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Investigation on the dynamic shear modulus and damping ratio of steel slag sand mixtures
Construction and Building Materials 162 (2018) 170–180
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Investigation on the dynamic shear modulus and damping ratio of steel slag sand mixtures Wei Li a, Lei Lang a,⇑, Da Wang a, Yang Wu b,c, Fudong Li a a
School of Civil Engineering, Shenyang Jianzhu University, Shenyang 110168, China School of Civil Engineering, Guangzhou University, Guangzhou 510006, China c Graduate School of Science and Technology for Innovation, Yamaguchi University, Ube 7558611, Japan b
h i g h l i g h t s We investigated the dynamic shear modulus and damping ratio of SSM and CSM. The effects of confining pressure, mix proportion and curing age on the dynamic shear modulus and damping ratio were studied. The dynamic shear modulus and damping ratio of SSM and CSM are significantly affected by mix proportion. It is feasible to use SSM instead of CSM as the foundation treatment materials.
a r t i c l e
i n f o
Article history: Received 29 August 2017 Received in revised form 3 December 2017 Accepted 5 December 2017
Keywords: Resonant column test Steel slag sand mixture Cement sand mixture Dynamic shear modulus Damping ratio
a b s t r a c t This paper aims to investigate the dynamic shear modulus (G) and damping ratio (D) of steel slag sand mixture (SSM), and compared with the cement sand mixture (CSM) under the same conditions. A series of resonant column tests were conducted to explore the effects of confining pressure, mix proportion and curing age on the dynamic shear modulus and damping ratio. The results show that the dynamic shear modulus increases with the increase of confining pressure, whereas the damping ratio is found to be less influenced by confining pressure. An increase in curing age leads to an increase in dynamic shear modulus and a slowly decrease in damping ratio. The mix proportion significantly affects the dynamic shear modulus and damping ratio of SSM and CSM. The dynamic shear modulus of SSM initially increases and then decreases with the increase of steel slag content, and reaches the maximum when steel slag content is 40%. The dynamic shear modulus of CSM gradually increases with the increase of cement content. As the increase of steel slag and cement in the mixture, the damping ratios of SSM and CSM tend to increase first and then decrease, and the maximum damping ratio (Dmax) also shows similar trend. When the steel slag content is 15%, the maximum dynamic shear modulus (Gmax) and maximum damping ratio (Dmax) of SSM are close to those of CSM with the 15% cement content. With the test findings, it is feasible to use 40% steel slag instead of 15% or less cement to mix with sand as the foundation treatment materials, which can not only improve the dynamic characteristics of the foundation, but also save resources and protect the environment. Ó 2017 Elsevier Ltd. All rights reserved.
1. Introduction The low-strain dynamic shear modulus (G) and damping ratio (D) are important characteristics that are often used to determine the dynamic response of soils [1]. The dynamic shear modulus reflects the bearing capacity of soils, and the damping ratio expresses the amplitude attenuation of dynamic load in soils. The traditional cement sand mixture (CSM) has its own advantages and disadvantages in foundation treatment. In recent years, utilization ⇑ Corresponding author. E-mail address: [email protected] (L. Lang). https://doi.org/10.1016/j.conbuildmat.2017.12.026 0950-0618/Ó 2017 Elsevier Ltd. All rights reserved.
of industrial by-products in engineering construction has received lots of attentions from researchers [2]. Steel slag is a by-product that is produced during the steel slag manufacturing process and often features high hardness [3], which makes the steel slag sand mixture (SSM) a promising foundation treatment material. However, past studies on the dynamic properties of SSM are still very limited and less information is available. So it is necessary to explore the feasibility of using steel slag instead of cement to mix with sand as foundation treatment materials. The experimental investigations of the dynamic shear modulus and damping ratio of soils have been used by various researchers. Yong et al. [4] investigated the dynamic properties (shear modulus
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and damping ratio) of two selected tropical residual soils (sandy silt and silty sand) in Malaysia under different overburden pressures. Zhao et al. [5] studied the dynamic properties of silica gel, including small-strain shear modulus and damping ratio through a series of resonant column tests. Golpazir et al. [6] performed a series of cyclic triaxial tests to investigate the dynamic properties of polyurethane (PU) foams and PU foam-sand mixtures from intermediate to large strains. Song et al. [7] studied the smallstrain stress-strain properties during cyclic loading of Lanzhou loess deposits, characterized by a very high void ratio, and they found that shear modulus at low strain levels was very sensitive to water content while the effect of water content on smallstrain damping was relatively smaller. Ehsani et al. [8] investigated the dynamic properties of sand-granulated rubber mixtures prior to practical applications, and the results showed that tire inclusion significantly reduced the shear modulus and increased the damping ratio of the mixtures. Kumar et al. [9–11] conducted a series of resonant column tests to examine the effects of vibration cycles and cyclic strain history on the dynamic properties of sand. It needs to be mentioned that previous studies on dynamic shear modulus and damping ratio were mainly based on traditional geotechnical materials, whereas no research effort has been devoted to investigate the dynamic properties of combining use of steel slag and sand. Steel slag is obtained as industrial by-product and its recycling utilization considering environmental protection has been a concern for people. According to Das et al. [12], 2–4 tons of waste are produced during the manufacture of every single tonne of steel. Most of BOF (basic oxygen furnace) steel slag has been recycled in developed countries [13]. About 1.5 million metric tons of BOF steel slag produced in Germany are used as an aggregate material in construction applications annually [14], and approximate 97% of BOF steel slag is recycled in the same ways in the U.K. [15]. Although a large amount of waste steel slag are recycled, there is still about 35% unused steel slag dumped as waste [16]. In China, the annual production of steel slag is about 30Mt, with only about 22% utilization rate [17,18]. The chemical composition of steel slag varies due to its highly variable production method and raw materials [19]. On the whole, its chemical composition consists of CaO, SiO2, Al2O3, Fe2O3 and MgO. It should be noted that steel slag contains about 10% of MgO and 40% of CaO in which there is more than 5% of free CaO [20]. This risk can be eliminated or greatly reduced by weathering the steel slag in outdoor condition for a sufficient period of time before [21]. In addition, traditional Portland cement is not an environmental friendly material due to its manufacture creates a large mount of greenhouse gas emissions, and it also consumes a great deal of natural resources and energy [19]. Based on previous studies, effective utilization of steel slag as a substitution of traditional Portland cement in foundation treatment would save resources and protect the environment. The present research aims to replace traditional Portland cement with steel slag as the main material in foundation treatment, and to investigate the dynamic shear modulus and damping ratio of SSM using resonant column tests. The test results of SSM are also compared with those of CSM under similar conditions. The test results will provide a theoretical foundation for the practical application of SSM so that it can be widely applied in foundation treatment.
