Research Experimental Study on the Dynamic Mechanical Properties of a Jointed Rock Mass under Impact Loading

Te propagation law of blast stress waves in jointed rock masses is closely related to the characteristics of the joint flling medium. Te water content and thickness of the flling medium afect the propagation characteristics of the blast stress wave in the joint surface. Based on similarity theory, mortar-red clay-mortar composite specimens with diferent moisture contents (36%, 39%, 42%, and 45%) and medium thicknesses (3mm, 6mm, and 9mm) were prepared with red clay as the flling medium. Te dynamic uniaxial compression test of the specimen under diferent strain rates was carried out by using a variable cross-section split Hopkinson compression bar with a diameter of 50mm. Te efects of strain rate, moisture content, and medium thickness on the stress wave propagation characteristics, dynamic stress-strain curve, peak stress, crushing energy consumption density, and crushing characteristics of mortar-red clay-mortar composite specimens were analyzed. Te results show that the blocking efect of joints on stress waves increases signifcantly with increasing flling medium thickness and water content. With increasing strain rate, the peak stress and energy of the composite specimen increase and there is an obvious strain rate efect. With the increase in the thickness and moisture content of the flling medium, the peak stress, dynamic elastic modulus, energy consumption density per unit volume, and crushing degree of the specimen gradually decrease and the nonlinear deformation is more obvious. Tere is a good linear relationship between the peak stress and the thickness and moisture content of the flling medium. Te existence of joints greatly weakens the damage efect of stress waves on the specimens behind the joints, and with the increase in the thickness and water content of the flling medium, the degree of damage to the specimens behind the joint surface decreases under the same impact pressure and the weakening efect becomes increasingly signifcant.


