency and quality of concrete construction, but also has an important impact on the volume stability and durability of concrete. The strength of concrete is directly related to the safety, applicability and durability of concrete. Therefore, improving and enhancing the workability and strength of concrete has always been an important topic in the research of concrete materials. In order to improve and enhance the workability and strength of concrete, measures such as high-efficiency superplasticizer, reducing water-glue ratio, and rational use of rubber and mineral admixtures can be used. In addition, it is necessary to optimize the aggregate gradation and its mixing, especially with the continuous reduction of natural river sand resources, the demand for the application of solid waste resources such as tailings in concrete is getting higher and higher, and the research on aggregate mixing optimization is becoming more and more important.
The design methods of concrete mix ratio in China's current specifications are mass method and volume method, and fineness modulus and grading area are mainly used to evaluate the gradation of fine aggregates. However, there are deficiencies in the actual use of the current specification: the fineness modulus can be used as an index to characterize the thickness of fine aggregates, but it cannot reflect the real situation of particle gradation; For the grading area, practical experience has also proved that not all aggregates that fall into the classification area recommended by the code meet the requirements for use, and those that are out of scope are not all unusable. The current code does not take into account the mutual filling effect between coarse and fine aggregates, and fails to consider the overall aggregate grading and optimization perspective. 1. Aggregate gradation optimizationIn the concrete composition materials, the aggregate volume accounts for about 70% of the total volume, and the rest of the volume contains cement slurry and air. Before the mixture hardens, the cement slurry plays a lubricating role, so that the mixture has a certain plasticity. After the mixture hardens, the cement slurry plays the role of cementing the aggregate and filling, while the aggregate plays the role of the skeleton, transmitting stress, and maintaining the good volume stability and high durability of the concrete. The quality of the aggregate gradation will also affect the workability of the concrete mixture. From the perspective of the composition of the mixture, the key factor affecting workability is the gradation of the aggregate. If the particle size distribution of coarse and fine aggregates is too different and the intermediate size is missing, the mixture is easy to stratify; If the fine aggregate is too small, the pores of the coarse aggregate will not be filled, resulting in increased friction between aggregates and poor workability. At present, the most commonly used grading theories mainly include the maximum density curve theory and the particle interference theory, which are based on the purpose of achieving the maximum density after mixing aggregates with different particle sizes. Among them, the former mainly describes the particle size distribution of continuous gradation, which is used to calculate continuous gradation; The latter can be used to calculate both continuous and intermittent gradations. 1.1. Maximum density curveThe theoretical maximum density curve is a theoretical curve based on a large number of experimental data. In 1907, Fuller and Thompson mixed solid particles of different particle sizes according to a certain ratio, and theoretically obtained a mixed aggregate with the highest density and the smallest void. Its maximum density curve can be expressed by the following formula
The main purpose of bolomey is also to require the aggregate to achieve the minimum porosity, but this method is not to reduce the void volume to the minimum, in addition to the minimum void volume, it should also contain the surplus volume of cement slurry, which is mainly to ensure that there is sufficient slurry surrounded on the surface of the aggregate to play a lubricating role, and improve the workability, transportation and pumping performance of the concrete mixture. In 1923, Talbot and Ichart argued that the Fuller curve was too idealistic, and that the maximum density would actually fluctuate within a certain range, so they thought that the exponent should not be 05 constants, but should be variables. So change the fuller maximum density curve to the general form of the nth power,
For spherical aggregates, when n=0The maximum density of the mixed aggregate is obtained at 5, and the n value for the crushed stone aggregate is about 04 to get the maximum density. For asphalt concrete, when n=0At 45, the densest mixed aggregate can be obtained, and then the highest strength concrete can be mixed. 1.2. Aggregate optimization methodIn 1990, in order to obtain a well-graded mixed aggregate, including fine aggregate, intermediate aggregate and coarse aggregate, the roughness factor (COARSE FACTOR, CF) was obtained according to the aggregate statistics in different regions. This method only requires knowledge of aggregate size distribution, as described by the U.S. Department of Transportation and the American Concrete Institute in the Concrete Slab Design Guidelines (ACI 302.).1 04). The CF table takes the CF value as the abscissa and the workability factor (WF) as the ordinate, and divides the landing point into 5 areas, each of which corresponds to different workability requirements and uses of concrete, as shown in Figure 1. Among them, the interval fault gradation, the zone is suitable for ready-mixed concrete with a maximum particle size of 20 40mm, and the zone is suitable for ready-mixed concrete with a maximum particle size of less than 20mm, the viscosity of the zone is large, and the zone is dry and hard, and it is difficult to compact. 
For ready-mixed concrete, a reasonable optimization interval is Zone II. The boundary points of Zone II are (75, 285)，(75，39)，(45，43.5)，(45，33)。According to the cf and wf values of the boundary points and equations (4) and (5), the percentage of various particle size ranges in the aggregate can be calculated, the aggregate gradation curve corresponding to the cut-off point can be obtained, and the range of the sub-counting screening percentage of the aggregate particle size of interval II can be obtained, as shown in Figure 2. 
