Vertical Vibration Theory Of Pipe Pile Based On The Additional Mass Model And Its Application In Pile Testing

The stress wave velocity is an important factor for the dynamic testing of the pile.Whereas,the apparent phase velocity of the pile after installation is distinctly lower than its material wave velocity due to the existence of the soil,and the present dynamic soil-pile interaction models cannot reflect this phenomenon.Therefore,a new soil-pile interaction model,the additional mass model,is proposed to investigate the influence of the soil mass on the dynamic response of the pile.The additional mass model is a new soil-pile dynamic interaction model,which can consider the influence of soil mass and the displacement phase difference between soil and piles on the dynamic response of the pile.The high-frequency interference at the pile head has an adverse effect on the dynamic testing of the pile.However,present studies have no uniform understanding or systematic conclusions on the formation mechanism of the high-frequency interference,either having a method to efficiently suppress the adverse influence of the high-frequency interference.The formation mechanism of the high-frequency interference is analyzed using the analytical method.Also,the double-velocity symmetrical superposition method is proposed herein to suppress the influence of the high-frequency interference.First,the additional mass model is employed to simulate the dynamic interaction between the soil plug and pipe pile.An analytical solution that can consider the stress wave propagating both in the vertical and circumferential directions is derived based on the additional mass model.Utilizing the developed solution,a parametric study is performed to illustrate the influence of soil plug properties,pipe pile properties and the impulse width of impact force on dynamic velocity response of pipe piles.Based on the additional mass model and the fictitious ring-soil pile model,an analytical solution,which can consider the soil plug effect and the soil embedded in the crack or neck defect along the pile shaft,is derived for the dynamic response of defect pipe piles using the transfer matrix method.The formation mechanism of the high-frequency interference during low strain testing of pipe piles has been clarified.The double-velocity symmetrical superposition method(DVSSM),which consists of superimposing and averaging two synchronization signals measured at two symmetrical points of the neutral plane of flexural vibration(in an angle of 90°),is proposed to eliminate the influence of the high-frequency interference during low strain testing.The DVSSM has much higher detection accuracy than the conventional method,and can serve as an efficient method to detect small defects near the pile head.Then,the general additional mass model is developed to account for the soil continuity condition and additional mass boundary,and the influence of the additional mass effect of the surrounding soil on the vertical dynamic response of pipe piles is investigated.An analytical solution of the stress wave velocity of pipe piles was derived using the general additional mass model.The developed solution has been proved that can not only calculate the stress wave velocity of pipe piles during low strain testing,but also the stress wave velocities during pile driving,through the comparison of predictions and measurements.Finally,based on the general additional mass model,the mechanism of the stress wave propagation in the pile is investigated from the viewpoint of wave energy.The main conclusions can be drawn as:(1)The influence of soil plug effect on the dynamic response of large diameter pipe piles is investigated based on the additional mass model.First,an analytical solution that can consider the stress wave propagating both in the vertical and circumferential directions is derived in the frequency domain through the transfer function method.Then,the corresponding quasi-analytical solution in the time domain for the pipe pile subjected to a vertical semi-sinusoidal impact force is obtained by utilizing the Fourier transform technique.Finally,utilizing the developed solution,a parametric study is performed to illustrate the influence of soil plug properties,pipe pile properties and the impulse width of impact force on dynamic velocity response of pipe piles.The validity and accuracy of the solution presented in this paper is compared against a series of model pipe pile experiments and field experiments.The result shows that: The soil plug leads to a decrease of composite propagation velocity of pipe pile,and a weaker applicability of the plane-section assumption for pipe pile;owing to the soil plug,the apparent wave velocity of pipe pile(AWVPP)decreases with the decrease of wall thickness and Young's modulus,and the increase of Poisson's ratio of pipe pile.The width of the reflected signal from pipe pile toe is widened due to the soil plug effect.