Influence of curing time on impact energy absorption characteristics of artificially cemented sand

2.1. Preparation of artificially cemented sand specimens

In three-dimensional geomechanical model experiment, the proportion and type of similar materials are determined by Froude’s similarity law and basic physical mechanical properties of deep rock. Generally, similar materials give first priority to raw materials with abundant source and low price. Artificially cemented sand is such a similar material which is made by sand, Portland cement, gypsum and water [13]. The mass ratio of sand, composite Portland cement (P.C 32.5), gypsum and water is 1:0.13:0.05:0.10. In order to improve the precision and accuracy of the experiment, fine sand with diameter less than 1.18 mm is adopted. After mixing them according to designed proportion, the mixture is put into mould with a certain pressure. The mould are removed after 24 hours and artificially cemented sand specimens are cured with a thin plastic film cover.

Former research indicates that when length-diameter ratio of specimen is about 0.5, both the inertial effect and the frictional effect in impact uniaxial compression tests will reach its minimum value [14]. In impact uniaxial compression tests, artificially cemented sand specimens are manufactured into disc specimens. Its diameter is 37 mm and its length is 19 mm. Artificially cemented sand specimens in disc shape are shown in Fig. 1. The end faces of artificially cemented sand specimens should be flat. The deviation of two parallel end faces should be controlled within 0.05 mm and the deviation of end face flatness should be controlled within 0.02 mm.

Fig. 1Artificially cemented sand specimens

During three-dimensional geomechanical model experiment, relatively long loading stage should be proceeded when the strength of artificially cemented sand is in an essentially constant period. Considering the strength growth curve of composite Portland cement and reasonable cycle time of geomechanical model experiments, three curing times, 7 days, 14 days, and 21 days, are chosen. After curing 7 days, 14 days, and 21 days, the static uniaxial compressive strength of artificially cemented sand specimens are 3.65 MPa, 4.79 MPa, and 5.28 MPa, respectively. And their elastic wave velocities are 2117 m/s, 2355 m/s, and 2407 m/s, respectively.

2.2. Modified SHPB apparatus

Impact uniaxial compression tests for artificially cemented sand have been carried out in impact dynamics laboratory of Anhui University of Science and Technology. As shown in Fig. 2, aluminium split Hopkinson pressure bar apparatus is adopted. The diameters of all pressure bars are 37 mm. The length of striker is 800 mm. The lengths of incident bar and transmitted bar are both 2000 mm.

Fig. 2Aluminium split Hopkinson pressure bar apparatus

In a typical impact uniaxial compression test, incident stress wave is generated by impact of striker on incident bar. Generally, the striker is launched by a sudden release of compressed air in gas gun. Seven striker velocities have been carried out by changing air pressure. To facilitate stress equilibrium, vaseline is used to extend the rising time of the incident wave by smearing them on the impact face of incident bar [15].

The strain waves associated with one-dimensional stress waves are measured by strain gauges mounted symmetrically on the pressure bar surface across the diameter. Then strain gauges are connected into a Wheatstone bridge. Dynamic strain test system composed of strain gauges, super dynamic strain amplifier and dynamic testing analyzer are used to collect and record incident strain wave, reflected strain wave, and transmitted strain wave.

Ordinary foil type resistance strain gauges have been used for incident bar to capture incident strain wave and reflected strain wave. For relatively low wave impedance of artificially cemented sand, semiconductor strain gauges have been adopted for transmitted bar to capture extremely weak transmitted strain wave, and the sensitivity coefficient of semiconductor strain gauges is 110 which is about 50 times bigger than that of ordinary foil type resistance strain gauges [16, 17].

As the semiconductor strain gauges are easily influenced by temperature, four semiconductor strain gauges are connected into a complete Wheatstone bridge. Two working strain gauges mounted symmetrically on the transmitted bar are connected to the opposite legs of the complete Wheatstone bridge. To eliminate the influence of temperature, two temperature compensation strain gauges are mounted on a aluminium plate in same material with transmitted bar subjecting to no load.

