Method for determining optimal content and slenderness ratio of fiber in compression cast fiber-reinforced concrete

A method for determining an optimal fiber content and fiber slenderness ratio in compression-cast fiber-reinforced concrete (CCFRC), comprising the following steps:

• step 1, selecting and fixing a fiber content and fiber slenderness ratio that meets a specification requirement;
• setting a first compressive stress, a pressurization amount, and a pressurizing time;
• pouring fresh concrete into a mold, and controlling, based on the first compressive stress and the pressurizing time, a pressurizing structure to apply a pressure on the concrete, to obtain a first average compressive strength of the concrete;
• determining a second compressive stress of the concrete based on the pressurization amount and the first compressive stress, pouring the fresh concrete into the mold, and controlling, based on the second compressive stress and the pressurizing time, the pressurizing structure to apply a pressure to the concrete, to obtain a second average compressive strength of the concrete, and by analogy to obtain an Nth average compressive strength, wherein in the process, a compressive stress that is correspondingly applied each time is gradually increased based on the pressurization amount, and when the Nth average compressive strength is less than an (N−1)th average compressive strength, stopping increasing the compressive stress, drawing a relationship curve of a compressive strength and the compressive stress of the CCFRC, and determining an optimal range of the compressive stress of the CCFRC;
• step 2, taking a fixed value within the optimal range of the compressive stress of the CCFRC in step 1 as an acceptable optimal compressive stress;
• applying the optimal compressive stress to the fresh concrete by compression casting, maintaining the optimal compressive stress for a specific period of time, and performing a uniaxial compression test after demolding and curing for a preset number of days, to obtain a mechanical property of the CCFRC under the optimal compressive stress;
• step 3, keeping the slenderness ratio of the fiber in step 1 and the optimal compressive stress in step 2 unchanged, decreasing or increasing the content of the fiber, keeping a content of another material unchanged, repeating step 2 to obtain a mechanical property of CCFRC with a different content of the fiber under the optimal compressive stress, drawing a relationship curve of average toughness and the content of the fiber in the CCFRC, to statistically determine an optimal range of the content of the fiber;
• step 4, keeping the content of the fiber in step 1 and the optimal compressive stress in step 2 unchanged, decreasing or increasing the slenderness ratio of the fiber, keeping the content of another material unchanged, and repeating step 2 to obtain a mechanical property of CCFRC with a different slenderness ratio under the optimal compressive stress, drawing a relationship curve of average toughness and the slenderness ratio of the fiber in the CCFRC, to statistically determine an optimal range of the slenderness ratio of the fiber;
• wherein step 1 comprises:
• first step, in the premise of meeting a national specification and standard, selecting and fixing a content and slenderness ratio of the fiber, determining a mix proportion of the CCFRC, and selecting a raw material required for preparation of the CCFRC, comprising a coarse aggregate, a fine aggregate, fiber, and cement;
• second step, in the premise of meeting a loading capacity of current compression casting equipment, setting an initial pre-compressive stress Sx=0, an initial step x=0, and an increment ΔS of a compressive stress applied each time;
• third step, preparing the CCFRC mixture, pouring the CCFRC mixture into the mold, pressurizing the CCFRC mixture to preset compressive stress by the pressurizing structure, removing an outer mold after maintaining the preset compressive stress for a first preset time, removing an inner mold after a second preset time, performing the uniaxial compression test on a specimen after standard curing of the CCFRC mixture for a third preset time, calculating an average compressive strength of three specimens in a same group, and denoting the average compressive strength as fx;
• if fx<fx−1, performing the fifth step;
• or if fx≥fx−1, performing the fourth step;
• fourth step, increasing the pre-compressive stress to Sx+ΔSx=x+1, and performing the second step;
• fifth step, obtaining a relationship curve of the average compressive strength fx and the pre-applied compressive stress Sx of the CCFRC, wherein x=0, 1, 2, . . . , n, determining a minimum value and a maximum value within the optimal range of the compressive stress based on the curve, wherein fo=fco represents a compressive strength of ordinary concrete, a compressive strength fct represents a designed minimum compressive strength of the CCFRC, when a compressive strength fa is greater than and closest to a designed compressive strength fct, a compressive stress Sa corresponding to the compressive strength fa is the minimum compressive stress in the optimal range, a compressive stress strength Sh corresponding to a compressive strength fh at a highest point is the maximum compressive stress in the optimal range, and when determining the selected content and slenderness ratio of the fiber in the first step, determining the optimal range of the compressive stress of the CCFRC;
• sixth step, repeating the second step to the fifth step with the same concrete material and mix proportion, in the premise that a content and slenderness ratio of the fiber is the same as those in the first step, if the optimal range of the compressive stress of the CCFRC is the same as that in the fifth step, determining a result, or if the optimum compressive stress range for the CCFRC is not the same as in the fifth step, repeat the second step to the sixth step until repeatable results are obtained;