2. Experimental 2.1. Test equipment The resonant column apparatus had been used for testing the SSM and CSM specimens. It is a fixed-free apparatus in which the
cylindrical specimen is fixed at its bottom and only its top is vibrating. The resonant column test was performed by applying a sinusoidal torque via an electromagnetic drive system to the specimen. The drive system consists of a four-arm rotor that has a permanent magnet fitted to the end of each arm and a support cylinder to which four pairs of wire coils are fitted. The basic principle of the resonant column test is to vibrate a cylindrical soil specimen in a fundamental mode of vibration, in torsion or flexure. Once the fundamental mode is established, measurements of resonant frequency and amplitude of vibration are made, and then the dynamic shear modulus and shearing strain amplitude of specimen can be obtained. 2.2. Materials The materials tested are steel slag, Portland cement and sand. The physical and mechanical properties of steel slag are shown in Table 1. The chemical compositions of steel slag may vary with the changes in composition of the raw ore and manufacturing process. Based on the statistical results, most steel slag consists primarily of CaO, MgO, SiO2, Al2O3 and FeO. The minerals of the steel slag determined by X-ray diffraction are mainly C3S (3CaOSiO2), b-C2S (2CaOSiO2), 2CaOAl2O3, 2CaOFe2O3, RO phase (a CaO-FeO-MnO-MgO solid solution), free CaO and free MgO, etc [18]. Besides, steel slag also has a large hydraulicity. Due to the impact of CaO, the PH value of steel slag can reach 10–12 when reacts with water [22]. Therefore, the use of steel slag for foundation treatment will also play an important role in corrosion resistance. The major chemical compositions of Portland cement (P.O32.5) are 3CaOSiO2, 2CaOSiO2, 3CaOAl2O3 and 4CaOAl2O3Fe2O3. It can be better hardened when meet with water, then maintains and develops its strength. The major technical indexes of Portland cement are shown in Table 2 [22]. The steel slag and sand used in this test were obtained by manual screening. The particle size of steel slag and sand is controlled below 4 and 2 mm, respectively. The particle size distribution curves of the steel slag and sand are shown in Fig. 1. Based on the particle size distribution curves, the uniformity coefficients of steel slag and sand are 5.72 and 2.31, respectively, and the curvature coefficients of steel slag and sand are 0.85 and 1.22, respectively. 2.3. Mix proportions The tests were carried out on specimens with the same water content. The mass ratio of water to solid material was 15%. For SSM, the content of solid materials represented by steel slag is 20, 30, 40 and 50%, and represented by symbols Gs20, Gs30, Gs40 and Gs50, respectively. Similarly, for CSM, the content of solid materials represented by cement is 8, 12 and 15%, and represented
Table 1 Physical and mechanical properties of steel slag. Number
Indexes
Norm
Test results
1 2 3 4 5 6 7 8 9 10
Crushing value (%) Apparent relative density Water absorption (%) Soft stone content (%) Asphalt adhesion (level) Wear loss in Los Angeles Polished stone value Free-calcium oxide (f-CaO) (%) Immersion expansion rate (%) Impact value (%)
26 2.60 2 3 4 28 42 3 2 25
17.5 3.30 2.3 2.6 4.2 18.5 45 0.14 0.43 14
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Table 2 The major technical indexes of Portland cement (P.O32.5). Index
Unit
Norm
Test results
Fineness Initial setting time Final setting time Stability Strength
% min min mm MPa
10.0 45 390 5.0 3 days 28 days 3 days 28 days
6.1 62 295 2.5 3.6 7.6 13.5 37.5
Fracture
Mass percentage less than a particle size (%)
Renitency
2.5 5.5 11.0 32.5
2.5. Test scheme
100 Steel slag Sand
90
Three kinds of confining pressure of 50, 100 and 150 kPa were selected in this test. For each kind of mix proportion, the 9 specimens were tested under three kinds of confining pressure, and 3 specimens under each confining pressure were maintained for 1, 3 and 7 days, respectively. The specific test schemes are shown in Table 4.
80 70 60 50 40
2.6. Testing procedure
30 20 10 0 10
1
0.1
0.01
Particle size (mm) Fig. 1. Particle size distribution of steel slag and sand.
by symbols Gc8, Gc12 and Gc15, respectively. The types of mixes and mix-designs are shown in Table 3.
2.4. Specimen preparation The cylindrical specimens of diameter 50 mm and height 100 mm were prepared in this experiment. The specimens were prepared in cylindrical molds with a diameter of 50 mm. According to mix proportions, steel slag and cement were mixed with sand respectively in a container and was placed in the cylindrical mold in four sequential layers. The surface of each layer was scraped after tamping in specimen preparation process to eliminate the delamination effect. The mode was carefully removed to confirm that the specimens were not damaged and then maintained under standard conditions for 1, 3 and 7 days, respectively. All specimens were prepared in the same method, so as to ensure approximately the same compaction energy applied to the specimens. A total of 63 specimens were prepared in this experiment, and each mix proportion consists of 9 specimens. The actual preparation process of specimens is shown in Fig. 2.
Table 3 Mix proportions design of SSM and CSM. Mixes
Mass of steel slag/cement (g)
Mass of sand (g)
Mass of water (g)
Gs20 Gs30 Gs40 Gs50 Gc8 Gc12 Gc15
100 150 200 250 40 60 75
400 350 300 250 460 440 425
75 75 75 75 75 75 75
The dynamic shear modulus and damping ratios of the specimens were determined according to the ASTM D4015 Specification [23], and the schematic diagram of testing procedure is shown in Fig. 3. The specific test procedures are as follows: (1) excluded the gas in the resonant column equipment and eliminated the residual water in the equipment; (2) put the filter paper on the top, bottom and periphery of the specimen, and then installed the specimen, it is worth noting that the installation process needs to use the rubber leather sheath entangle the specimen, and installed the permeable stone, then the inferior rubber leather sheath was attached to the base and the upper and lower end should be sealed; (3) slowly poured into the purified water to ensure no bubbles were produced; (4) installed the resonant column electromagnetic drive system and then installed the pressure chamber; (5) the saturated specimen was taken by picking up the suction; (6) the chosen initial driving voltage value was 0.01 V, regulated the driving voltage until the shearing strain was detected near 106, then increased the driving voltage until the shearing strain was detected near 104; (7) the dynamic shear modulus and damping ratio were determined according to the experimental data. The dynamic shear modulus depended on the resonance frequency, specimen density, specimen geometry and boundary condition is obtained from the following expression.
2 2pfh G¼q b
ð1Þ
where G is the dynamic shear modulus, MPa; q is the mass density, g/cm3; f is the resonance frequency of torsional vibration, Hz; h is the height of the specimen, mm; b is the eigenvalue of the torsional vibration frequency equation. The damping ratio was determined from the free-vibration decay curve, which was recorded after turning off power at resonance. The logarithmic decrement (d) of the decay curve is calculated as follows.
d¼
1 h1 ln n hnþ1
ð2Þ
wheren is the number of cycles between peaks h1 and hnþ1 ; h1 is the amplitude of the peak response after excitation; hnþ1 is the amplitude of the peak responsen cycles after h1 :
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(a) Mixture preparation
(b) Cylindrical mold
(c) Compaction
(d) Cylindrical specimens Fig. 2. Specimens preparation.
Table 4 Test schemes of SSM and CSM. Mixes
Confining pressure 50 kPa 1 days p p p p p p p
Gs20 Gs30 Gs40 Gs50 Gc8 Gc12 Gc15
100 kPa 3 days p p p p p p p
7 days p p p p p p p
1 days p p p p p p p
To ensure that the decay curve is close to the straight line, between 10 and 20 cycles are used in this test. The damping ratio (D) is calculated from the logarithmic decrement (d) as follows.
D¼
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi d2 4p2 þ d2
100%
ð3Þ
3. Results and discussion 3.1. Dynamic shear modulus To investigate the effects of confining pressure, mix proportion and curing age on the dynamic shear modulus of SSM and CSM, the
150 kPa 3 days p p p p p p p
7 days p p p p p p p
1 days p p p p p p p
3 days p p p p p p p
7 days p p p p p p p
variations of the dynamic shear modulus (G) with shearing strain (c) are provided in Figs. 4–6. In this study, all the test results of SSM and CSM are available and only the representative test results are selected and analyzed. Other tests with different parameters also showed similar trends Fig. 4 shows the variation of the dynamic shear modulus with shearing strain for different confining pressures (50, 100 and 150 kPa). For the given mix proportion and curing age, it can be observed that the magnitudes of dynamic shear modulus increase continuously with the increase of confining pressure, and the varying trends of SSM and CSM are the same. The increase in dynamic shear modulus is caused by confining pressure due to the further compaction of the mixture, this will lead to (1) a decrease in the void ratio, (2) an increase in the relative density, (3) an increase
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(a) Pressure chamber
(b) Data acquisition system
(c) Resonant test
(d) Damping test Fig. 3. The schematic diagram of testing procedure.
160
50 kPa 100 kPa 150 kPa
150 140 130 120 110 100 90 80 0.0001
50 kPa 100 kPa 150 kPa
150
Dynamic shear modulus (%)
Dynamic shear modulus (MPa)
160
140 130 120 110 100 90 80
0.0010
0.0100
Shearing strain (%)
(a) SSM (Gs40-7days)
0.1000
70 0.0001
0.0010
0.0100
Shearing strain (%)
(b) CSM (Gc15-7days)
Fig. 4. The variation of G with shearing strain for different confining pressures.