Introduction
As the product of long-term complex geological processes in nature, the internal structure of a rock mass is complex and there are numerous weak structural planes, such as joints, fssures, and faults. As one of the most representative structural planes in rock masses, joints often contain flling materials such as soft mud, sand, and rock debris, that is, flling joints. Teir low strength and large deformation characteristics will change the mechanical properties of structural planes and even the whole rock mass and increase the instability of engineering rock masses [1][2][3][4][5][6][7][8][9]. During the drilling and blasting construction of a rock mass, when the explosion stress wave acts on the joint surface, the stress wave will be refected and transmitted, resulting in the reduction of wave strength and the sharp attenuation of stress wave energy, which seriously hinders the propagation of waves. At the same time, the joints lead to the premature escape of explosion energy and explosion gas, overexcavation and underexcavation of rock contours, excessively large blasting rubble, and poor blasting efect, which seriously afect the efciency and safety of the project [10][11][12][13][14][15][16][17][18][19][20]. Terefore, studying the stress wave propagation law of jointed rock masses under dynamic loads is of great signifcance to evaluate the stability of engineering rock masses and the safety of tunnel, slope, and underground engineering construction under blasting loads.
At present, scholars at home and abroad have carried out extensive research on the mechanical properties of jointed rock masses under dynamic loads using numerical simulations, model tests, and other methods. Dong et al. [21] studied the mesoscopic failure mode of a nonpenetrating jointed rock mass under impact loading, and the results showed that the longer the joint length was, the smaller the compressive strength of the specimen. Deng et al. [22] used the split Hopkinson pressure bar (SHPB) test device to analyze the mechanical properties of jointed rock masses from diferent aspects, such as geometric characteristics, aspect ratio efect, and strain rate. Te research results are of great signifcance for understanding the dynamic mechanical properties of engineering rock masses and improving engineering blasting quality. Ma et al. [23] studied the dynamic mechanical properties of sandstone in deep roadways with diferent joint inclination angles. Te results showed that the dynamic compressive strength and peak strain of the specimens frst decreased and then increased with increasing joint inclination angle. Tsubota et al. [24] took gneiss as the research object, carried out dynamic tests on natural rock joints, revealed the mechanical properties of natural joints for the frst time, and concluded that the surface conditions of rock joints, such as roughness, hardness, and degree of weathering, have a signifcant impact on the shear resistance of rocks. Niktabar et al. [25] conducted shear tests on joint specimens with diferent rough undulation angles and found that the shear strength of the specimens is in direct proportion to the rough undulation angle. Walton et al. [26] studied the infuence of preset joints on main rock mass parameters such as stifness, peak strength, and residual strength. Zhu et al. [27][28][29][30] systematically discussed the efects of joint mechanical parameters and incident wave parameters on stress wave propagation and the energy dissipation ratio in a jointed rock mass from two aspects of test and theoretical analysis. Li et al. [31] theoretically studied the propagation characteristics of stress waves in jointed rock masses flled with viscoelastic deformation characteristics by using the improved time domain recursive method. Te variation trend of the transmission coefcient and refection coefcient of the jointed rock mass with incident angle is considered the same. Research on the dynamics of flled jointed rock masses focuses mainly on the infuence of flled joints on the propagation, attenuation, crack propagation mode, and energy propagation law of stress waves. Lei et al. [32] conducted an experimental study on the shear strength damage characteristics of jointed rock masses under freeze-thaw cycles. Te results show that the damage variables of cohesion and friction angle of jointed rock increase nonlinearly with the increase in the number of freeze-thaw cycles. Terefore, the evolution model of joint shear damage under freeze-thaw cycles is established. Lin et al. [33] studied the distribution of the frost heaving stress of a water-bearing jointed rock mass under freeze-thaw cycles. Te results show that the frost heaving stress of the specimens decreases signifcantly with the increase in the number of freeze-thaw cycles and water migration loss and increases with the increase in the mechanical strength and joint geometric size of the rocks and ice. In terms of numerical simulation, Bian [34] used ANSYS/LS-DYNA software to study the propagation and attenuation of stress waves corresponding to joints and the infuence of joint geometry and fllings on its isolation efect. Liu et al. [35], Zhao et al. [36], and Yang et al. [37] used the universal discrete element code (UDEC) to simulate the propagation characteristics of stress waves in jointed rock masses. However, the infuence of the thickness and water content of the joint flling body on the stress wave propagation law is rarely discussed.
Tis study is based on the cutting slope blasting project of the Panxian-Xingyi Expressway in Guizhou Province. Te construction site is a karst medium low mountain landform. Te subgrade is situated in the middle and upper parts of the slope, with steep and gentle slopes. Te bedrock in the middle and upper parts of the slope is the limestone of the Yongningzhen Formation in the Lower Triassic system. Horizontal bedded joints have been developed; each layer is 0.3∼0.5 m thick, and vertical joints have also been developed and flled with mud. During blasting excavation, the rock will bear a dynamic load. Based on the principle of similarity theory, the red clay in the engineering site was used as the flling medium to prepare mortar-red clay-mortar composite specimens with diferent moisture contents and thicknesses. Uniaxial impact compression tests were carried out on the specimens using a variable cross-section split Hopkinson pressure bar device with a diameter of 50 mm. Te characteristics of stress wave propagation, dynamic stress-strain curve, dynamic compressive strength, energy dissipation, the change law of specimen breakage, and fracture characteristics of mortar-red clay-mortar composite specimens with diferent media moisture contents and thicknesses under impact load have been obtained. Tis study provides an experimental basis for engineering practice.

Sample Preparation.
Due to the difculty of on-site raw rock sampling, by drawing lessons from the research of domestic and foreign researchers in the feld of rock simulation and taking advantage of the characteristics of easy preparation, easy availability of raw materials, and low cost of cement mortar, cement mortar was selected as the simulation material of jointed rock mass. In the test, the cement is P·O 32.5 ordinary Portland cement produced in Bagongshan, Huainan. Te fne aggregate is natural river sand with a fneness modulus of 2.8, the water is natural tap water, and the mix proportion of the test piece is cement : medium sand : water � 2 : 2 : 1. After pouring, the test block was placed in the curing chamber with a curing humidity ≥95% and a temperature maintained at 20 ± 2°C for standard curing for 28 d. After coring, cutting, and grinding, the test piece was made into a cylindrical standard specimen with a diameter of 50 mm and height of 25 mm. Te 28 d uniaxial compressive strength is 37 MPa, which meets the test requirements. To reduce the infuence of the discrete type of specimen on the test results, it is necessary to measure the longitudinal wave velocity of the processed mortar specimen and select the mortar specimen with a similar longitudinal wave velocity for the test [38]. At the same time, to distinguish the failure mode of the mortar specimens on both sides of the joint during the impact test, the mortar specimens close to the transmission rod are sprayed with red paint.
Red clay samples with water content of 36%, 39%, 42%, and 45% were prepared according to the test requirements. Te required mass of soil and water was obtained through calculation, and then, the soil samples cooled to room temperature were successively added with water of corresponding quality through the steps of grinding, 2 mm screening, and drying. At the same time, the soil was fully stirred with a soil-mixing knife to evenly mix the red clay and water, and then, the mouth of the soil container was sealed with a fresh-keeping flm. At the same time, the freshkeeping flm was covered with a wet towel and held for 24 hours so that the water could fully penetrate into the red clay. Te red clay was made as shown in Figure 1.

