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Shear Friction Characteristics and Modification Factor of Concrete Prepared Using Expanded Bottom Ash and Dredged Soil Granules
International Journal of Concrete Structures and Materials volume 13, Article number: 50 (2019)
Abstract
The objective of this study is to assess the shear friction characteristics of lightweight aggregate concrete (LWAC) prepared using artificially expanded bottom ash and dredged soil granules. A total of 37 concrete mixtures were prepared under the classification of three series. In the first and second series, the natural sand content for replacing lightweight fine aggregates and the watertocement ratio varied to obtain different densities and compressive strengths of concrete. The third series was designed to estimate the effect of the maximum aggregate size on the friction resistance along the shear crack plane of the monolithic interfaces. The frictional angle of the LWAC tested was formulated as a function of the ratio of the effective tensile and compressive strengths of concrete through the expansion of the integrated mathematical models proposed by Kwon et al., based on the upperbound theorem of concrete plasticity. When predicting the shear friction strength of LWAC, the present mathematical model exhibits relatively good accuracy, yielding the mean and standard deviation of the ratios between experiments and predictions of 1.06 and 0.14, respectively, whereas the empirical equations proposed by the AASHTO provision and Mattock underestimated the results. Ultimately, an advanced modification factor for shear design of LWAC is proposed as a function of the density and compressive strength of concrete and the maximum size of aggregates.
1 Introduction
Shear friction action is a primary load transfer mechanism at concretetoconcrete interfaces found in the connections between columns and corbels, between squat shear walls and foundations, of dappedend beams, and shear keys (ACIASCE Committee 426 1973). The shear friction mechanism in concrete interfaces was first identified in 1966 (Santoa and Júlio 2012), and the design codes (AASHTO 2014; ACI Committee 318 2014; fib 2010; EN 199211 2004) for reinforced concrete structures has progressed based on extensive test results compiled from normalweight concrete (NWC) pushoff specimens subjected to pure shear. According to the concrete plasticity and shear friction theorem, shear friction transfer capacity (\( \tau_{f} \)) at monolithic concrete interfaces depends on the frictional angle of concrete (Committee and 426. 1973; fib 2010; Nielsen and Hoang 2011). This implies that the \( \tau_{f} \) of a concrete interface without transverse reinforcement is affected significantly by the compressive strength and type of concrete (Yang et al. 2012). However, experimental studies to ascertain the shear friction characteristics of a lightweight aggregate concrete (LWAC) interface are still indistinct although the qualities of artificial lightweight aggregates have improved gradually, thereby expanding the practical ranges for the compressive strength of such concrete.
A few experimental studies (Yang et al. 2012; Tang et al. 2008; Mattock et al. 1976) demonstrated that shear cracks in LWAC interfaces primarily penetrate through aggregate particles, unlike the typical observations in NWC interfaces that are governed by the crack propagation through a cement matrix around aggregate particles. Thus, shear friction transfer via aggregate interlock is reduced significantly along LWAC interface cracks. Most design codes (ACI Committee 318 2014; fib 2010; EN 199211 2004) introduce the modification factor to account for the reduced shear transfer capacity of LWAC owing to the softened aggregate interlock along the cracks in the concrete interfaces or reinforced concrete beams. ACI 31814 (2014) adopted the modification factor proposed by Ivey and Buth (1967) which was empirically fitted using the limited test data of 26 LWAC beam specimens. However, the logicality and reliability of this modification factor remain controversial because of insufficient mathematical consensus on the shear friction transfer mechanism along crack interfaces in LWAC elements. Yang and Ashour (2011, 2015) reported that the modification specified in ACI 31814 (2014) for the shear transfer capacity of LWAC beams must be revised to improve the safety of the shear design provision based on the rational mathematical approach to explicate the reduced friction properties along the LWAC interfaces.
Recently, various industrial byproducts and waste materials such as fly ash, bottom ash, dredged soil, reservoir sludge, and oil palm shell have been used as a source material to produce artificial lightweight aggregates. The disparity in physical properties and chemical compositions of the source materials results in different particle characteristics including shape, angularity, substrate state, porosity, modulus of elasticity and strength of aggregates (ACI Committee 213 2014). The porous structure and relatively smooth substrate characteristic of lightweight aggregate particles yield poor resistance against crack propagations, and a weak interfacial transition zone with a cement matrix. Lee et al. (2019) demonstrated that lightweight aggregate concrete made using expanded bottom ash and dredged soil granules (referred to as LWACBS hereinafter) exhibited a faster decrease at the postpeak branch of the stress–strain curve and a higher direct tensile strength than lightweight aggregate concrete made using expanded clay and/or fly ash granules (LWACCF) at the same compressive strength (\( f_{c}^{'} \)) of concrete. This implies that the shear friction resistance of LWAC is affected by the type and characteristics of lightweight aggregates because the crack propagation at the pure shear plane is affected by the tensile resistance of aggregate and concrete under principal tensile stresses (Nielsen and Hoang 2011). Therefore, the type and characteristics of lightweight aggregates need to be considered carefully in investigating the shear friction properties at the LWAC interfaces and the modification factor.
