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BY GENKI KUBO, MAKOTO OKAMOTO, HAJIME KUBO
A Study on Estimating Concrete Compressive Strength by Mechanical Impedance Mechanical impedance can be calculated by dividing the maximum force, when a hammer collides concrete surface, with initial velocity of the hammer rebound. Photos and figures provided by Nitto Construction Inc.
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urrently, the rebound hammer is widely used for estimation of compressive strength of concrete as general testing method. Although rebound hammer has made great contribution for compressive strength test of concrete structures through its long history, its measurement accuracy and application is still considered as debatable. On the other hand, the mechanical impedance method is proposed as a new method for estimation of compressive strength in these days. Although both methods require direct impact on concrete surface in order to estimate compressive strength, basic principle is different. The rebound number, that rebound hammer measures,
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is depending on the degree of absorption of kinetic energy during the plastic deformation process of concrete surface generated by hammering. On the other hand, the mechanical impedance method measures mechanical impedance between a hammer and concrete surface at the contact point. The mechanical impedance is derived from Young’s modulus, and is used for estimation of compressive strength of concrete. This study shows consideration for basic principle of the mechanical impedance method for compressive strength estimation of concrete, and its application and measurement accuracy are discussed through a field experiment. BASIC PRINCIPLES Assuming that concrete is perfectly elastic body, we consider a phenomenon of collision between a hammer with mass (M), velocity (V0) and concrete with spring constant (K), figure 1 (page 23). The kinetic energy (EH) of a hammer is, EH=1/2MV02. On the other hand, putting the maximum displacement as Dmax and the strain energy (EC) of concrete by hammer impact is, EC=1/2KDmax2. Considering equilibrium of energy,
1/2MV02=1/2KD2max. From the Hooke’s law, the maximum impact force Fmax is, Fmax=KDmax. Solve for Dmax, and substitute the formula for the equilibrium of energy, 1/2MV02=1/2K F2max / K 2 ➲ K = 1/M * (Fmax/V0)2. When the maximum impact force Fmax and the velocity of a hammer V0 is obtained, the spring constant of concrete surface can be measured. However, in case of collision between an elastic body with flat surface and an elastic body with spherical surface, the maximum impact force becomes proportional to the impact velocity to the power 1.2 based on the contact mechanics. Therefore, velocity correction should be considered as K = 1/M * (Fmax/V01.2)2. Its possible to measure the deceleration of a hammer by a waveform with an accelerometer. From the waveform, the maximum impact force and the velocity can be calculated as (equation 7): Fmax = MA max V R = ∫∞T A(t)dt
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Here, A is an acceleration and max is a subscript that shows the maximum value. At the actual calculation, velocity is calculated from the waveform, and the waveform is divided in 2 part at the time T when the impact force is the maximum. Deformation of concrete surface becomes maximum at the time T, and the motion of hammer stops. In other words, the first half of the waveform shows the process of deformation of concrete by hammer impact (Active side), and the second
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6/10/21 9:13 AM