Te Test Process.
Te orthogonal test method was used, and the test variables were the thickness of the flling medium (d), moisture content of the flling medium (W), and strain rate. Te range of thicknesses of the flling medium was 3 mm, 6 mm, and 9 mm, and the range of the water content of the flling medium was 36%, 39%, 42%, and 45%, respectively. Diferent impact pressures were selected to obtain diferent strain rates. At the same time, the impact pressure had an efect on the fracture morphology of the specimen. If the air pressure is small, the specimen cannot be destroyed in the impact test, so the infuence law of the flling medium thickness and water content on the specimen fracture morphology cannot be compared. After test punching, four kinds of impact pressures (0.3, 0.4, 0.5, and 0.6 MPa) were fnally selected to obtain diferent strain rates. According to the density, thickness and moisture content of the red clay, the required mass of the red clay is weighed in turn and then sandwiched between two mortar specimens to form the mortar-red clay-mortar composite specimen. To prevent water evaporation during the test, only one red clay sample with moisture content was confgured during each impact test and the impact test was conducted immediately after the specimen was prepared. To ensure the accuracy of the test data and reduce the test error, three parallel test pieces were made for the same type of test, with a total of 144 mortar-red clay-mortar composite test pieces, and the test results were analyzed by selecting the group of test pieces closest to the average value. Te structure of the specimen is shown in Figure 2.

SHPB Test Device.
Te impact compression test uses a 50 mm-diameter variable cross-section split Hopkinson compression bar test device system from the Impact Dynamics Laboratory of Anhui University of Technology. Te impact rod, incident rod, and transmission rod are made of alloy steel, with a density of 7850 kg/m 3 , an elastic modulus of 210 GPa, and a longitudinal wave velocity of 5190 m/s. Te strain gauge at the incident rod adopts a BX120-3AA-type resistance strain gauge, the resistance value is 120 ± 0.1 Ω, and the sensitivity coefcient is 2.08 ± 0.1%. Due to the small amplitude of the signal received by the transmission rod in the test, to make the data collected by the strain gauge meet the accuracy requirements, the HU-101B-120 semiconductor strain gauge was selected on the transmission rod, with a resistance value of 120 ± 5% Ω and a sensitive coeffcient of 110 ± 5% [39]. Te structure of the test device is shown in Figure 3.
Four diferent impact pressures (0.3, 0.4, 0.5, and 0.6 MPa) were used for three diferent medium thicknesses (3 mm, 6 mm, and 9 mm), four diferent moisture content (36%, 39%, 42%, and 45%) composite specimens were subjected to shock compression tests, and the collected data were processed by the three-wave method [40,41]. Te relevant calculation formulas are as follows: where ε i (t), ε r (t), and ε t (t) are the incident strain, refected strain, and transmitted strain at time t, respectively, dimensionless; l s is the thickness of the specimen, m; C 0 , E are the compressional wave velocity and elastic modulus of the compression bar, m/s and MPa, respectively; A, A S are the cross-sectional area of the pressure bar and the cross-sectional area of the specimen, m 2 ; W i is the incident energy, W r is the refected energy, W t is the transmitted energy, and W t is the dissipated energy, J; ε d is the crushing energy dissipation density, J/cm 3 ; V is the specimen volume, cm 3 .