As a sustainable activity in the concrete industry in response to the global requirements to conserve natural resources and curtailing the issue of natural aggregate depletion, the Korean government has strived to produce artificially expanded lightweight aggregates through the calcination process of bottom ash and dredged soil powders. This study primarily aims to evaluate the \( \tau_{f} \) of LWACBS interfaces, and to assess the effect of the type of artificially expanded lightweight aggregates on the frictional angle (\( \phi \)) of concrete. A total of 37 LWACBS mixtures were prepared with the test parameters of the design compressive strength (\( f_{cd} \)) and dry density (\( \rho_{c} \)) of concrete, watertocement ratio (\( W/C \)), and maximum aggregate size (\( d_{a} \)). The variation in \( \rho_{c} \) was controlled by the natural sand content (\( R_{s} \)) for the replacement of lightweight fine aggregates. The previous mathematical model (Kwon et al. 2017) derived based on the upperbound theorem of concrete plasticity was applied to determine the frictional angle and modification factor of LWACBS. The reliability of the existing empirical equations (AASHTO 2014; Mattock 2001) and the proposed model for LWAC were examined through comparisons with the present test.
2 Research Significance
This study provides extensive data on the \( \tau_{f} \) of monolithic LWAC interface made using expanded bottom ash and dredged soil granules. The different values for the frictional angle of concrete were examined with respect to the type of artificially expanded lightweight aggregates. The present study also confirms that the empirical equations proposed by the AASHTO provision (2014) and Mattock (2001) need to be revised because they provide a constant shear friction strength for the LWAC interface without transverse clamping forces, irrespective of \( f_{c}^{'} \) and \( \rho_{c} \). Moreover, the derived modification factor for the shear design of LWAC elements represents well the reduced shear friction resistance along the crack surface of LWAC.
3 Experimental Details
3.1 Concrete Specimens
A total of 37 LWACBS mixtures classified into three series were tested, as presented in Table 1. The first series included three groups categorized according to the \( f_{cd} \) at an age of 28 days as follows: Lgroup (18 MPa), Mgroup (24 MPa), and Hgroup (35 MPa). In each group, \( R_{s} \) was selected as the primary parameter, which varied from 0 to 100% at an interval of 25%, for the different values of \( \rho_{c} \) and tensile resistance of concrete. In the second series, \( W/C \) varied from 0.30 to 0.50 at an interval of 0.05 under fixed \( R_{S} \) values of 0% (S0 group) and 50% (S50 group). Thus, \( f_{cd} \) was not targeted previously in the concrete mixes of the second series. The third series was designed to examine the effect of \( d_{a} \) on the shear friction performance of LWACBS with different compressive strengths and densities. Considering the practical production of expanded bottom ash and dredged soil granules and the ASTM requirements (2013) for lightweight aggregate particles, \( d_{a} \) was selected as 4.75 mm, 9.5 mm, and 19 mm in each group categorized as the following four groups: S0M (\( R_{S} \) = 0% and \( f_{cd} \) = 24 MPa); S0H (\( R_{S} \) = 0% and \( f_{cd} \) = 35 MPa); S100M (\( R_{S} \) = 100% and \( f_{cd} \) = 24 MPa); and S100H (\( R_{S} \) = 100% and \( f_{cd} \) = 35 MPa). The present tests identified the concrete mixes with \( R_{S} \) = 0% as allLWACBS and the other mixes with \( R_{S} \) ≥ 25% as sandLWACBS.
The mixture proportions of all the concrete specimens for the targeted requirements were determined in accordance with the procedure proposed by Yang et al. (2014a). The use of natural sand in LWAC strengthens the restraining action of the aggregate particles against the lateral expansion of cement pastes under axial loads, which contributes to enhancing the strength of the mortar matrix. Thus, the value of \( W/C \) in each group of the first series decreased slightly with the decrease in \( R_{S} \) to achieve \( f_{cd} \), as presented in Table 1. A lower value of the unit water content (\( W \)) was designed with the increase in \( f_{cd} \) to restrict the segregation and immoderate bleeding in fresh concrete. No waterreducing agent was added in any of the concrete mixes.