0.1000
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Dynamic shear modulus (MPa)
160
Gs20 Gs30 Gs40 Gs50 Gc8 Gc12 Gc15
150 140 130 120 110 100 90 0.0001
0.0010
0.0100
0.1000
Shearing strain (%) Fig. 5. The variation of G with shearing strain for different mix proportions (150 kPa-7 days).
in the contract point between the particles, (4) an increase in the propagation velocity of stress wave. Fig. 5 shows the variation of the dynamic shear modulus with shearing strain for different mix proportions. For the given confining pressure and curing age, the dynamic shear modulus of CSM increases with the increase of cement content, whereas the dynamic shear modulus of SSM initially increases and then decreases with the increase of steel slag content. The dynamic shear modulus of SSM is the largest when the steel slag content is 40%, and the dynamic shear modulus of CSM is the largest when cement content is 15%. From the view of strengthening mechanism, it is known that portland cement is a hydraulic cementitious material, whereas steel slag has similar advantages. Steel slag contains high concentrations of CaO and MgO. The CaO and MgO were changed to Ca(OH)2 and Mg(OH)2 due to chemical reaction and it caused immediate and long-term expansions, and the sustained expansions would increase the density of soils. In other words, the content of C3S (3CaOSiO2) and b-C2S (2CaOSiO2) in steel slag mixed with soils, Ca(OH)2、CaSiO3 will be produced, it will cause harden effects and the mixture is agglomerated which accelerates
the consolidation of mixture, then the dynamic shear modulus of mixture is improved. Fig. 6 shows the variation of the dynamic shear modulus with shearing strain for different curing ages (1, 3 and 7 days). It can be observed that the dynamic shear modulus of SSM and CSM increases with the increase of curing age. The reason is that with the increase of curing age, the consolidation degree of the mixture increased gradually, then the dynamic shear modulus was improved. Generally, the strength of portland cement will reach the maximum value and tends to be stable when the curing age is about 28 days. The present research focuses on the variation in the dynamic shear modulus of SSM with the change of curing age. Therefore, the optimum curing time of the mixture can’t be determined in this investigation, which is needed to make a further research. In addition, Figs. 4–6 also show that the dynamic shear modulus of SSM and CSM decreases nonlinearly with the increase of the shearing strain. At relatively small shearing strains (106 < c < 1 0 5), the dynamic shear modulus decreased gently, then the dynamic shear modulus began to decrease sharply as the increase of shearing strain. It should be mentioned that for shearing strain less than 106, the dynamic shear modulus remain constant. Similar trends have also been verified in a single material, the effects of vibration cycles and cyclic strain history on shear modulus of dry sand were studied respectively by Kumar et al. [9–11]. The decreases in dynamic shear modulus with shearing strain is mainly due to the nonlinear and hysteretic behavior of the dynamic stressstrain relationship. 3.2. Maximum dynamic shear modulus The maximum dynamic shear modulus (Gmax) of SSM and CSM, at a strain level of 106, under three different confining pressures (50, 100, and 150 kPa) and three different curing ages (1, 3, and 7 days) for testing series Gs20, Gs30, Gs40, Gs50, Gc8, Gc12 and Gc15 was studied. Since the smallest strain level of SSM and CSM from resonant tests was 106, the Gmax was determined through regression analyses. Hardin and Drnevich proposed an approximate method of computing shear modulus (G) at any strain level (c). Assuming hyperbolic stress-strain relations, and the following expressions are obtained [24,25]:
G 1 ¼ Gmax 1 þ c a c
ð4Þ
r
160 1 days 3 days 7 days
150
Dynamic shear modulus (MPa)
Dynamic shear modulus (MPa)
160
140 130 120 110 100
140 130 120 110 100 90
90 80 0.0001
1 days 3 days 7 days
150
0.0010
0.0100
Shearing strain (%)
(a) SSM (Gs40-150 kPa)
0.1000
80 0.0001
0.0010
0.0100
Shearing strain (%)
(b) CSM (Gc15-150 kPa)
Fig. 6. The variation of G with shearing strain for different curing ages.
0.1000
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where G=Gmax is normalized dynamic shear modulus; cr is the reference strain; and a is a curve-fitting variable named curvature parameter. The reference strain is described as follows.
cr ¼ cr1
r0m
k ð5Þ
pa
125 120 115 110 105 100 95 90 85 80 75 70 65 60 55 50 45 0
50
3.3. Damping ratio Damping ratio (D) is another typical parameter to characterize the energy dissipation characteristics of a material. For all the tested SSM and CSM specimens, the variations of damping ratio with shearing strain for different values of confining pressure, mix proportion and curing age were studied. In order to explore the effects of confining pressure, mix proportion and curing age on the damping ratio, only some representative test results are
Gmax (MPa)
Gs20 Gs30 Gs40 Gs50 Gc8 Gc12 Gc15
100
150
140 135 130 125 120 115 110 105 100 95 90 85 80 75 70 65
Gs20 Gs30 Gs40 Gs50 Gc8 Gc12 Gc15
0
200
50
Confining pressure(kPa)
160 155 150 145 140 135 130 125 120 115 110 105 100 95 90 85
100
(b) Curing for 3 days Gs20 Gs30 Gs40 Gs50 Gc8 Gc12 Gc15
0
150
Confining pressure (kPa)
(a) Curing for 1 days
Gmax (MPa)
Gmax(MPa)
where cr1 is the reference strain at the effective mean stress of 100 kPa; pa is the reference stress of 100 kPa; r0m is effective mean stress; k is stress correction exponent. Fig. 7 shows the variation of Gmax with confining pressures for different mix proportions and curing ages. The Gmax increases almost linearly with the increase of confining pressure, this trend also exists in the test results of Honghua Zhao and Louis Ge, their test results also indicated that the Gmax of silica gel increased almost linearly with confining pressure [5]. In addition, for the given confining pressure, mix proportion and curing age also play an important role in the values of Gmax. Fig. 8 shows the variation of Gmax with mix proportion of SSM and CSM. It can be observed that the Gmax of SSM initially increased with the increase of steel slag content, and attained the peak value when the steel slag content is 40%. When the steel slag content increased to 50%, the Gmax decreased, which indicates that the optimum mix proportion of SSM is Gs40. Further analysis, when steel slag content was 40%, the hydration reaction was the most sufficient, and the dynamic
shear modulus reached the maximum. However, when steel slag content was 20% and 30%, the steel slag was not enough and the hydration reaction was incomplete, so the dynamic shear modulus didn’t reach the maximum. Furthermore, when steel slag was 50%, the steel slag was too much, and the remaining steel slag was not involved in hydration reaction, then the remaining steel slag as waste material existed in mixture, thus reduced the dynamic shear modulus. The Gmax of CSM also increased linearly with the increase of cement content. When cement content is 15%, the Gmax of CSM is close to the Gmax of SSM when the steel slag content is 40%. It is worth noting that when the amount of cement is too large, it is easy to produce the dry shrinkage and temperature shrinkage cracks [22], whereas using steel slag as aggregate of the mixture will improve such problems effectively.
50
100
150
Confining pressure (kPa)
(c) Curing for 7 days Fig. 7. The variation of Gmax with confining pressure of SSM and CSM.
200
200
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Fig. 8. The variation of Gmax with mix proportion of SSM and CSM.
selected, and other tests with different parameters also showed similar trends. Fig. 9 depicts the variation of damping ratio with shearing strain for different confining pressures. It is observed from Fig. 9 that confining pressure does not strongly affect damping ratio, especially at
9
7
7
6 5 4
6 5 4 3
3
2
2 1 0.0001
0.0010
0.0100
0.1000
1 0.0001
0.0010
0.0100
Shearing strain (%)
Shearing strain (%)
(a) Curing for 1 days
(b) Curing for 3 days
7
6
Damping ratio (%)
Damping ratio (%).
8
Gs40-50kPa Gs40-100kPa Gs40-150kPa Gc15-50kPa Gc15-100kPa Gc15-150kPa
8
Gs40-50kPa Gs40-100kPa Gs40-150kPa Gc15-50kPa Gc15-100kPa Gc15-150kPa
Damping ratio (%).
10
low strains, this phenomenon is more obvious. However, it can also be seen that the damping ratio tends to decrease with the increase of confining pressure. Fig. 10 shows the variation of damping ratio with shearing strain for different mix proportions. An increase in cement content leads to an increase in damping ratio of CSM, and the damping ratio of SSM initially increases and then decreases with the increase of steel slag content. This trend is observed in all the test results. This shows that damping ratios of specimens are significantly affected by mix proportion. It is known that when the shear modulus of a material becomes greater, its damping ratio is expected to become lower. So, the test results are not expected at first glance. This seemingly contradictory test result is likely to be related to the effects of the interaction of two materials on the energy dissipation. The damping ratio of soils represents the amount of energy dissipated during wave propagation through its mass. It should be mentioned that a similar increase in the damping ratio obtained by increasing the amount of cement was observed by Saxena et al. [26], they investigated the dynamic moduli and damping ratios for cemented sands at low strains, and their test results are similar to the results of CSM specimens in this test. In their findings, they reported that the energy spent for the wave to propagate through a weakly cemented sand specimen was larger than the energy spent by
5
Gs40-50kPa Gs40-100kPa Gs40-150kPa Gc15-50kPa Gc15-100kPa Gc15-150kPa
4
3 2
1 0.0001
0.0010
0.0100
0.1000
Shearing strain (%)
(c) Curing for 7 days Fig. 9. The variation of D with shearing strain for different confining pressures (Gs40, Gc15).