Efects of Strain Rate and Filling Medium on Stress Wave
Propagation. Figure 4 shows the efective stress-time history curves of the mortar-red clay-mortar composite specimens with a flling medium moisture content W of 42% and a flling medium thickness d of 3 mm at diferent strain rates.
Shock and Vibration Figure 4 shows that the efective stresses of the composite specimens with strain rates of 75.8 s −1 , 67.8 s −1 , 53.7 s −1 , and 43.2 s −1 are 24.25 MPa, 18.33 MPa, 13.79 MPa, and 10.87 MPa, respectively, and the time required to reach the peak stress is 25.4 μs, 28.7 μs, 31.0 μs, and 32.1 μs, respectively. With increasing loading pressure, the efective stress of the specimen increases, but the time required to reach the peak stress decreases because the energy carried by the stress wave (incident energy) gradually increases with increasing loading air pressure and the moisture content and thickness of the flling medium remain unchanged at this time. Terefore, the blocking efect of the flling medium on the stress wave is the same. Te energy consumed by the flling medium is the same, and the strength of the transmitted stress wave increases with increasing impact air pressure, which shortens the propagation time of the stress wave.
Te diferent thicknesses and water contents of the flling medium have a direct impact on the propagation of the stress wave in the specimen. When the strain rate is 75.8 s −1 and the water content W is 36%, the infuence of diferent thicknesses of the flling medium on the stress-time history curve of the specimen is shown in Figure 5. Figure 5 shows that when the strain rate is consistent with the water content, the peak stress of the composite specimen decreases gradually with the increase of the thickness of the flling medium and the time to reach the peak stress increases gradually with the increase in the thickness d of the flling medium. Compared with the specimen with a thickness of 3 mm, the efective stress decreases of the specimens with thicknesses of 6 mm and 9 mm are 8.2% and 20.6%, respectively, and the propagation time to the peak stress increases by 4.0% and 17.6% because the wave impedance of the joint (red clay) does not match the wave impedance of the mortar on both sides. When the stress wave passes through the mortar-joint-mortar composite specimen, the stress wave will be refected at the two interfaces of the mortar and red clay. When the thickness of the flling medium d increases, the refection time gradually decreases and the greater the infuence of the thickness of the flling medium on the propagation of the stress wave will be. Te flling medium consumes a large amount of energy carried by the stress wave, and the attenuation of the stress wave energy intensifes. Te peak stress of the specimen decreases with the decrease in the transmitted stress wave. Te greater the thickness of the medium is, the longer the wave propagation time in the medium and the longer the time for the specimen to reach the peak stress. Figure 6 shows the relationship between the water content and efective stress of the composite specimen when the strain rate is consistent with the flling thickness. Figure 6 shows that when the strain rate is consistent with the flling thickness, as the water content of the flling medium increases, the lag time of stress wave propagation is longer and the efective stress of the composite decreases accordingly. Compared with the specimen with a water content of 36%, the efective stress decreases by 13.2%, 31.0%, and 54.4% when the water content is 39%, 42%, and 45%, respectively. Te propagation time to peak stress increased by 8.3%, 18.4%, and 21.9% because with the increase in the water content in the flling medium, the propagation velocity V of the stress wave in the flling medium decreases gradually and the time for the stress wave to reach the peak stress increases accordingly. As the water content of the flling medium increases, the wave impedance decreases gradually, the refected wave of the stress wave increases   Shock and Vibration gradually at the interface between the flling medium and mortar, the transmission wave decreases, and the peak stress decreases accordingly. Figure 7 shows the infuence of the thickness and water content of the flling medium on the stress-strain curve of the composite specimen under the same impact pressure. Figure 7 shows that under the same strain rate, as the thickness and water content of the flling medium increase, the slope of the curve of the specimen in the elastic stage decreases signifcantly, the elastic variation section of the specimen becomes shorter, and the corresponding initial elastic modulus decreases. Te dynamic compressive strength and dynamic elastic modulus also decrease signifcantly with increasing thickness and water content of the flling medium, and the nonlinear deformation of the specimen is more obvious with increasing thickness and water content of the flling medium.

Stress-Strain Curve.
Te decline form of the postpeak stress-strain curve represents the degree of failure of the specimen. Te decline form of the mortar-joint-mortar composite specimen with      diferent water contents and thicknesses of the flling medium is diferent after reaching the stress peak. According to the stress-strain curve, the thickness d and water content W of the flling medium increase, the slope of the postpeak curve decreases signifcantly, the peak strain of the specimen increases signifcantly, and the postpeak deformation is aggravated. Te results show that the plastic deformation capacity of the specimen increases with increasing thickness d and water content W of the flling medium, mainly because the flling medium (red clay) has a strong plastic deformation ability and the increase in the thickness and water content of the flling medium enhances the plastic deformation ability of the specimen.