• the step of determining an optimal range of a content of the fiber comprises:
• seventh step, on the basis of the optimal range of the compressive stress determined in the sixth step, selecting and fixing an integer compressive stress Sk within the range as the acceptable optimal compressive stress;
• eighth step, while the fixed slenderness ratio of the fiber is the same as that in the first step and i=0, setting an initial content of the fiber Pi=0%, and determining an addition increment ΔP of the fiber;
• ninth step, preparing the CCFRC mixture, pouring the CCFRC mixture into the mold, pressurizing the CCFRC mixture by the pressurizing structure to Sk, removing an outer mold after maintaining the preset compressive stress for a first preset time, removing an inner mold after a second preset time, performing the uniaxial compression test on a specimen after standard curing of the CCFRC mixture for a third preset time, calculating average toughness of three specimens in a same group, and denoting the average toughness as Ti, if Ti<Ti−1, performing the eleventh step, or if Ti≥Ti−1, performing the tenth step;
• tenth step, increasing the content of the fiber to Pi+ΔP, i=i+1, and performing the eighth step;
• eleventh step, in the premise that the fixed slenderness ratio of the fiber is the same as that in the first step, obtaining a relationship curve of average toughness Ti and the content of the fiber in the CCFRC under optimal compressive stress Sk, wherein i=0, 1, 2, . . . , n, determining a minimum value and a maximum value within an optimal range of the content of the fiber based on the curve, wherein To=Tco represents toughness of ordinary concrete, and toughness Tct represents designed minimum toughness of the CCFRC, when toughness Tg is greater than and closest to a designed toughness Tct, a content Pg of the fiber corresponding to the toughness Tg is the minimum content within the optimal range, and a content Pm of the fiber corresponding to toughness Tm at the highest point of the curve is the maximum content within the optimal range;
• and
• twelfth step, repeating the eighth step to the eleventh step with the same concrete material and mix proportion, if the minimum content and the maximum content of the fiber is within the optimal range and that is obtained based on the relationship curve of average toughness and the content of the fiber in the CCFRC are the same as those in the eleventh step, determining a result, or if the minimum content and the maximum content of the fiber that are within the optimal range and that are obtained based on the relationship curve of average toughness and the content of the fiber in the CCFRC are not the same as that in the eleventh step, repeating the eighth step to the twelfth step until that a reproducible result is obtained;
• the step of an optimal range of a slenderness ratio of the fiber comprises:
• seventh step, on the basis of the optimal range of the compressive stress determined in the sixth step, selecting and fixing the integer compressive stress Sk within the range as the optimal compressive stress;
• eighth step, while the content of the fiber is the same as that in the first step and e=0, setting an initial slenderness ratio of the fiber λe=0, and setting an increment Δλ=(le−le−1)/d, wherein l represents a length of the fiber, and d represents a diameter of the fiber;
• ninth step, preparing the CCFRC mixture, pouring the CCFRC mixture into the mold, pressurizing the CCFRC mixture by the pressurizing structure to Sk, and removing an outer mold after maintaining the preset compressive stress for a first preset time, removing an inner mold after a second preset time, performing the uniaxial compression test on a specimen after standard curing of the CCFRC mixture for a third preset time, calculating average toughness of three specimens in a same group, and denoting the average toughness as Te, if Te<Te−1, performing the eleventh step, or if Te≥Te−1, performing the tenth step;
• tenth step, increasing the slenderness ratio of the fiber to λe+Δλ, e=e+1, and performing eighth step;
• eleventh step, in the premise that the content of the fiber is the same as that in the first step, obtaining a relationship curve of average toughness Te and the slenderness ratio of the fiber in the CCFRC under the optimal compressive stress Sk, wherein e=0, 1, 2, . . . , n, determining a minimum value and a maximum value within the optimal range of the slenderness ratio of the fiber based on the curve, wherein To=Tco represents toughness of ordinary concrete, and toughness Tct represents designed minimum toughness of the CCFRC, when toughness Tj is greater than and closest to a designed toughness Tct, a slenderness ratio λj of the fiber corresponding to the toughness Tj is the minimum slenderness ratio within the optimal range, and a slenderness ratio λw corresponding to toughness Tw at the highest point of the curve is the maximum slenderness ratio within the optimal range;
• twelfth step, repeating the eighth step to the eleventh step with the same concrete material and mix proportion, if the minimum value and the maximum value within the optimal range of the slenderness ratio of the fiber that are obtained based on the relationship curve of average toughness and the content of the fiber in the CCFRC are the same as those in the eleventh step, determining a result, or if the minimum value and the maximum value within the optimal range of the slenderness ratio of the fiber that are obtained based on the relationship curve of average toughness and the content of the fiber in the CCFRC are not the same as those in the eleventh step, repeating the eighth step to the twelfth step until that a reproducible result is obtained;
• and finally determining ranges of an optimal content and slenderness ratio of the fiber to be added to the CCFRC under the optimal compressive stress.