涂 园 ,王奎华 ,刘 鑫 ,Faheem Rizvi,邱欣晨
AuthorsHTML:涂 园 ^{1, 2}，王奎华 ^{1, 2}，刘 鑫 ^{1, 2}，Faheem Rizvi^{1, 2}，邱欣晨 ^{1, 2}
AuthorsListE:Tu Yuan,Wang Kuihua,Liu Xin,Faheem Rizvi,Qiu Xinchen
AuthorsHTMLE:Tu Yuan^{1, 2}，Wang Kuihua^{1, 2}，Liu Xin^{1, 2}，Faheem Rizvi^{1, 2}，Qiu Xinchen^{1, 2}
Unit:1. 浙江大学滨海和城市岩土工程研究中心，杭州 310058；
2. 浙江省城市地下空间开发工程技术研究中心，杭州 310058

Unit_EngLish:1. Research Center of Coastal and Urban Geotechnical Engineering，Zhejiang University，Hangzhou 310058，China；
2. Engineering Research Center of Urban Underground Development Zhejiang Province，Hangzhou 310058，China

Abstract_Chinese:研究了桩底截面处的行波反射特征，以探讨桩基低应变无损检测中定量判断桩底支撑条件的可能．首先采 用黏弹性模型模拟桩底土的作用，基于一维行波理论，分别推导了桩底截面处上行波与下行波之间的位移、速度和 应力频率响应函数，并由此分析了特殊桩底条件下的反射特征；利用 MATLAB 编程并结合频响函数，研究了桩底 为一般支撑、下行波速度为半正弦函数条件下，上行波速度时域曲线与桩底土刚度系数、阻尼系数之间的关系；最 后采用 3 种类型的桩底支撑进行模型试验，对理论计算结果进行了验证．结果表明：桩底行波反射特征仅与桩底界 面频响函数有关，桩底速度频响函数与位移频响函数相同，与力波频响函数相反；黏弹性桩底支撑条件下，桩底土 相对刚度系数和相对阻尼系数共同影响上行波速度曲线的方向、波峰数量和峰值大小；桩底由自由边界过渡到固定 边界时，反射波速度与入射波速度之间的关系由完全的同向相等逐渐过渡到完全的反向相等；模型试验的实测速度 曲线验证了理论计算结果．研究成果完善了一般支撑条件下桩底反射特征的理论，并提供了一种分离入射波和反射 波的理论方法，对桩底条件定量检测的工程应用也具有一定的潜在价值．
Abstract_English:The characteristics of wave reflection at pile tip were studied to explore the possibility of quantitative de\u0002termination of the pile bottom conditions in low-strain nondestructive testing of the pile foundation. First，the viscoe\u0002lastic model was used to simulate the soil resistance beneath the pile tip. Based on the one-dimensional wave theory， the frequency response functions(FRFs)of displacement，velocity，and force at the pile tip between upward and downward waves were derived. Then using MATLAB program and the FRFs，the relationship between the velocity curve of upward wave in the time domain and the stiffness and damping coefficients of pile base soil was studied un\u0002der the common support conditions of the pile tip，supposing that the downward wave velocity was a semi-sinusoidal function. Finally，three types of support conditions of the pile tip were used to conduct model tests，the results of which were compared with theoretical results. The results showed that the reflection characteristics of the traveling wave at the pile tip were only related to the FRFs of pile-soil interface. The FRF of velocity is the same as that of dis\u0002placement and opposite to that of force. Under the viscoelastic support conditions of pile bottom，the relative stiffness and relative damping coefficients of pile subsoil can affect the direction，number of wave peaks，and magnitude of the upward wave velocity curve. When the pile tip transitions from free boundary condition to fixed boundary condi-tion，the reflected and incident velocities gradually transition from having the same direction to having opposite di\u0002rections with same magnitude. The measured velocity curve of model test verified the theoretical calculation results. The research results can improve the theory of the reflection characteristics of the pile tip under common support con\u0002ditions and provide a theoretical method to separate the incident and reflected waves，which has potential value for engineering application to quantitative detection of pile bottom conditions.
Keyword_Chinese:桩底反射特征；桩底检测；低应变检测；反射叠加
Keywords_English:reflection characteristic of pile tip；detection of pile tip；low strain test；reflection superposition

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