Relationship between Peak Stress and Strain Rate, Tickness of the Filling Medium, and Water Content.
When the water content of the flling medium W is 36%, the ftting curve of the peak stress and strain rate of the mortarred clay-mortar composite specimens with diferent flling medium thicknesses d is shown in Figure 8. When the flling medium thickness d is 3 mm, the ftting curve of the peak stress and strain rate of the mortar-red clay-mortar composite specimens with diferent joint water contents W is shown in Figure 9.
Te ftting curves in Figures 8 and 9 show that the specimen of the mortar-red clay-mortar composite has an obvious strain rate efect. With an increasing strain rate, the composite peak stress increases and there is a strong power correlation. Te increase in the strain rate shortens the action time of the impact load, and the specimen does not have enough time to accumulate energy. According to the functional principle, the specimen can only balance the external energy by increasing the stress, so the peak stress increases gradually with an increasing strain rate. Te ftting curve relationship also shows that the thickness and water content of the flling medium also afect the rate correlation of the strength of the composite specimen, but with the increase in the thickness and water content of the flling medium, the slope of the ftting curve gradually decreases, indicating that with the increase in the thickness and water content of the flling medium, the sensitivity of the peak stress of the composite specimen to the strain rate gradually decreases.
When the strain rate is 75.8 s −1 , the ftting curve between the flling medium thickness and water content and the peak stress of the composite specimen is shown in Figure 10, and the ftting relationship is shown in Table 1. Figure 10 and Table 1 show that with increasing thickness d and water content W of the flling medium, the peak stress of the mortar-joint-mortar combination specimen gradually decreases and there is a good linear negative correlation between the thickness, water content, and peak stress because when the stress wave passes through the flling medium, flling medium thickness d, and the increase of water content W, more stress wave refection and absorption cut through the joints and the stress wave, namely, flling medium stress wave energy expenditures increase and the barrier for the flling medium of the stress wave along with the increase in the thickness and the moisture content is signifcantly enhanced. Te stronger the weakening efect on the peak stress of the composite specimen is, the lower the peak stress is macroscopically.

Variation Law of Energy Dissipation of Composite
Specimens. Te damage and failure process of the assembly can be regarded as the result of the mutual transformation of diferent forms of energy. Te stress-strain state of the material at diferent time periods corresponds to the corresponding energy state. Energy analysis can avoid analyzing the complex deformation process, which is more conducive to the study of the failure essence of the composite specimen [42]. Te energy variation law of the composite specimen under diferent strain rates is shown in Figure 11. When the strain rate is 75.8 s −1 , the infuence law of the medium thickness and moisture content on the crushing energy consumption density of the composite specimen is shown in Figure 12. According to Figure 11, with increasing strain rate, each energy increases continuously. Under diferent strain rates, the incident energy > the refection energy > the dissipation energy > the transmission energy. From the slope of the curve, the transmission energy increases relatively gently with increasing strain rate. Te analysis shows that due to the large diference in wave impedance between the mortar specimen and compression bar and between the red clay and mortar specimen, when the incident wave acts on the incident bar and the front mortar end face, due to the poor matching of wave impedance between the mortar and incident bar, more energy is refected back to the incident bar to form refected energy and a small part of the energy passes through the front mortar specimen into red clay. At this time, due to the large diference in wave impedance between the red clay and the rear mortar specimen, more energy is refected and a small part of the energy passes through the red clay and is transmitted to the rear mortar specimen. Similarly, due to the large diference between the wave impedance of the rear mortar specimen and the transmission rod, only a small part of the energy is transferred to the transmission rod to form the transmission energy. At the same time, with the increase in joint thickness and water content, the joint consumes more energy from the stress wave, the energy attenuation of the stress wave intensifes, and the transmission energy is smaller. Figure 12 shows that the thickness and moisture content of the backfll medium have an impact on the crushing energy density of the composite specimen. When the thickness of the medium is the same, the crushing energy density of the specimen increases signifcantly with increase in moisture content of the medium. When the thickness of the medium is 3 mm, compared with the sample with 36% moisture content, when the water content was 39%, 42%, and 45%, the crushing energy consumption decreased by 2.13%, 6.53%, and 11.06%, respectively, and the decrease gradually increased. Under the same water content, with the increase in flling medium thickness, the energy dissipation density of the specimen also decreases and the increase in flling medium thickness and water content will reduce the energy dissipation density of the composite specimen. Figure 13 shows the failure morphology of the mortar-red claymortar composite specimens with diferent water contents and diferent flling medium thicknesses (d) in the flling medium at a strain rate of 75.8 s −1 . Figure 13 shows the same flling medium thickness, moisture content, and strain rate; contact with the broken incident bar mortar test block was signifcantly higher than contact with the transmission rod mortar test block because the joint surface occurred in the stress wave propagation attenuation, the joint surface energy was received by its back-end mortar test block below the front specimen, and the degree of specimen breakage was reduced. Te change in the flling medium thickness will lead to the diference in the degree of fracture and fragment size of the mortar specimen on both sides of the joint. Under the same loading pressure, with the increase of d, there is no signifcant diference in the degree of breakage of the mortar specimen at the incident rod end, while the degree of breakage of the mortar specimen at the transmission rod end decreases signifcantly. Tis is because when the impact pressure remains unchanged, the energy absorbed by the specimen at the incident rod end is similar, and the damage degree does not change much. With the increase in d, the energy absorbed by    the flling body increases, while the energy that reaches the rear mortar specimen through the flling joint surface is less. When the stress wave spreads to the rear mortar, the energy value received by the specimen decreases, so the degree of damage to the rear mortar decreases gradually with an increasing d.