0.1000
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6
Gs20 Gs30 Gs40 Gs50 Gc8 Gc12 Gc15
Damping ratio (%)
5
4
3
2
1
0 0.0001
0.0010
0.0100
0.1000
Shearing strain (%) Fig. 10. The variation of D with shearing strain for different mix proportions (150 kPa-7 days).
9
7 6
7
5 4
6 5 4 3
3
2
2 1 0.0001
Gs40-1days Gs40-3days Gs40-7days Gc15-1days Gc15-3days Gc15-7days
8
1
0.0010
0.0100
0.1000
0.0001
0.0010
Shearing strain (%)
8 7 6 5
(b) Confining pressure is 100kPa
Gs40-1days Gs40-3days Gs40-7days Gc15-1days Gc15-3days Gc15-7days
4 3 2 1 0.000
0.0100
Shearing strain (%)
(a) Confining pressure is 50kPa
Damping ratio (%)
Damping ratio (%)
8
9
Gs40-1days Gs40-3days Gs40-7days Gc15-1days Gc15-3days Gc15-7days
Damping ratio (%)
10
the wave to propagate through a similar but clean, uncemented specimen (prepared under similar condition). In addition, the fact that the damping ratio during wave propagation increases as the degree of coating (cleanliness) decreases was also reported by Duffy and Mindlin [27]. Therefore, when the cement content is small, the cement is coated in the areas of the contacts between the individual sand grains and then increases the damping ratio. As the increase of cement content, the cement gradually acts as a gelling agent, and then the mixture tends to solidify and reduces the damping ratio. Based on some similar characteristics of steel slag and Portland cement, we think that the similar dissipating mechanism is also suitable for the SSM specimens. Additionally, for SSM, the hydration reaction of steel slag and sand had been occurred. The specific process has been described in the previous section. This not only increased the degree of density of SSM, and improved the dynamic shear modulus, but also strengthened the connection between soil particles and improved the cohesion. Then the rearrangement of soil particles required more energy and increased damping ratio of SSM. The additives (such as Portland cement, steel slag, lime,
0.001
0.010
0.100
Shearing strain (%)
(c) Confining pressure is 150kPa Fig. 11. The variation of D with shearing strain for different curing ages (Gs40, Gc15).
0.1000
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Fig. 12. The variation of Dmax with mix proportion of SSM and CSM.
etc.) content which corresponds to the maximum damping ratio is ‘‘coating level” (CL). So, in this study, we think that the CL of CSM may be more than 15%, and the CL of SSM may be about 40%. Compared with the results which reported by Saxena et al. [26], their test results showed that the CL of cemented sands is between 5% and 8%, it should be mentioned that the confining pressures in their tests are more higher than ours. Thus, the CL of mixture may be affected by other factors. Another similar increase in the damping ratio obtained by increasing the cement content was reported by Yong and Chiang [28], their test results showed that the CL is between 0 and 6%. In addition, the number of cycles chosen to determine the damping forms an important parameter and it affects the damping quite significantly. It is necessary to do more research to make a further explanation. Fig. 11 shows the variation of damping ratio with shearing strain for different curing ages. It is observed that the curing age does not strongly affect the damping ratio when the shearing strain is small, as the increase of shearing strain, the damping ratio decreases slowly with the increase of curing age. Generally, damping ratio initially increased almost linearly with the increasing of the shearing strain and the followed by a rapid nonlinear increasing behavior, which means that when the shearing strain is relatively small, the energy attenuation of the mixtures is relatively slow, and with the increase of shearing strain, the energy attenuation of the mixtures will increase dramatically. 3.4. Maximum damping ratio The variation of the maximum damping ratio (Dmax) with mix proportion for different values of confining pressure and curing age has been investigated in this study. The empirical correlation given by Kondner and the relation expression of damping curve modified by Hu are adopted [29,30], and the expressions are shown as follows.
G 1 ¼ Gmax 1 þ c=cr D ¼ Dmax
c=cr 1 þ c=cr
ð6Þ m ð7Þ
where Gmax is the maximum dynamic shear modulus, MPa; G=Gmax is normalized dynamic shear modulus; c is the shearing strain; cr is the reference shearing strain; Dmax is the maximum damping ratio, %; m is the experimental parameter. The comparison of the Dmax with mix proportion for different values of confining pressure and curing age is provided in Fig. 12. For the given confining pressure and curing age, the Dmax of SSM increases initially and then decreases with the increase of steel slag
179
content, and reaches the peak when the steel slag is 40%. Under the same conditions, for CSM, the Dmax increases with the increase of cement content, and when the cement content is 15%, the Dmax of CSM is the largest. By comparison, we can indicate that when the steel slag content is 40%, the Dmax of SSM is close to that of CSM when the cement content is 15%. It also can be observed that when the cement content of CSM is less than 15%, by adjusting the mix proportion of SSM, the SSM with the same energy attenuation characteristics can be found. Furthermore, the curing age have remarkable effect on the Dmax of SSM and CSM, the longer the curing age is, the smaller the Dmax value is. On the other hand, Dmax is not significantly affected by confining pressure. It should be mentioned that the selection of empirical correlation also affects the fitting results of Dmax. So, more research will be needed to optimize the empirical correlation. This comparison means that the similarity of the dynamic behavior of SSM and CSM. Therefore, it is feasible to use SSM instead of CSM as the foundation treatment materials. 4. Conclusions A series of resonant column tests were performed to investigate the low strain dynamic characteristics of SSM and CSM, and the following conclusions could be drawn from this study: (1) The dynamic shear modulus (G) increases with the increase of confining pressure, and the varying trends of SSM and CSM are similar. The G of CSM increases with the increase of cement content, whereas the G of SSM initially increases and then decreases with the increase of steel slag content. The G of SSM and CSM increases with the increase of curing age. (2) The G of SSM and CSM decreases nonlinearly with the increasing of the shearing strain. The G initially decreases gently, and then decreases sharply as the increase of shearing strain. The G of SSM and CSM remains constant when the shearing strain is less than 106. (3) The maximum dynamic shear modulus (Gmax) of SSM and CSM increases almost linearly with the increase of confining pressure. The Gmax initially increases and then decreases with the increasing of steel slag content, and attains the maximum value when steel slag content is 40%. The Gmax of CSM increases linearly with the increasing of cement content. (4) The damping ratios (D) of SSM and CSM are not strongly affected by simple confining pressure, but are significantly affected by mix proportion. As the increase of steel slag and cement in the mixture, the D of SSM and CSM tend to increase first and then decrease. As the increase of shearing strain, the D decreases slowly with the increase of curing age. (5) For the given confining pressure and curing age, the maximum damping ratio (Dmax) of SSM increases initially and then decreases with the increase of steel slag content. Under similar conditions, the Dmax of CSM increases with the increase of cement content. When the steel slag content is 40%, the Dmax of SSM is close to that of CSM with the 15% cement content. It is feasible to use SSM instead of CSM as the foundation treatment materials. Acknowledgements This study was supported by the National Natural Science Foundation of China (Grant No. 51308355) and Liaoning Province Natural Science Foundation of China (Grant No. 20170540735).