With the help of dynamic strain test system, the actual measured incident strain wave, reflected strain wave, and transmitted strain wave are shown in Fig. 3.

Fig. 3Actual measured incident strain wave, reflected strain wave, and transmitted strain wave

a) Incident strain wave and reflected strain wave

b) Transmitted strain wave

3.1. Energy calculation in impact uniaxial compression tests

In impact uniaxial compression tests, there are mainly four kinds of energies involved, which are incident energy $W_I$, reflected energy $W_R$, transmitted energy $W_T$ and absorbed energy $W_S$ of artificially cemented sand specimen [18-20]. Incident energy $W_I$, reflected energy $W_R$, and transmitted energy $W_T$ can be calculated by following equations:

where ${\epsilon }_I\left(t\right)$, ${\epsilon }_R\left(t\right)$, and ${\epsilon }_T\left(t\right)$ stand for incident strain wave, reflected strain wave, and transmitted strain wave, respectively. $E$, $A$, and $C$ are elastic modulus, cross-sectional area, and elastic wave velocity of aluminium pressure bar, respectively.

In impact uniaxial compression tests, frictional contact energy loss can be negligible. According to the law of energy conservation, absorbed energy $W_S$ of artificially cemented sand specimen can be calculated by following equation:

Based on the stress uniform assumption, Eq. (4) can be simplified as below:

Specific energy absorption (SEA) is a significant indicator for impact energy absorption characteristics. Specific energy absorption (SEA) is defined as absorbed energy $W_S$ divided by its volume during impact uniaxial compression tests, which is the area below the dynamic stress-strain curve. It reflects the energy absorbed by material per unit volume [21], and can be calculated by following equation:

where $A_S$ and $l_S$ are cross-sectional area and length of artificially cemented sand specimen, respectively.

3.2. Impact energy absorption analyses of artificially cemented sand

According to mentioned calculation equations, time-history curves of incident energy $W_I$, reflected energy $W_R$, transmitted energy $W_T$, and absorbed energy $W_S$ of artificially cemented sand specimen can be seen in Fig. 4.

Fig. 4Curve of energy versus time for artificially cemented sand specimen

Seen from Fig. 4, both incident energy $W_I$ and reflected energy $W_R$ increase with loading time ($t$) increasing. For relatively low wave impedance of artificially cemented sand, most of incident wave is reflected, therefore transmitted energy $W_T$ is relatively small. Absorbed energy $W_S$ of artificially cemented sand specimen also increases with loading time increasing.

Artificially cemented sand absorbed energy is mainly used for damage evolution, crack propagation, and fracture. With the striker velocity increasing, some micro-cracks which will not propagate under low strain rate develop into macro-cracks and connect with each other under high strain rates. This will consume more energy. Moreover, artificially cemented sand shows an obvious strain rate effect during impact uniaxial compression tests. Both dynamic uniaxial compressive strength and ultimate strain of artificially cemented sand increase with strain rate increasing [13]. As the specific energy absorption (SEA) is the area below the dynamic stress-strain curve, specific energy absorption (SEA) also increases with strain rate or striker velocity increasing.

The relation between average specific energy absorption (SEA) and striker velocity ($v$) for artificially cemented sand cured 7 days, 14 days, and 21 days are shown in Fig. 5.

Fig. 5Curve of specific energy absorption versus striker velocity for artificially cemented sand

Seen from Fig. 5, specific energy absorption (SEA) of artificially cemented sand cured 7 days, 14 days, and 21 days increase in an approximate power relation with striker velocity. Through fitting analyses, specific energy absorption and striker velocity meets the following relation:

where $a$ is a pending fitting coefficient.

Fitting results indicate that a positive linear relation exists between specific energy absorption and squared striker velocity. Pending fitting coefficient $a$ and fitting relation coefficient $R^2$ for artificially cemented sand cured 7 days, 14 days, and 21 days are shown in Table 1. Coefficient $a$ increases with curing time increasing.