In the first series, unit water content (\( W \)) was fixed as 185 kg/m^{3} and 170 kg/m^{3} for the Lgroup and Hgroup mixes, respectively, whereas the Mgroup mixes used the \( W \) of 175 kg/m^{3} or 185 kg/m^{3} for achieving the required slump value. In the second series mixes, \( W \) varied from 120 to 200 kg/m^{3} at the constant unit cement content (\( C \)) of 400 kg/m^{3} with respect to the investigated variations in \( W/C \). The fine aggregatetototal aggregate ratio (\( S/a \)) was fixed to be 40% for all the concrete mixes in the first and second series. In the third series, the fixed \( C \) and \( W/C \) were used for each group as follows: 375 kg/m^{3} and 0.5 for S0M; 450 kg/m^{3} and 0.25 for S0H; 350 kg/m^{3} and 0.55 for S100M; and 450 kg/m^{3} and 0.32 for S100H, respectively. A lower \( W/C \) was selected for allLWAC mixes when compared with the companion concrete mixes with \( R_{s} \) of 100% at the same \( f_{cd} \). The values of \( S/a \) in the concrete mixes of the third series varied slightly between 0.45 and 0.48 to achieve an appropriate slump without bleeding. Note that the specimens with \( d_{a} \) of 4.75 mm can be regarded as mortar mixtures without coarse aggregates, resulting in an \( S/a \) of 1.00.
3.2 Materials
Ordinary Portland cement (OPC) conforming to ASTM Type I [18] was used as the primary cementitious material for all mixes. Locally available artificially expanded granules were used for lightweight aggregates. The quality of the artificially expanded granules satisfies the requirements for structural lightweight aggregates specified in ASTM C330 (2013). The screened bottom ash and dredged soil powders used as source materials underwent various manufacturing processes including calcination and expansion in large rotary kilns at approximately 1200 °C. This process is almost identical to that for artificially expanded clay granules. For coarse lightweight aggregates, expanded granules with \( d_{a} \) of 19 mm were used for the first and second series mixes and those with \( d_{a} \) of 19 mm or 9.5 mm were used for the third series mixes. For all the mixes, artificially expanded granules with \( d_{a} \) of 4.75 mm were used for lightweight fine aggregates. In the mixes of the first and second series, natural sand with \( d_{a} \) of 1.2 mm was used for partially replacing the lightweight fine aggregates. In the third series mixes, natural sand with \( d_{a} \) of 4.75 mm was used for fully replacing the lightweight fine aggregates to examine the effect of aggregate size on the shear friction of concrete.
The physical properties of the aggregates used are summarized in Table 2. Lightweight aggregates feature a spherical shape and a porous core structure. Thus, lightweight aggregates generally possess higher water absorption and lower density than natural sand. The apparent density and water absorption were 1.0 g/cm^{3} and 17.2%, respectively, for the lightweight coarse particles, and 1.1 g/cm^{3} and 12.9%, respectively, for the lightweight fine particles. The apparent density of the lightweight aggregates was approximately 35% lower, whereas higher water absorptions as much as 10.8 times and 6.8 times were measured for lightweight coarse and fine aggregates, respectively, when compared with those of natural sand. The moduli of fineness of the lightweight particles with \( d_{a} \) of 19 mm, 9.5 mm, and 4.75 mm were 6.4, 5.9, and 4.4, respectively. The corresponding values for sand particles of 4.75 mm and 1.2 mm were 2.7 and 2.2, respectively.
3.3 Casting, Curing, and Testing
All the aggregates were prepared in a saturated surfacedry state, and dry mixed with cement in a 0.35 m^{3}capacity mixer for 1 min. Lightweight aggregates were prewetted for 24 h and subsequently dried in the shade for 24 h. Immediately prior to mixing, the moisture content in the aggregates was measured and subsequently accounted for the calculation of the net unit water content of each mixture proportion. Distinct segregation or floating of lightweight aggregate particles was not observed during the mixing phase. The slump and air content of fresh concrete were measured in accordance with ASTM C143 and ASTM C231 (2013), respectively. The values of \( f_{c}^{'} \) and \( \rho_{c} \) of the hardened concrete were measured using cylindrical specimens of dimensions 100 mm × 200 mm in accordance with ASTM C 39 and ASTM C 642 (2013), respectively. To measure the \( \tau_{f} \) of the prepared LWAC mixes, pushoff specimens were prepared with the dimensions of 300mm wide, 820mm high, and 120mm thick. The area of the frictional plane under pure shear in the pushoff specimens were 200 mm × 120 mm. Three specimens were prepared for each concrete mix.