The coarse aggregate used in the test is ordinary gravel, the fine aggregate is natural river sand, and after the coarse and fine aggregates are mixed, the gradation of the overall aggregate should be within the interval shown in Figure 2, 0The sieve allowance range of 16mm sieve particle size is 15% 5%, sieve allowance range on sieves with the largest pore size 4% 12%, 03mm and 0The sieve allowance range of 8% to 15% for 6mm sieve holes and 8% to 22% for the rest of the sieve levels is consistent with the recommendations of ACI 302 for the distribution of aggregates at all levels of concrete. As can be seen from Figure 2, the percentages of smaller and larger particles are smaller in the aggregate gradation corresponding to interval II, while the percentage of each particle size range in the intermediate particle size is relatively uniform, larger than that of both large and small particle sizes. This shows that the aggregates are filled with each other to achieve the minimum porosity and the maximum bulk density, which is actually the theoretical basis of the reasonable interval of CF WF. In order to further analyze and prove the relationship between the reasonable interval of CF WF and the void ratio and bulk density of aggregates, this paper first analyzes the changes of the void ratio and bulk density of various aggregates with CF and WF. On this basis, the variation of strength and workability with CF and WF was analyzed. 2. Analysis of the influence of WF and CF on the porosity of aggregatesTable 1 is to prepare different aggregate systems according to different CF WF values, that is, different aggregate gradations, and measure their porosity and bulk density. Figure 3-6 shows the change of aggregate void ratio with CF and WF. 
As can be seen from Table 1, with the increase of WF and the decrease of CF, the porosity decreases and the bulk density increases. The difference between the maximum and minimum porosity is about 5%, and the bulk density difference is about 200kg m3. It can be seen from the figure that when the WF is 35 45 and the CF is 70 85, the size particles fill each other better, and the void ratio of the aggregate is relatively small, about 20%. Compared with the reasonable interval II in Fig. 1, the area with small porosity is basically consistent with the II region, indicating that the reasonable interval of CF WF is the interval with the smallest porosity and the largest bulk density, that is, the reasonable interval of CF WF is the interval in which aggregates are filled with each other to achieve the maximum density optimization. Figure 5 shows the relationship between porosity and bulk density. 3. The influence of aggregate porosity and water-glue ratio on slump was optimized by the above method, and then concrete with different strength grades and different water-glue ratios was prepared, and the effects of CF and WF on strength and slump were experimentally studied. The strength of the trial concrete is C35, C40 and C45, and the water-glue ratio is respectively. 36。When the value of (cf,wf) is in the zone, the concrete mixture does not appear to be segregated and leaked, and the workability of the concrete mixture is better at this time. According to the "Standard for Test Methods for the Performance of Ordinary Concrete Mixtures" (GB T50080-2002), the slump (SL) is determined, see Table 2. Draw the slump of the concrete mixture with the porosity, as shown in Figure 7. 
As can be seen from Table 2, with the increase of WF and the decrease of CF, the porosity decreases, and the slump of concrete of each strength grade increases. The results show that the slump increases with the decrease of aggregate porosity under other conditions. That is, the greater the bulk density of the aggregate, the smaller the voids, and the better the fluidity of the concrete mixture. When the void ratio is about 20% to 21%, the slump does not change much. That is, from the perspective of the fluidity of the mixture, when the porosity is maintained at about 20% to 21%, good fluidity can be obtained. From the comparison of the slump bar diagram in Fig. 7, the lower the strength of the concrete, the smaller the slump, and the less easy it is to obtain better fluidity under the condition that the aggregate void ratio is the same. Because the fluidity of concrete mixture is not only related to aggregate gradation, but also related to factors such as water-glue ratio and slurry-bone ratio. For concrete with low strength, due to the relatively small slurry-to-bone ratio, the contribution of slurry to fluidity is small, the aggregate has a greater impact on workability, and when the void is large, the fluidity is worse. Therefore, from the perspective of fluidity, the fluidity of the mixture of concrete with low strength is more dependent on aggregate and requires smaller porosity. In the case of the same void ratio, the smaller the water-glue ratio, the larger the pulp-bone ratio, and the better the fluidity. 4. The effect of aggregate porosity on the strength of concrete
Table 3 and Fig. 8 13 show the experimental results of strength as a function of aggregate porosity. From the experimental results, it can be seen that the measured strength of the same mix ratio increases with the decrease of porosity, whether it is 7d or 28d. That is, under the same mix ratio, the porosity of the aggregate is different, and its strength will also change. Therefore, good aggregate gradation not only has an effect on improving the workability of concrete, but also on improving the strength of concrete. Moreover, for the concrete with relatively low strength, reducing the porosity of the aggregate has a more obvious effect on improving the strength of the concrete. 5ConclusionWith the increase of WF and the decrease of CF, the porosity decreases and the bulk density increases. In the optimization interval II, the aggregate void ratio is the smallest, and the bulk density is the largest. That is, in the II zone, the aggregates are filled with each other to achieve the maximum density. Under the condition that other conditions remain constant, the greater the bulk density of the aggregate, the smaller the void, and the better the fluidity of the concrete mixture. For concrete with low strength, due to the relatively small slurry-to-bone ratio, the contribution of slurry to fluidity is small, the aggregate has a greater impact on workability, and when the void is large, the fluidity is worse. Therefore, from the perspective of fluidity, the fluidity of the mixture of concrete with low strength is more dependent on aggregate and requires smaller porosity. In the case of the same void ratio, the smaller the water-glue ratio, the larger the pulp-bone ratio, and the better the fluidity. Under the same mix ratio, the porosity of the aggregate is different, and its strength will also change. Good aggregate grading not only has an effect on improving the workability of concrete, but also has an effect on improving the strength of concrete. Moreover, for the concrete with relatively low strength, reducing the porosity of the aggregate has a more obvious effect on improving the strength of the concrete.