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[16] H. Motz, J. Geiseler, Products of steel slag an opportunity to save natural resources, Waste Manage. 21 (2001) 285–293. [17] Y.X. Shao, E.B. Ahmed, Z. He, et al., Carbon dioxide-activated steel slag for slagbonded wallboard application, J. Mater. Civ. Eng. 04014119 (2005). [18] T.S. Zhang, Q.J. Yu, J.X. Wei, et al., Investigation on mechanical properties, durability and micro-structural development of steel slag blended cements, J. Therm. Anal. Calorim. 110 (2012) 633–639. [19] T.S. Zhang, Q.J. Yu, J.X. Wei, et al., Efficient utilization of cementitious materials to produce sustainable blended cement, Cem. Concr. Compos. 34 (2012) 692– 699. [20] J. Hu, Comparison between the effects of superfine steel slag and superfine phosphorus slag on the long-term performances and durability of concrete, J. Therm. Anal. Calorim. 128 (2017) 1251–1263. [21] X. Yu, Z. Tao, T.Y. Song, et al., Performance of concrete made with steel slag and waste glass, Constr. Build. Mater. 114 (2016) 737–746. [22] W. Li, L. Lang, Z.Y. Lin, et al., Characteristics of dry shrinkage and temperature shrinkage of cement-stabilized steel slag, Constr. Build. Mater. 134 (2017) 540–548. [23] ASTM International, Standard test methods for modulus and damping of soils by resonant column method, Annual book of ASTM standards, ASTM –15, 2015, West Conshohocken, PA. [24] B.O. Hardin, V.P. Drnevich, Shear modulus and damping in soils: measurement and parameter effects, J. Soil Mech. Found. Div. 98 (6) (1972) 603–624. [25] S.K. Saxena, K.R. Reddy, Dynamic modulic and damping ratios for Monterey No.0 sand by resonant column tests, Soils Found. 29 (2) (1989) 37–51. [26] S.K. Saxena, A.S. Avramidis, K.R. Reddy, Dynamic moduli and damping ratios for cemented sands at low strains, Can. Geotech. J. 25 (1988) 353–368. [27] J. Duffy, R.D. Mindlin, Stress-strain relations of a granular medium, J. Appl. Mech. 24 (1956) 585–593. [28] S.C. Yong, Y.C. Chiang, Dynamic properties of cement treated soils, Highway Res. Rec. 379 (1972) 39–51. [29] R.L. Kondner, Hyperbolic stress-strain response: cohesive soils, J. Soil Mech. Found. Div. 89 (1) (1963) 115–143. [30] W.Y. Hu, T.L. Wang, Shear modulus and damping of cohesive soil under earthquake loading conditions, Chin. J. Geotech. Eng. 2 (3) (1980) 82–94.
Contents lists available at ScienceDirect
Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Investigation on the dynamic shear modulus and damping ratio of steel slag sand mixtures Wei Li a, Lei Lang a,⇑, Da Wang a, Yang Wu b,c, Fudong Li a a
School of Civil Engineering, Shenyang Jianzhu University, Shenyang 110168, China School of Civil Engineering, Guangzhou University, Guangzhou 510006, China c Graduate School of Science and Technology for Innovation, Yamaguchi University, Ube 7558611, Japan b
h i g h l i g h t s We investigated the dynamic shear modulus and damping ratio of SSM and CSM. The effects of confining pressure, mix proportion and curing age on the dynamic shear modulus and damping ratio were studied. The dynamic shear modulus and damping ratio of SSM and CSM are significantly affected by mix proportion. It is feasible to use SSM instead of CSM as the foundation treatment materials.
a r t i c l e
i n f o
Article history: Received 29 August 2017 Received in revised form 3 December 2017 Accepted 5 December 2017
Keywords: Resonant column test Steel slag sand mixture Cement sand mixture Dynamic shear modulus Damping ratio
a b s t r a c t This paper aims to investigate the dynamic shear modulus (G) and damping ratio (D) of steel slag sand mixture (SSM), and compared with the cement sand mixture (CSM) under the same conditions. A series of resonant column tests were conducted to explore the effects of confining pressure, mix proportion and curing age on the dynamic shear modulus and damping ratio. The results show that the dynamic shear modulus increases with the increase of confining pressure, whereas the damping ratio is found to be less influenced by confining pressure. An increase in curing age leads to an increase in dynamic shear modulus and a slowly decrease in damping ratio. The mix proportion significantly affects the dynamic shear modulus and damping ratio of SSM and CSM. The dynamic shear modulus of SSM initially increases and then decreases with the increase of steel slag content, and reaches the maximum when steel slag content is 40%. The dynamic shear modulus of CSM gradually increases with the increase of cement content. As the increase of steel slag and cement in the mixture, the damping ratios of SSM and CSM tend to increase first and then decrease, and the maximum damping ratio (Dmax) also shows similar trend. When the steel slag content is 15%, the maximum dynamic shear modulus (Gmax) and maximum damping ratio (Dmax) of SSM are close to those of CSM with the 15% cement content. With the test findings, it is feasible to use 40% steel slag instead of 15% or less cement to mix with sand as the foundation treatment materials, which can not only improve the dynamic characteristics of the foundation, but also save resources and protect the environment. Ó 2017 Elsevier Ltd. All rights reserved.
1. Introduction The low-strain dynamic shear modulus (G) and damping ratio (D) are important characteristics that are often used to determine the dynamic response of soils [1]. The dynamic shear modulus reflects the bearing capacity of soils, and the damping ratio expresses the amplitude attenuation of dynamic load in soils. The traditional cement sand mixture (CSM) has its own advantages and disadvantages in foundation treatment. In recent years, utilization ⇑ Corresponding author. E-mail address: [email protected] (L. Lang). https://doi.org/10.1016/j.conbuildmat.2017.12.026 0950-0618/Ó 2017 Elsevier Ltd. All rights reserved.
of industrial by-products in engineering construction has received lots of attentions from researchers [2]. Steel slag is a by-product that is produced during the steel slag manufacturing process and often features high hardness [3], which makes the steel slag sand mixture (SSM) a promising foundation treatment material. However, past studies on the dynamic properties of SSM are still very limited and less information is available. So it is necessary to explore the feasibility of using steel slag instead of cement to mix with sand as foundation treatment materials. The experimental investigations of the dynamic shear modulus and damping ratio of soils have been used by various researchers. Yong et al. [4] investigated the dynamic properties (shear modulus
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and damping ratio) of two selected tropical residual soils (sandy silt and silty sand) in Malaysia under different overburden pressures. Zhao et al. [5] studied the dynamic properties of silica gel, including small-strain shear modulus and damping ratio through a series of resonant column tests. Golpazir et al. [6] performed a series of cyclic triaxial tests to investigate the dynamic properties of polyurethane (PU) foams and PU foam-sand mixtures from intermediate to large strains. Song et al. [7] studied the smallstrain stress-strain properties during cyclic loading of Lanzhou loess deposits, characterized by a very high void ratio, and they found that shear modulus at low strain levels was very sensitive to water content while the effect of water content on smallstrain damping was relatively smaller. Ehsani et al. [8] investigated the dynamic properties of sand-granulated rubber mixtures prior to practical applications, and the results showed that tire inclusion significantly reduced the shear modulus and increased the damping ratio of the mixtures. Kumar et al. [9–11] conducted a series of resonant column tests to examine the effects of vibration cycles and cyclic strain history on the dynamic properties of sand. It needs to be mentioned that previous studies on dynamic shear modulus and damping ratio were mainly based on traditional geotechnical materials, whereas no research effort has been devoted to investigate the dynamic properties of combining use of steel slag and sand. Steel slag is obtained as industrial by-product and its recycling utilization considering environmental protection has been a concern for people. According to Das et al. [12], 2–4 tons of waste are produced during the manufacture of every single tonne of steel. Most of BOF (basic oxygen furnace) steel slag has been recycled in developed countries [13]. About 1.5 million metric tons of BOF steel slag produced in Germany are used as an aggregate material in construction applications annually [14], and approximate 97% of BOF steel slag is recycled in the same ways in the U.K. [15]. Although a large amount of waste steel slag are recycled, there is still about 35% unused steel slag dumped as waste [16]. In China, the annual production of steel slag is about 30Mt, with only about 22% utilization rate [17,18]. The chemical composition of steel slag varies due to its highly variable production method and raw materials [19]. On the whole, its chemical composition consists of CaO, SiO2, Al2O3, Fe2O3 and MgO. It should be noted that steel slag contains about 10% of MgO and 40% of CaO in which there is more than 5% of free CaO [20]. This risk can be eliminated or greatly reduced by weathering the steel slag in outdoor condition for a sufficient period of time before [21]. In addition, traditional Portland cement is not an environmental friendly material due to its manufacture creates a large mount of greenhouse gas emissions, and it also consumes a great deal of natural resources and energy [19]. Based on previous studies, effective utilization of steel slag as a substitution of traditional Portland cement in foundation treatment would save resources and protect the environment. The present research aims to replace traditional Portland cement with steel slag as the main material in foundation treatment, and to investigate the dynamic shear modulus and damping ratio of SSM using resonant column tests. The test results of SSM are also compared with those of CSM under similar conditions. The test results will provide a theoretical foundation for the practical application of SSM so that it can be widely applied in foundation treatment.