Failure Mode of the Composite Specimen.
Te water content of the flling medium also afects the failure mode of the composite specimen. When d and strain rate are the same, the change of water content W makes the damage degree of the specimen diferent. Te damage degree of the transmission rod end specimen decreases with the increase of W. Joint plane wave impedance decreases, with the increase of W in the mortar-joint surface refecting wave increases and the joints and absorbed energy gradually increase. Te attenuation of stress wave energy through the joint plane to the specimen at the back end is intensifed, the energy absorbed by the mortar specimen at the back end of the joint plane is reduced, and the degree of failure of the specimen is reduced.

Conclusions
(1) When the strain rate was 75.8 s −1 , 67.8 s −1 , 53.7 s −1 , and 43.2 s −1 , the efective stresses of the specimens were 24.25 MPa, 18.33 MPa, 13.79 MPa, and 10.87 MPa, respectively. Te time required to reach the peak stress was 25.4 μs, 28.7 μs, 31.0 μs, and 32.1 μs, respectively. With increasing strain rate, the peak value of the stress wave increases and the time to reach the peak stress decreases.
(2) When the strain rate is 75.8 s −1 and the water content W is 36%, compared with the specimens with a thickness of 3 mm, the peak stress of the specimens with thicknesses of 6 mm and 9 mm decreases by 8.2% and 20.6%, respectively, and the propagation time to reach the peak stress increases by 4.0% and 17.6%. When d is 6 mm, compared with the specimen with 36% moisture content, the peak stress decreases by 13.2%, 31.0%, and 54.4% at 39%, 42%, and 45% moisture content, respectively, and the propagation time to peak stress increases by 8.3%, 18.4%, and 21.9%. With the increase in the thickness and water content of the flling medium, the peak stress of the specimen gradually decreases and the time to reach the peak stress gradually increases. (3) Te peak stress and energy of the specimens increased with an increasing strain rate. When the strain rate is 75.8 s −1 and the thickness of the medium is 3 mm, compared with the samples with 36% water content, the breakage energy consumption decreases by 2.13%, 6.53%, and 11.06% at 39%, 42%, and 45% water content. Te increase in thickness d and moisture content W of the flling medium reduces the peak stress and energy dissipation density of crushing, and there is a linear negative correlation between peak stress and thickness d and moisture content W of the flling medium. (4) Under the same flling medium thickness, water content, and strain rate, the degree of failure of the mortar specimen at the incident rod end is higher than the degree of failure of the mortar specimen at the transmitted rod end and the existence of a joint plane causes stress wave attenuation during the propagation process. With the increase in the flling medium thickness d and water content W, the stress wave energy attenuation is aggravated and the degree of fracture of the test block at the back of the joint surface is reduced.

Data Availability
Te data presented in this study are available on request from the corresponding author.

Conflicts of Interest
Te authors declare that they have no conficts of interest.