All pushoff specimens were tested to failure under a concentric load acting as pure shear in the shear plane of the test zone. Steel plates and hinges were installed at the top and bottom loading points that were aligned with the shear plane. The top and bottom stubs of the test specimens were strengthened with carbon fiber sheets to prevent flexural failure at the interface between the test zone and both stubs. The tests were conducted at the age of 91 days for the first and second series specimens, and at the age of 28 days for the third series specimens. All pushoff specimens exhibited no shrinkage cracks until the specified ages of the tests.
4 Test Results and Discussions
Table 3 summarizes the test results measured in each concrete mix. The compressive strength of concrete measured at the same age of pushoff tests was used for the present discussion. All the mixtures with the exception of specimens S030, S5030, S0H19, S0H10, S0H5, and S100H19 exhibited high slump values exceeding 150 mm. The initial slump (\( S_{i} \)) of LWAC tended to decrease as \( R_{s} \) and \( W/C \) decreased but was marginally affected by \( d_{a} \). The air content of LWAC was insignificantly affected by \( R_{s} \), \( W/C \) and \( d_{a} \). The air content mostly ranged between 4.0 and 6.0%, and satisfied the requirements recommended for an airentrained LWAC that is not exposed to freezing (ACI Committee 213 2014).
In general, the increasing rates of the tensile and shear resistances of concrete are lower than those of \( f_{c}^{'} \). Most the code equations (AASHTO 2014; ACI Committee 318 2014; fib 2010; EN 199211 2004) for the tensile and shear transfer capacities of concrete have been proposed as a power function of \( f_{c}^{'} \). Lee et al. (2019) demonstrated that the empirical equation for \( \tau_{f} \) can be fitted using the parameter of \( \sqrt {f_{c}^{'} } \) in the regression analysis of LWACBS test data. Thus, the following discussions are focused on the \( \tau_{f} \) normalized by \( \sqrt {f_{c}^{'} } \), with respect to each test parameter.
4.1 Typical Failure Mode
A typical crack propagation and failure plane of the pushoff specimens is presented in Fig. 1. An initial crack suddenly appeared along the critical shear plane at the 90–95% of the peak load, indicating that the concrete specimens reached their shear friction capacities immediately after the crack occurred. No additional cracks were developed outside the shear plane. Thus, the failure of the specimens was primarily governed by the propagation of the initial single shear crack. Ultimately, the specimens were divided into two blocks at failure. The same failure modes were observed in all the specimens irrespective of the test parameters. The observation of the failure surfaces clearly demonstrated that crack propagation penetrated into the bulk of the lightweight aggregate particles. The failure surfaces were relatively smooth, although a slightly more squarrose surface was observed in the concrete with high volume sand content when compared with the allLWAC specimen. The rupture of aggregate particles owing to the propagation of the single crack can result in a reduction in the aggregate interlock resistance and coefficient of friction of concrete (Mattock et al. 1976; Choi et al. 2014).
4.2 Effect of \( R_{s} \) (\( \rho_{c} \)) on \( {{\tau_{f} }}/{f_{c}^{'}} \)
Figure 2 shows the effect of \( R_{s} \) on \( {{\tau_{f} }}/{f_{c}^{'}} \) in the series I specimens. The value of \( {{\tau_{f} }}/{f_{c}^{'}} \) increased with the increase in \( R_{s} \), revealing a similar increasing rate in three groups with different sand contents. When \( R_{s} \) increased from 0 to 100%, the increasing rates of \( {{\tau_{f} }}/{f_{c}^{'}} \) were 37.8%, 31.9%, and 33.1% for the L, M, and Hgroup specimens, respectively. The frictional failure of a concrete member under pure shear is critically governed by the magnitude of the primary tensile stress along the shear cracking planes. Thus, the shear and tensile capacities of concrete are indispensable to each other. This implies that the replacement of lightweight fine aggregates using natural sand is favorable for enhancing the tensile and shear friction resistances of LWAC. It is also interesting that the value of \( {{\tau_{f} }}/{f_{c}^{'}} \) were somewhat independent of the compressive strength of concrete, as given in Table 3.