2. Experimental 2.1. Test equipment The resonant column apparatus had been used for testing the SSM and CSM specimens. It is a fixed-free apparatus in which the
cylindrical specimen is fixed at its bottom and only its top is vibrating. The resonant column test was performed by applying a sinusoidal torque via an electromagnetic drive system to the specimen. The drive system consists of a four-arm rotor that has a permanent magnet fitted to the end of each arm and a support cylinder to which four pairs of wire coils are fitted. The basic principle of the resonant column test is to vibrate a cylindrical soil specimen in a fundamental mode of vibration, in torsion or flexure. Once the fundamental mode is established, measurements of resonant frequency and amplitude of vibration are made, and then the dynamic shear modulus and shearing strain amplitude of specimen can be obtained. 2.2. Materials The materials tested are steel slag, Portland cement and sand. The physical and mechanical properties of steel slag are shown in Table 1. The chemical compositions of steel slag may vary with the changes in composition of the raw ore and manufacturing process. Based on the statistical results, most steel slag consists primarily of CaO, MgO, SiO2, Al2O3 and FeO. The minerals of the steel slag determined by X-ray diffraction are mainly C3S (3CaOSiO2), b-C2S (2CaOSiO2), 2CaOAl2O3, 2CaOFe2O3, RO phase (a CaO-FeO-MnO-MgO solid solution), free CaO and free MgO, etc [18]. Besides, steel slag also has a large hydraulicity. Due to the impact of CaO, the PH value of steel slag can reach 10–12 when reacts with water [22]. Therefore, the use of steel slag for foundation treatment will also play an important role in corrosion resistance. The major chemical compositions of Portland cement (P.O32.5) are 3CaOSiO2, 2CaOSiO2, 3CaOAl2O3 and 4CaOAl2O3Fe2O3. It can be better hardened when meet with water, then maintains and develops its strength. The major technical indexes of Portland cement are shown in Table 2 [22]. The steel slag and sand used in this test were obtained by manual screening. The particle size of steel slag and sand is controlled below 4 and 2 mm, respectively. The particle size distribution curves of the steel slag and sand are shown in Fig. 1. Based on the particle size distribution curves, the uniformity coefficients of steel slag and sand are 5.72 and 2.31, respectively, and the curvature coefficients of steel slag and sand are 0.85 and 1.22, respectively. 2.3. Mix proportions The tests were carried out on specimens with the same water content. The mass ratio of water to solid material was 15%. For SSM, the content of solid materials represented by steel slag is 20, 30, 40 and 50%, and represented by symbols Gs20, Gs30, Gs40 and Gs50, respectively. Similarly, for CSM, the content of solid materials represented by cement is 8, 12 and 15%, and represented
Table 1 Physical and mechanical properties of steel slag. Number
Indexes
Norm
Test results
1 2 3 4 5 6 7 8 9 10
Crushing value (%) Apparent relative density Water absorption (%) Soft stone content (%) Asphalt adhesion (level) Wear loss in Los Angeles Polished stone value Free-calcium oxide (f-CaO) (%) Immersion expansion rate (%) Impact value (%)
26 2.60 2 3 4 28 42 3 2 25
17.5 3.30 2.3 2.6 4.2 18.5 45 0.14 0.43 14
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Table 2 The major technical indexes of Portland cement (P.O32.5). Index
Unit
Norm
Test results
Fineness Initial setting time Final setting time Stability Strength
% min min mm MPa
10.0 45 390 5.0 3 days 28 days 3 days 28 days
6.1 62 295 2.5 3.6 7.6 13.5 37.5
Fracture
Mass percentage less than a particle size (%)
Renitency
2.5 5.5 11.0 32.5
2.5. Test scheme
100 Steel slag Sand
90
Three kinds of confining pressure of 50, 100 and 150 kPa were selected in this test. For each kind of mix proportion, the 9 specimens were tested under three kinds of confining pressure, and 3 specimens under each confining pressure were maintained for 1, 3 and 7 days, respectively. The specific test schemes are shown in Table 4.
80 70 60 50 40
2.6. Testing procedure
30 20 10 0 10
1
0.1
0.01
Particle size (mm) Fig. 1. Particle size distribution of steel slag and sand.
by symbols Gc8, Gc12 and Gc15, respectively. The types of mixes and mix-designs are shown in Table 3.
2.4. Specimen preparation The cylindrical specimens of diameter 50 mm and height 100 mm were prepared in this experiment. The specimens were prepared in cylindrical molds with a diameter of 50 mm. According to mix proportions, steel slag and cement were mixed with sand respectively in a container and was placed in the cylindrical mold in four sequential layers. The surface of each layer was scraped after tamping in specimen preparation process to eliminate the delamination effect. The mode was carefully removed to confirm that the specimens were not damaged and then maintained under standard conditions for 1, 3 and 7 days, respectively. All specimens were prepared in the same method, so as to ensure approximately the same compaction energy applied to the specimens. A total of 63 specimens were prepared in this experiment, and each mix proportion consists of 9 specimens. The actual preparation process of specimens is shown in Fig. 2.
Table 3 Mix proportions design of SSM and CSM. Mixes
Mass of steel slag/cement (g)
Mass of sand (g)
Mass of water (g)
Gs20 Gs30 Gs40 Gs50 Gc8 Gc12 Gc15
100 150 200 250 40 60 75
400 350 300 250 460 440 425
75 75 75 75 75 75 75
The dynamic shear modulus and damping ratios of the specimens were determined according to the ASTM D4015 Specification [23], and the schematic diagram of testing procedure is shown in Fig. 3. The specific test procedures are as follows: (1) excluded the gas in the resonant column equipment and eliminated the residual water in the equipment; (2) put the filter paper on the top, bottom and periphery of the specimen, and then installed the specimen, it is worth noting that the installation process needs to use the rubber leather sheath entangle the specimen, and installed the permeable stone, then the inferior rubber leather sheath was attached to the base and the upper and lower end should be sealed; (3) slowly poured into the purified water to ensure no bubbles were produced; (4) installed the resonant column electromagnetic drive system and then installed the pressure chamber; (5) the saturated specimen was taken by picking up the suction; (6) the chosen initial driving voltage value was 0.01 V, regulated the driving voltage until the shearing strain was detected near 106, then increased the driving voltage until the shearing strain was detected near 104; (7) the dynamic shear modulus and damping ratio were determined according to the experimental data. The dynamic shear modulus depended on the resonance frequency, specimen density, specimen geometry and boundary condition is obtained from the following expression.
2 2pfh G¼q b
ð1Þ
where G is the dynamic shear modulus, MPa; q is the mass density, g/cm3; f is the resonance frequency of torsional vibration, Hz; h is the height of the specimen, mm; b is the eigenvalue of the torsional vibration frequency equation. The damping ratio was determined from the free-vibration decay curve, which was recorded after turning off power at resonance. The logarithmic decrement (d) of the decay curve is calculated as follows.
d¼
1 h1 ln n hnþ1
ð2Þ
wheren is the number of cycles between peaks h1 and hnþ1 ; h1 is the amplitude of the peak response after excitation; hnþ1 is the amplitude of the peak responsen cycles after h1 :
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(a) Mixture preparation
(b) Cylindrical mold
(c) Compaction
(d) Cylindrical specimens Fig. 2. Specimens preparation.
Table 4 Test schemes of SSM and CSM. Mixes
Confining pressure 50 kPa 1 days p p p p p p p
Gs20 Gs30 Gs40 Gs50 Gc8 Gc12 Gc15
100 kPa 3 days p p p p p p p
7 days p p p p p p p
1 days p p p p p p p
To ensure that the decay curve is close to the straight line, between 10 and 20 cycles are used in this test. The damping ratio (D) is calculated from the logarithmic decrement (d) as follows.
D¼
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi d2 4p2 þ d2
100%
ð3Þ
3. Results and discussion 3.1. Dynamic shear modulus To investigate the effects of confining pressure, mix proportion and curing age on the dynamic shear modulus of SSM and CSM, the
150 kPa 3 days p p p p p p p
7 days p p p p p p p
1 days p p p p p p p
3 days p p p p p p p
7 days p p p p p p p
variations of the dynamic shear modulus (G) with shearing strain (c) are provided in Figs. 4–6. In this study, all the test results of SSM and CSM are available and only the representative test results are selected and analyzed. Other tests with different parameters also showed similar trends Fig. 4 shows the variation of the dynamic shear modulus with shearing strain for different confining pressures (50, 100 and 150 kPa). For the given mix proportion and curing age, it can be observed that the magnitudes of dynamic shear modulus increase continuously with the increase of confining pressure, and the varying trends of SSM and CSM are the same. The increase in dynamic shear modulus is caused by confining pressure due to the further compaction of the mixture, this will lead to (1) a decrease in the void ratio, (2) an increase in the relative density, (3) an increase
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(a) Pressure chamber
(b) Data acquisition system
(c) Resonant test
(d) Damping test Fig. 3. The schematic diagram of testing procedure.
