Numerical Research On Micro-crack Detection Of Concrete Based On Broadband Excitation Nonlinear Modulation

Concrete materials,since it was invented,have been the most widely used material in the fields of building construction,bridges,roads and water conservancy,due to its advantages such as cost-effectiveness,strong durability,convenient construction,etc.However,in the initial stage of formation,different degrees of microcracks are often formed inside the concrete structure due to the influence of internal and external factors such as the concrete mix ratio,temperature stress,construction quality,curing conditions,etc.Ordinary concrete structures can work with cracks which can not be too large during their service life.But cracks are not allowed for many special structures and important structures,such as structures with long-term fatigue loads which include large pools,DAMS,containment vessels of nuclear power plants,etc.For these structures,under the action of external loads,the microcracks will be further enlarged,which will greatly accelerate the damage of the structure.once a macroscopic crack is formed,the crack will expand rapidly until it breaks under the action of fatigue load.Therefore,the early str uctural damage assessment of concrete is very important.In the field of non-destructive monitoring,the most widely used metho d is linear ultrasonic technology,but this method is not sensitive to the early stages of cracking,so nonlinear ultrasonic tech nology has been proposed.When ultrasonic waves pass through degraded materials,different degrees of non-linear ultrasonic phenomena can be detected.Scholars exactly use this phenomenon to evaluate the damage degree of materials or locate the damage.Among them,the nonlinear sound field modulation method has great prospects in engineering applications,because this method is more sensitive to microcracks than other non-linear ultrasonic nondestructive testing techniques.At present,in the field of non-linear sound field modulation,the most studied is non-linear sound field modulation based on dual-frequency excitation.But the shortcomings of this method limit its widespread use.For example,it is difficult to select two suitable excitation signals;the low-frequency vibration signal will affect the structure;the signal is greatly disturbed by the environment.Based on this,this paper proposes a nonlinear modulation method based on broadband excitation,which can advoids the shortcomings of dual-frequency excitation.At the same time,the damage factor was defined to evaluate the early damage of concrete,and theoretical and numerical simulations were studied.In this paper,when acoustic attenuation and initial phase are considered,hysteresis nonlinearity and high-order nonlinearity are neglected,the solution of nonlinear wave equations based on broadband excitation and the mechanism of nonlinear ultrasonic modulation of microcracks under one-dimensional conditions are studied.The relationship between the second-order nonlinear coefficient,the fundamental frequency amplitude and the first-order modulation side-frequency amplitude obtained by the theoretical derivation is consistent with the numerical simulation results.This proves the correctness of the numerical model.At the same time,the nonlinear sound field modulation sign al based on dual-frequency excitation is analyzed firstly,and the concrete model with different microcracks strikes is built.Then higher harmonics and first-order and second-order modulated waves can be extracted from the response signal.It is proved that the nonlinear sound field modulation metho d based on dual-frequency excitation can detect microcracks with different orientations.On the basis of dual-frequency excitation,the nonlinear sound field modulation signal based on broadband excitation is an alyzed.Since the response signal is very complex under wide-band excitation,the concept and calculation method of the damage factor are proposed.The change of the defined damage factor can reflect the change of the number and amplitude changes of the modulation sideband in the response signal.Based on this,the concrete model with different microcrack strikes was created.It is proved that the damage factor is sensitive to concrete microcracks and the feasibility of monitoring concrete microcracks.The relationship between the three variables whic h are the number of microcracks,the size of the microcracks,the modulus of elasticity of the concrete and the damage factor was studied by controlling the single variable method.The results show that when the number of microcracks increases uniformly,the peak of the damage factor increases significantly,but the growth gradient is not linear.This is consistent with the trend of peak damage factor in the experimental analysis.For models with different micro-crack sizes,it was found that the peak value of the damage factor gradually increased with the increase of the crack length,but decreased with the increase of the micro-crack width.Otherwise,as the degree of damage increases,the elastic modulus of the concrete decreases,and the peak value of th e damage factor gradually increases.The effect of the microcracks length and width obtained by the above analysis on the damage factor is reversed.In this paper,based on the actual development of concrete microcracks under fatigue loading,a model contr olled by multiple variables is established.The multiple variables are different microcrack lengths,different microcrack widths and different elastic moduli.The research results are consistent with the experimental analysis,that is,the peak value of th e damage factor increases non-linearly with the increase of the damage degree,which proves the feasibility of the method in this paper to detect the relative situation of the damage degree of concrete.