An increase in the content of natural sand leads to the increase in \( \rho_{c} \), as shown in Table 3. Thus, the increase in \( R_{s} \) yields an increasing \( \rho_{c} \). The values of \( \rho_{c} \) ranged between 1301 kg/m^{3} and 1540 kg/m^{3}, 1366 kg/m^{3} and 1698 kg/m^{3}, and 1605 kg/m^{3} and 1783 kg/m^{3} for the L, M, and Hgroup specimens, respectively, indicating that a higher \( \rho_{c} \) is typically obtained for LWAC with a higher \( f_{cd} \). This is because a more cement content was used in concrete mixtures with a higher \( f_{cd} \). As aforementioned, the values of \( {{\tau_{f} }}/{f_{c}^{'}} \) increased with the increase in \( \rho_{c} \). However, a lower \( {{\tau_{f} }}/{f_{c}^{'}} \) value was observed in LWAC with a higher \( f_{cd} \) at the same level of \( \rho_{c} \).
4.3 Effect of \( W/C \) on \( {{\tau_{f} }}/{f_{c}^{'}} \)
It is commonly accepted (Yang et al. 2014a) that the decrease in \( W/C \) leads to the increase in \( f_{c}^{'} \). Thus, a higher \( \tau_{f} \) was measured in the concrete specimens with a lower \( W/C \), as shown in Table 3. Meanwhile, it was found that the value of \( {{\tau_{f} }}/{f_{c}^{'}} \) was practically independent of the \( W/C \), as presented in Fig. 3, although extraordinarily \( {{\tau_{f} }}/{f_{c}^{'}} \) value was obtained in specimen S5045. The shear friction resistance of concrete significantly depends on its compressive strength. Thus, as proposed by Lee et al. (2019), the \( \tau_{f} \) of LWAC is approximately proportional to the square root of \( f_{c}^{'} \) at the same level of \( \rho_{c} \).
4.4 Effect of \( d_{a} \) on \( {{\tau_{f} }}/{f_{c}^{'}} \)
Figure 4 shows the variation in \( {{\tau_{f} }}/{f_{c}^{'}} \) with respect to \( d_{a} \) in concrete specimens with different \( f_{cd} \) and \( R_{s} \) values. Mortar specimens with \( d_{a} \) of 4.75 mm typically exhibited lower shear friction resistance than their counterpart concrete specimens. The increasing rate in \( {{\tau_{f} }}/{f_{c}^{'}} \) with respect to \( d_{a} \) was similar in both sandLWAC and allLWAC specimens, irrespectively of \( f_{cd} \). When \( d_{a} \) varied from 4.75 mm to 19 mm, the increasing rates of \( {{\tau_{f} }}/{f_{c}^{'}} \) were 131% for S0M group, 137% for S0H group, 140% for S100M group, and 137% for S100H group. The shear friction resistance at the shear plane is significantly affected by the substrate roughness along the shear crack (Yang and Ashour 2011). The lightweight coarse aggregates unpierced by the crack propagation contribute to resisting the shear slip along the shear crack. Thus, a slightly higher shear friction resistance can be expected for a monolithic LWAC interface with a larger aggregate size.
5 Modeling of Shear Friction Parameters
5.1 Model Back Ground
Several researchers (Yang et al. 2012; Lee and Hong 2015; Kwon et al. 2017) proposed a mathematical model to reasonably evaluate the shear friction strength of concrete at the monolithic interfaces on the basis of the upperbound theorem of concrete plasticity. In their model, concrete was regarded as an equivalent rigid perfectly plastic material obeying a modified Coulomb failure criteria by introducing effectiveness factors that are determined from equating the area of the rigidperfectly plastic stress–strain curve to that of the actual stress–strain curve, as summarized in Table 4. Kwon et al. (2017) determined the effectiveness factors based on the compressive stress–strain relationship generalized by Yang et al. (2014b) and the revised version (Yang et al. 2012) of the tensile stress–strain relationship proposed by Hordijk (1991) to simulate the actual stress–strain curves of concrete. The stress–strain relationship in compression proposed by Yang et al. was fitted using the test data compiled from various types including LWACCF, NWC, and heavyweight concrete. Using the determined effectiveness factors, the frictional angle of concrete was formulated as a function of \( f_{c}^{'} \), \( \rho_{c} \), and \( d_{a} \). Kwon et al. verified that the proposed model exhibits superior accuracy to the design models (AASHTO 2014; ACI Committee 318 2014; Shaikh 1978) in predicting the shear friction strength, resulting in mean and standard deviation of the ratios between the measured and predicted values of 0.95 and 0.15 for LWACCF, respectively. Hence, the present study expands Kwon et al. mechanical approach by adopting the compressive stress–strain relationship (Lee et al. 2019) and tensile strength fitted using the LWACBS data to assess the shear friction parameters of such concrete.