160
50 kPa 100 kPa 150 kPa
150 140 130 120 110 100 90 80 0.0001
50 kPa 100 kPa 150 kPa
150
Dynamic shear modulus (%)
Dynamic shear modulus (MPa)
160
140 130 120 110 100 90 80
0.0010
0.0100
Shearing strain (%)
(a) SSM (Gs40-7days)
0.1000
70 0.0001
0.0010
0.0100
Shearing strain (%)
(b) CSM (Gc15-7days)
Fig. 4. The variation of G with shearing strain for different confining pressures.
0.1000
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Dynamic shear modulus (MPa)
160
Gs20 Gs30 Gs40 Gs50 Gc8 Gc12 Gc15
150 140 130 120 110 100 90 0.0001
0.0010
0.0100
0.1000
Shearing strain (%) Fig. 5. The variation of G with shearing strain for different mix proportions (150 kPa-7 days).
in the contract point between the particles, (4) an increase in the propagation velocity of stress wave. Fig. 5 shows the variation of the dynamic shear modulus with shearing strain for different mix proportions. For the given confining pressure and curing age, the dynamic shear modulus of CSM increases with the increase of cement content, whereas the dynamic shear modulus of SSM initially increases and then decreases with the increase of steel slag content. The dynamic shear modulus of SSM is the largest when the steel slag content is 40%, and the dynamic shear modulus of CSM is the largest when cement content is 15%. From the view of strengthening mechanism, it is known that portland cement is a hydraulic cementitious material, whereas steel slag has similar advantages. Steel slag contains high concentrations of CaO and MgO. The CaO and MgO were changed to Ca(OH)2 and Mg(OH)2 due to chemical reaction and it caused immediate and long-term expansions, and the sustained expansions would increase the density of soils. In other words, the content of C3S (3CaOSiO2) and b-C2S (2CaOSiO2) in steel slag mixed with soils, Ca(OH)2、CaSiO3 will be produced, it will cause harden effects and the mixture is agglomerated which accelerates
the consolidation of mixture, then the dynamic shear modulus of mixture is improved. Fig. 6 shows the variation of the dynamic shear modulus with shearing strain for different curing ages (1, 3 and 7 days). It can be observed that the dynamic shear modulus of SSM and CSM increases with the increase of curing age. The reason is that with the increase of curing age, the consolidation degree of the mixture increased gradually, then the dynamic shear modulus was improved. Generally, the strength of portland cement will reach the maximum value and tends to be stable when the curing age is about 28 days. The present research focuses on the variation in the dynamic shear modulus of SSM with the change of curing age. Therefore, the optimum curing time of the mixture can’t be determined in this investigation, which is needed to make a further research. In addition, Figs. 4–6 also show that the dynamic shear modulus of SSM and CSM decreases nonlinearly with the increase of the shearing strain. At relatively small shearing strains (106 < c < 1 0 5), the dynamic shear modulus decreased gently, then the dynamic shear modulus began to decrease sharply as the increase of shearing strain. It should be mentioned that for shearing strain less than 106, the dynamic shear modulus remain constant. Similar trends have also been verified in a single material, the effects of vibration cycles and cyclic strain history on shear modulus of dry sand were studied respectively by Kumar et al. [9–11]. The decreases in dynamic shear modulus with shearing strain is mainly due to the nonlinear and hysteretic behavior of the dynamic stressstrain relationship. 3.2. Maximum dynamic shear modulus The maximum dynamic shear modulus (Gmax) of SSM and CSM, at a strain level of 106, under three different confining pressures (50, 100, and 150 kPa) and three different curing ages (1, 3, and 7 days) for testing series Gs20, Gs30, Gs40, Gs50, Gc8, Gc12 and Gc15 was studied. Since the smallest strain level of SSM and CSM from resonant tests was 106, the Gmax was determined through regression analyses. Hardin and Drnevich proposed an approximate method of computing shear modulus (G) at any strain level (c). Assuming hyperbolic stress-strain relations, and the following expressions are obtained [24,25]:
G 1 ¼ Gmax 1 þ c a c
ð4Þ
r
160 1 days 3 days 7 days
150
Dynamic shear modulus (MPa)
Dynamic shear modulus (MPa)
160
140 130 120 110 100
140 130 120 110 100 90
90 80 0.0001
1 days 3 days 7 days
150
0.0010
0.0100
Shearing strain (%)
(a) SSM (Gs40-150 kPa)
0.1000
80 0.0001
0.0010
0.0100
Shearing strain (%)
(b) CSM (Gc15-150 kPa)
Fig. 6. The variation of G with shearing strain for different curing ages.
0.1000
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where G=Gmax is normalized dynamic shear modulus; cr is the reference strain; and a is a curve-fitting variable named curvature parameter. The reference strain is described as follows.
cr ¼ cr1
r0m
k ð5Þ
pa
125 120 115 110 105 100 95 90 85 80 75 70 65 60 55 50 45 0
50
3.3. Damping ratio Damping ratio (D) is another typical parameter to characterize the energy dissipation characteristics of a material. For all the tested SSM and CSM specimens, the variations of damping ratio with shearing strain for different values of confining pressure, mix proportion and curing age were studied. In order to explore the effects of confining pressure, mix proportion and curing age on the damping ratio, only some representative test results are
Gmax (MPa)
Gs20 Gs30 Gs40 Gs50 Gc8 Gc12 Gc15
100
150
140 135 130 125 120 115 110 105 100 95 90 85 80 75 70 65
Gs20 Gs30 Gs40 Gs50 Gc8 Gc12 Gc15
0
200
50
Confining pressure(kPa)
160 155 150 145 140 135 130 125 120 115 110 105 100 95 90 85
100
(b) Curing for 3 days Gs20 Gs30 Gs40 Gs50 Gc8 Gc12 Gc15
0
150
Confining pressure (kPa)
(a) Curing for 1 days
Gmax (MPa)
Gmax(MPa)
where cr1 is the reference strain at the effective mean stress of 100 kPa; pa is the reference stress of 100 kPa; r0m is effective mean stress; k is stress correction exponent. Fig. 7 shows the variation of Gmax with confining pressures for different mix proportions and curing ages. The Gmax increases almost linearly with the increase of confining pressure, this trend also exists in the test results of Honghua Zhao and Louis Ge, their test results also indicated that the Gmax of silica gel increased almost linearly with confining pressure [5]. In addition, for the given confining pressure, mix proportion and curing age also play an important role in the values of Gmax. Fig. 8 shows the variation of Gmax with mix proportion of SSM and CSM. It can be observed that the Gmax of SSM initially increased with the increase of steel slag content, and attained the peak value when the steel slag content is 40%. When the steel slag content increased to 50%, the Gmax decreased, which indicates that the optimum mix proportion of SSM is Gs40. Further analysis, when steel slag content was 40%, the hydration reaction was the most sufficient, and the dynamic
shear modulus reached the maximum. However, when steel slag content was 20% and 30%, the steel slag was not enough and the hydration reaction was incomplete, so the dynamic shear modulus didn’t reach the maximum. Furthermore, when steel slag was 50%, the steel slag was too much, and the remaining steel slag was not involved in hydration reaction, then the remaining steel slag as waste material existed in mixture, thus reduced the dynamic shear modulus. The Gmax of CSM also increased linearly with the increase of cement content. When cement content is 15%, the Gmax of CSM is close to the Gmax of SSM when the steel slag content is 40%. It is worth noting that when the amount of cement is too large, it is easy to produce the dry shrinkage and temperature shrinkage cracks [22], whereas using steel slag as aggregate of the mixture will improve such problems effectively.
50
100
150
Confining pressure (kPa)
(c) Curing for 7 days Fig. 7. The variation of Gmax with confining pressure of SSM and CSM.
200
200
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Fig. 8. The variation of Gmax with mix proportion of SSM and CSM.
selected, and other tests with different parameters also showed similar trends. Fig. 9 depicts the variation of damping ratio with shearing strain for different confining pressures. It is observed from Fig. 9 that confining pressure does not strongly affect damping ratio, especially at
9
7
7
6 5 4
6 5 4 3
3
2
2 1 0.0001
0.0010
0.0100
0.1000
1 0.0001
0.0010
0.0100
Shearing strain (%)
Shearing strain (%)
(a) Curing for 1 days
(b) Curing for 3 days
7
6
Damping ratio (%)
Damping ratio (%).
8
Gs40-50kPa Gs40-100kPa Gs40-150kPa Gc15-50kPa Gc15-100kPa Gc15-150kPa
8
Gs40-50kPa Gs40-100kPa Gs40-150kPa Gc15-50kPa Gc15-100kPa Gc15-150kPa
Damping ratio (%).