(2)The double-velocity symmetrical superposition method(DVSSM),which consists of superimposing and averaging two synchronization signals measured at two symmetrical points of the neutral plane of flexural vibration(in an angle of 90°),is proposed to investigate the mechanism of the high-frequency interference during low strain testing.Based on the additional mass model and the fictitious ring-soil pile model,an analytical solution,which can consider the soil plug effect and the soil embedded in the crack or neck defect along the pile shaft,is derived using the transfer matrix method.The calculated responses from the developed solution are compared with the experimental results for different receiving radius angles to evaluate the effectiveness of the developed solution.A parametric study is also conducted to investigate the suitability of the DVSSM.The findings demonstrate that the high-frequency interference is caused by a combination of the flexural behavior of the pile cross-section and the wave propagation along the pipe pile head.The flexural vibration mode comprises the primary component of the high-frequency interference,which can be eliminated through the DVSSM without increasing the predominant period of impact pulse.The DVSSM has much higher detection accuracy than the conventional method,and can serve as an efficient method to detect small defects near the pile head.(3)The apparent phase velocity of open-ended pipe piles after installation is difficult to predict owing to the soil plug effect.This paper derives an analytical solution to calculate the apparent phase velocity of pipe pile segment with soil plug filling inside(APVPSP)based on the additional mass model.The rationality and accuracy of the developed solution have been confirmed through the comparison with the solution derived using the Winkler model and experimental results.A parametric analysis was conducted to investigate the influence of parameters of the additional mass model,pile design properties and impulse widths of the impact force on the APVPSP.A parameter combination of the additional mass model that can be applied in most commonly used pipe piles is recommended.The attenuation mechanism of the soil plug on the APVPSP has been clarified.The findings from this study demonstrate that the APVPSP decreases with the mass per unit length of pipe plies,but has nothing to do with the material damping coefficient and material longitudinal wave velocity of pipe pile.The APVPSP decreases significantly as the impulse width increases,however,for pipe piles without soil plug filling inside,the impulse width has negligible influence on the apparent phase velocity.(4)The general additional mass model was proposed to consider the soil continuity condition,which can be used not only in the soil plug,but also the surrounding soil.The soil in the general additional mass model is divided into disturbed zone and undisturbed zone according to the distance from the pile wall.Assume only the soil in the disturbed zone taking part in the vibration of pipe pile shaft,and the soil in the undisturbed zone remains staic.The radially inhomogeneous soil model is introduced in the disturbed zone to determine the transmitting boundary of the vibration engergy of the pile,which is assumed to be the boundary of the additional soil.The additional soil mass is respectively connected to the pile wall and undisturbed soil zone through the Voigt model and Winkler model.The influence of soil on the vertical dynamic response of pipe piles was investigated based on the general additional mass model.Conclusions can be drawn as: the surrounding soil also leads to a decrease in the apparent phase velocity;the respectively additional soil boundary of the soil plug and surrounding soil is recommended to be 0.3 times inner and outer radii of pipe piles;the amplitude value of the reflected signal and the apparent phase velocity decrease with the increase of the contact interface area between the pile and soil;the amplitude value of the reflected signal is associated with the mass per unit length of the pile,but has nothing to do with the material longitudinal wave velocity of pipe pile.(5)An analytical solution of the stress wave velocity of pipe piles was derived with the consideration of the additional mass effect of the surrounding soil based on the general additional mass model.The developed solution has been proved that can not only calculate the stress wave velocity of pipe piles during low strain testing,but also the stress wave velocities during pile driving through the comparison of predictions and measurements.Owing to the soil effect,the stress wave velocity propagation in pile decreases as the impulse width of the impact force increases.However,the stress wave velocity tends to stabilize when the impulse width of the impact force exceeds a certain value,and further variation of the impulse width can hardly affect the stress wave velocity.The stress wave velocity calculated based on the general additional mass model is in accordance with that back analyzed from its dynamic velocity response.The directly calculated stress wave velocity based on the Winkler model has a big divergence with that back analyzed from its dynamic velocity response.The Winkler model cannot be used in the prediction of stress wave velocity of pipe piles.(6)When the pile is on the ground,the stress wave velocity of piles on the ground is equal to its material longitudinal wave velocity.However,after installation stress wave velocity is lower than its original material longitudinal wave velocity.The stress wave velocity decreases with the mass per unit length and frequency(impulse width of the impact force),which is closely associated with the wave energy.The lower mass per unit length and frequency,the lower wave energy,resulting in lower stress wave velocity.Therefore,the reduction of the stress wave velocity propagation in the two-phase medium may be associated with the wave energy.The mechanism of the stress wave propagation in the pile is investigated from the viewpoint of wave energy.The study shows that the stress wave velocity propagation in the pile is proportional to frequency,and has a positive correlation with the mass per unit length of the propagation medium,but has nothing to do with the vibration amplitude.