As summarized in Table 4, the shear friction parameters depend on the effective strengths of concrete in compression and tension. In accordance with the numerical analysis approach conducted by Kwon et al. the effectiveness factor (\( \nu_{c} \)) for concrete in compression could be determined using the actual compressive stress–strain relationship (Lee et al. 2019) of LWACBS. The slopes of the ascending and descending branches of the stress–strain curves of LWAC vary with the characteristics of the lightweight aggregates and compressive strength of concrete. Thus, the stress–strain model proposed by Lee et al. needs to be examined at LWACBS with \( f_{c}^{'} \) > 60 MPa.
For a parametric study to determine the shear friction parameters, LWACBS specimens with different ranges of \( f_{c}^{'} \) = 8–80 MPa and \( \rho_{c} \) = 800–2300 kg/m^{3}, and \( d_{a} \) = 4.75–25 mm were selected in reference to the lightweight concrete classification specified in fib (2010). The value of \( \nu_{c} \) was calculated for each concrete; subsequently, nonlinear multiple regression (NLMR) analysis was performed to establish a simple equation. As demonstrated by Yang et al. (2012), the value of \( \nu_{c} \) is significantly affected by \( f_{c}^{'} \) and \( \rho_{c} \), yet independent of \( d_{a} \). The influencing variables of \( f_{c}^{'} \) and \( \rho_{c} \) were combined and adjusted repeatedly by trial and error until a relatively high correlation coefficient (\( R^{2} \)) was obtained. Consequently, the simple equation for the \( \nu_{c} \) of LWACBS could be proposed as follows (Fig. 5):
where \( f_{0} \) (= 10 MPa) and \( \rho_{0} \) (= 2300 kg/m^{3}) are the reference values for the compressive strength and dry density, respectively, of concrete.
The tensile strength of LWAC is marginally affected by the types of expanded lightweight aggregates and \( d_{a} \) (Choi et al. 2014) because the tensile fracture of LWAC is typically governed by the separation failure divided by a single crack penetrating aggregate particle. In addition, very few, if any, reliable model was studied in developing the tensile stress–strain relationship for LWAC, because the postpeak tensile behavior of concrete depends on the propagation of the tensile crack width. Yang et al. (2012) revised the tensile stress–strain relationship proposed by Hordijk’s (1991) to account for a higher growth potential of crack opening in LWAC. Thus, the present study adopted the revised version (Yang et al. 2012) to determine the slopes of ascending and descending branches in tensile stress–strain relationship, at which the tensile strength was defined using the equation obtained empirically by Lee et al. (2019) for LWACBS. Overall, the effective strength ratio (\( f_{t}^{*} /f_{c}^{*} \)) of LWACBS required for the calculation of parameters \( l \) and \( m \) given in Table 4 could be solved in accordance with the numerical analysis approach by Kwon et al. using the aforementioned stress–strain relationships. From the parametric study conducted using the same variable ranges as that for deriving the simple equation of \( \nu_{c} \), the value of \( f_{t}^{*} /f_{c}^{*} \) calculated for each concrete was formulated through the NLMR analysis of the numerical results. Overall, the \( f_{t}^{*} /f_{c}^{*} \) for LWACBS can be expressed in the following form (Fig. 6):
where \( c_{0} \) (= 25 mm) is the reference value for the maximum aggregate size.
Following the concrete plasticity (Nielsen and Hoang 2011) describing the energy dissipated in concrete along the sliding failure surface, frictional angle (\( \phi \)) can be expressed as a function of \( f_{t}^{*} /f_{c}^{*} \) as follows:
The variables of \( l \) and \( m \) in the equation above are defined as \( 1  2\frac{{f_{t}^{*} }}{{f_{c}^{*} }}\frac{\sin \phi }{1  \sin \phi } \) and \( 1  2\frac{{f_{t}^{*} }}{{f_{c}^{*} }}\frac{1}{1  \sin \phi } \), respectively. Hence, the solution of \( \phi \) can be obtained from the numerical analysis for a given value of \( f_{t}^{*} /f_{c}^{*} \). For the typical ranges of \( f_{t}^{*} /f_{c}^{*} \) (= 0.005–0.07; see Fig. 6) of LWACBS, the \( \phi \) values calculated from the numerical analysis can be formulated as follows (Fig. 7):
Nielsen and Hoang (2011) regarded a constant \( \phi \) value as 37°, regardless of \( f_{c}^{'} \) and \( \rho_{c} \), whereas Kahraman and Altindag (2004) demonstrated that the \( \phi \) value depends on the material brittleness. Equation (4) also implies that the \( \phi \) value increases with the increase in \( f_{c}^{'} \) and decrease in \( \rho_{c} \), followed by the decrease in the energy dissipation in the stress–strain curves.