10
low strains, this phenomenon is more obvious. However, it can also be seen that the damping ratio tends to decrease with the increase of confining pressure. Fig. 10 shows the variation of damping ratio with shearing strain for different mix proportions. An increase in cement content leads to an increase in damping ratio of CSM, and the damping ratio of SSM initially increases and then decreases with the increase of steel slag content. This trend is observed in all the test results. This shows that damping ratios of specimens are significantly affected by mix proportion. It is known that when the shear modulus of a material becomes greater, its damping ratio is expected to become lower. So, the test results are not expected at first glance. This seemingly contradictory test result is likely to be related to the effects of the interaction of two materials on the energy dissipation. The damping ratio of soils represents the amount of energy dissipated during wave propagation through its mass. It should be mentioned that a similar increase in the damping ratio obtained by increasing the amount of cement was observed by Saxena et al. [26], they investigated the dynamic moduli and damping ratios for cemented sands at low strains, and their test results are similar to the results of CSM specimens in this test. In their findings, they reported that the energy spent for the wave to propagate through a weakly cemented sand specimen was larger than the energy spent by
5
Gs40-50kPa Gs40-100kPa Gs40-150kPa Gc15-50kPa Gc15-100kPa Gc15-150kPa
4
3 2
1 0.0001
0.0010
0.0100
0.1000
Shearing strain (%)
(c) Curing for 7 days Fig. 9. The variation of D with shearing strain for different confining pressures (Gs40, Gc15).
0.1000
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6
Gs20 Gs30 Gs40 Gs50 Gc8 Gc12 Gc15
Damping ratio (%)
5
4
3
2
1
0 0.0001
0.0010
0.0100
0.1000
Shearing strain (%) Fig. 10. The variation of D with shearing strain for different mix proportions (150 kPa-7 days).
9
7 6
7
5 4
6 5 4 3
3
2
2 1 0.0001
Gs40-1days Gs40-3days Gs40-7days Gc15-1days Gc15-3days Gc15-7days
8
1
0.0010
0.0100
0.1000
0.0001
0.0010
Shearing strain (%)
8 7 6 5
(b) Confining pressure is 100kPa
Gs40-1days Gs40-3days Gs40-7days Gc15-1days Gc15-3days Gc15-7days
4 3 2 1 0.000
0.0100
Shearing strain (%)
(a) Confining pressure is 50kPa
Damping ratio (%)
Damping ratio (%)
8
9
Gs40-1days Gs40-3days Gs40-7days Gc15-1days Gc15-3days Gc15-7days
Damping ratio (%)
10
the wave to propagate through a similar but clean, uncemented specimen (prepared under similar condition). In addition, the fact that the damping ratio during wave propagation increases as the degree of coating (cleanliness) decreases was also reported by Duffy and Mindlin [27]. Therefore, when the cement content is small, the cement is coated in the areas of the contacts between the individual sand grains and then increases the damping ratio. As the increase of cement content, the cement gradually acts as a gelling agent, and then the mixture tends to solidify and reduces the damping ratio. Based on some similar characteristics of steel slag and Portland cement, we think that the similar dissipating mechanism is also suitable for the SSM specimens. Additionally, for SSM, the hydration reaction of steel slag and sand had been occurred. The specific process has been described in the previous section. This not only increased the degree of density of SSM, and improved the dynamic shear modulus, but also strengthened the connection between soil particles and improved the cohesion. Then the rearrangement of soil particles required more energy and increased damping ratio of SSM. The additives (such as Portland cement, steel slag, lime,
0.001
0.010
0.100
Shearing strain (%)
(c) Confining pressure is 150kPa Fig. 11. The variation of D with shearing strain for different curing ages (Gs40, Gc15).
0.1000
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Fig. 12. The variation of Dmax with mix proportion of SSM and CSM.
etc.) content which corresponds to the maximum damping ratio is ‘‘coating level” (CL). So, in this study, we think that the CL of CSM may be more than 15%, and the CL of SSM may be about 40%. Compared with the results which reported by Saxena et al. [26], their test results showed that the CL of cemented sands is between 5% and 8%, it should be mentioned that the confining pressures in their tests are more higher than ours. Thus, the CL of mixture may be affected by other factors. Another similar increase in the damping ratio obtained by increasing the cement content was reported by Yong and Chiang [28], their test results showed that the CL is between 0 and 6%. In addition, the number of cycles chosen to determine the damping forms an important parameter and it affects the damping quite significantly. It is necessary to do more research to make a further explanation. Fig. 11 shows the variation of damping ratio with shearing strain for different curing ages. It is observed that the curing age does not strongly affect the damping ratio when the shearing strain is small, as the increase of shearing strain, the damping ratio decreases slowly with the increase of curing age. Generally, damping ratio initially increased almost linearly with the increasing of the shearing strain and the followed by a rapid nonlinear increasing behavior, which means that when the shearing strain is relatively small, the energy attenuation of the mixtures is relatively slow, and with the increase of shearing strain, the energy attenuation of the mixtures will increase dramatically. 3.4. Maximum damping ratio The variation of the maximum damping ratio (Dmax) with mix proportion for different values of confining pressure and curing age has been investigated in this study. The empirical correlation given by Kondner and the relation expression of damping curve modified by Hu are adopted [29,30], and the expressions are shown as follows.
G 1 ¼ Gmax 1 þ c=cr D ¼ Dmax
c=cr 1 þ c=cr
ð6Þ m ð7Þ
where Gmax is the maximum dynamic shear modulus, MPa; G=Gmax is normalized dynamic shear modulus; c is the shearing strain; cr is the reference shearing strain; Dmax is the maximum damping ratio, %; m is the experimental parameter. The comparison of the Dmax with mix proportion for different values of confining pressure and curing age is provided in Fig. 12. For the given confining pressure and curing age, the Dmax of SSM increases initially and then decreases with the increase of steel slag
179
content, and reaches the peak when the steel slag is 40%. Under the same conditions, for CSM, the Dmax increases with the increase of cement content, and when the cement content is 15%, the Dmax of CSM is the largest. By comparison, we can indicate that when the steel slag content is 40%, the Dmax of SSM is close to that of CSM when the cement content is 15%. It also can be observed that when the cement content of CSM is less than 15%, by adjusting the mix proportion of SSM, the SSM with the same energy attenuation characteristics can be found. Furthermore, the curing age have remarkable effect on the Dmax of SSM and CSM, the longer the curing age is, the smaller the Dmax value is. On the other hand, Dmax is not significantly affected by confining pressure. It should be mentioned that the selection of empirical correlation also affects the fitting results of Dmax. So, more research will be needed to optimize the empirical correlation. This comparison means that the similarity of the dynamic behavior of SSM and CSM. Therefore, it is feasible to use SSM instead of CSM as the foundation treatment materials. 4. Conclusions A series of resonant column tests were performed to investigate the low strain dynamic characteristics of SSM and CSM, and the following conclusions could be drawn from this study: (1) The dynamic shear modulus (G) increases with the increase of confining pressure, and the varying trends of SSM and CSM are similar. The G of CSM increases with the increase of cement content, whereas the G of SSM initially increases and then decreases with the increase of steel slag content. The G of SSM and CSM increases with the increase of curing age. (2) The G of SSM and CSM decreases nonlinearly with the increasing of the shearing strain. The G initially decreases gently, and then decreases sharply as the increase of shearing strain. The G of SSM and CSM remains constant when the shearing strain is less than 106. (3) The maximum dynamic shear modulus (Gmax) of SSM and CSM increases almost linearly with the increase of confining pressure. The Gmax initially increases and then decreases with the increasing of steel slag content, and attains the maximum value when steel slag content is 40%. The Gmax of CSM increases linearly with the increasing of cement content. (4) The damping ratios (D) of SSM and CSM are not strongly affected by simple confining pressure, but are significantly affected by mix proportion. As the increase of steel slag and cement in the mixture, the D of SSM and CSM tend to increase first and then decrease. As the increase of shearing strain, the D decreases slowly with the increase of curing age. (5) For the given confining pressure and curing age, the maximum damping ratio (Dmax) of SSM increases initially and then decreases with the increase of steel slag content. Under similar conditions, the Dmax of CSM increases with the increase of cement content. When the steel slag content is 40%, the Dmax of SSM is close to that of CSM with the 15% cement content. It is feasible to use SSM instead of CSM as the foundation treatment materials. Acknowledgements This study was supported by the National Natural Science Foundation of China (Grant No. 51308355) and Liaoning Province Natural Science Foundation of China (Grant No. 20170540735).
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