LWACBS exhibits a slightly higher value of \( \phi \) than LWACCF at the same \( f_{c}^{'} \) and \( \rho_{c} \), as shown in Fig. 8. The difference in \( \phi \) values between two concrete types increases with the increase in \( f_{c}^{'} \) and decrease in \( \rho_{c} \). This is because LWACBS has a more rapid decreasing rate in the descending branch of the stress–strain curve in compression than LWACCF with the same \( f_{c}^{'} \) and \( \rho_{c} \) (Lee et al. 2019). Meanwhile, the effect of \( d_{a} \) on the \( \phi \) values is similar in two types of LWAC.
5.2 Verification of the Expanded Model
Figure 9 presents the comparisons of the measured \( \tau_{f} \) of the present pushoff specimens and those predicted using the proposed mathematical model and the empirical equations of the AASHTO provision (2014) and Mattock (2001). In the same figure, the mean (\( \gamma_{m} \)) and standard deviation (\( \gamma_{s} \)) of the ratios (\( \gamma \)) between the measured and predicted values are also presented for comparisons. Additionally, these comparisons for each specimen are presented in Table 3. Note that \( \gamma \) values below 1.0 indicate an unsafe prediction of \( \tau_{f} \), whereas those exceeding 1.0 refer to an underestimation. The AASHTO equation highly underestimates the \( \tau_{f} \) of LWACBS, resulting in a greater underestimation with the increase in \( \rho_{c} \), \( f_{c}^{'} \), and \( d_{a} \). The values of \( \gamma_{m} \) and \( \gamma_{s} \) determined from the comparisons between the measured \( \tau_{f} \) and the AASHTO equation are 2.21 and 0.38, respectively. This is because the AASHTO equation assigns the constant \( \tau_{f} \) value of 1.65 MPa for LWAC interfaces without clamping forces that can be induced from transverse reinforcement and applied normal stresses. The equation by Mattock also gives quite underestimated results. According to Mattock’s equation, the \( \tau_{f} \) for a concrete interface without clamping forces is predicted as 1.7 MPa for sandLWAC and 1.4 MPa for allLWAC. The empirical equations of the AASHTO provision and Mattock were empirically fitted using extremely limited test data for the LWAC pushoff specimens. Thus, they do not consider the influencing variables on the \( \tau_{f} \) of the LWAC interfaces. The values of \( \gamma_{m} \) and \( \gamma_{s} \) determined from the comparisons were 2.38 and 0.34, respectively, for the Mattock equation. These values are very similar to those determined from the comparisons using the AASHTO equation.
The predictions from the model expanded in this study for LWACBS agree better with the test results, indicating the values of \( \gamma_{m} \) and \( \gamma_{s} \) of 1.06 and 0.14, respectively. The present models tend to underestimate the \( \tau_{f} \) of LWAC interfaces; however, the degree of underestimation is significantly reduced when compared with the existing empirical equations. This implies that the shear friction parameters for LWACBS can be estimated using the equations derived from the expanded mechanism analysis, accounting for the reduced aggregate interlock capacity of such concrete. The present mechanical approach needs to further consider the effect of precracks or crack inducers along the shear plane on the frictional angle of LWAC because shrinkage cracks are likely to be developed in practical concrete interfaces.
6 Modification Factor
According to the ACI 31814 provision (2014), the modification factor (\( \lambda \)) is defined as a ratio of shear transfer capacity of LWAC to that of the companion NWC. As the \( \lambda \) is introduced to account for the reduced frictional properties along the crack interfaces in LWAC, the following equation can be identified:
To calculate the value of \( \lambda \) using the equations for \( \tau_{f} \) summarized in Table 4 and Eq. (5), a numerical parametric study was conducted for different concrete specimens with \( f_{c}^{'} \) ranging from 8 and 80 MPa, \( d_{a} \) ranging from 4.75 mm and 25 mm, and \( \rho_{c} \) between 800 and 2300 kg/m^{3}. The concrete specimens with \( \rho_{c} \) of 2300 kg/m^{3} indicate NWC. The results obtained from the parametric study were formulated by the regression analysis approach, as plotted in Fig. 10; therefore, a modification factor for LWACBS can be finally proposed:
Figure 10 shows the comparisons of the measured \( \lambda \) values and predictions by the equation above. To examine the reliability of Eq. (6), NWC pushoff specimens were additionally tested at the same parameters as the series III specimens. When determining the \( \lambda \) values, \( \tau_{f} \) is normalized by the square root of \( f_{c}^{'} \) to neglect the inevitable difference of \( f_{c}^{'} \) between the NWC and LWAC pushoff specimens at the same test parameters. The predicted \( \lambda \) values are in relatively good agreement with the test results. Unlike the constant \( \lambda \) values specified in the ACI 31814 provision, the \( \lambda \) values calculated from the proposed equation tend to decreases with the increase in \( f_{c}^{'} \) and the decrease in \( \rho_{c} \). The ACI 31814 provision tends to overestimate the \( \lambda \) values for LWACBS. Additionally, the predicted \( \lambda \) values are slightly influenced by \( d_{a} \). Thus, it can be concluded that the proposed modification factor rationally explains the reduced frictional properties along the shear crack interfaces.
7 Conclusions
From the extensive tests and expanded mathematical models to assess the shear friction characteristic at the monolithic concrete interfaces made using artificially expanded bottom ash and dredged soil granules, the following conclusions may be drawn:

1.
The normalized shear friction strength (\( {{\tau_{f} }}/{f_{c}^{'}} \)) of LWAC increased with the increase in sand contend (\( R_{s} \)) for the replacement of lightweight fine aggregates; however, the increasing rate of \( {{\tau_{f} }}/{f_{c}^{'}} \) with respect to \( R_{s} \) was independent of the compressive strength of concrete (\( f_{c}^{'} \)).

2.
The value of \( {{\tau_{f} }}/{f_{c}^{'}} \) tended to decrease with the increase in \( f_{c}^{'} \) at the same level of dry density (\( \rho_{c} \)) of concrete.

3.
The increasing rate in \( {{\tau_{f} }}/{f_{c}^{'}} \) with respect to the maximum size of aggregate (\( d_{a} \)) was similar in both sandLWAC and allLWAC specimens. When \( d_{a} \) varied from 4.75 mm to 19 mm, the increasing rates of \( {{\tau_{f} }}/{f_{c}^{'}} \) were 131–137% for the allLWAC and 137–140% for the sandLWAC.

4.
The frictional angle (\( \phi \)) of concrete using expanded bottom ash and dredged soil granules was estimated to be slightly higher than that of concrete using expanded clay and fly ash granules.

5.
The empirical equations proposed by the AASHTO provision and Mattock underestimated significantly the \( \tau_{f} \) of concrete using expanded bottom ash and dredged soil granules, resulting in a greater underestimation with the increase in \( \rho_{c} \), \( f_{c}^{'} \), and \( d_{a} \). Meanwhile, the predictions obtained from the present mathematical model agreed better with the test results, in which the mean and standard deviation of the ratios between the measured and estimated shear friction strengths were 1.06 and 0.14, respectively.

6.
The modification factor determined from the mathematical models for the shear friction strength of the concrete interface agreed relatively well with the test results, unlike the overestimation trend observed in the ACI 31814 provision.
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Abbreviations
 AllLWAC:

concrete in which both the coarse and fineaggregate components are lightweight aggregates
 LWAC:

lightweight aggregate concrete
 LWACBS:

lightweight aggregate concrete made using expanded bottom ash and dredged soil granules
 LWACCF:

lightweight aggregate concrete made using expanded clay and/or fly ash granules
 NLMR:

nonlinear multiple regression
 NWC:

normalweight concrete
 OPC:

Ordinary Portland cement
 SandLWAC:

concrete with coarse lightweight aggregate and fine normalweight aggregate
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Acknowledgements
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea Government (MSIP) (No. NRF2017R1A2B3008463) and Basic Science Research Program through NRF Funded by the Ministry of Science, ICT & Future Planning (No. 2015R1A5A1037548).
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All the authors contributed to this research with respect to the followings: the first and second authors designed the present experimental program and conducted testing; and the second author also derived the mathematical model. All authors read and approved the final manuscript.
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Yang, KH., Lee, KH. Shear Friction Characteristics and Modification Factor of Concrete Prepared Using Expanded Bottom Ash and Dredged Soil Granules. Int J Concr Struct Mater 13, 50 (2019). https://doi.org/10.1186/s400690190364x
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DOI: https://doi.org/10.1186/s400690190364x
Keywords
 lightweight aggregate concrete
 shear friction
 monolithic interface
 modification factor