JP4382383B2 - Input wave calculation system and input wave calculation method - Google Patents

Description

【００２５】
【式２】

【００２６】
＜ニ＞棒状体端部の軸方向力の算出
棒状体端部１１の軸方向力Ｆ（０、ｔ）は、棒状体端部（ｘ＝０）における進行波Ｆ_ｄ（ｘ_０、ｔ＋ｔ_０）と後退波Ｆ_ｕ（ｘ_０、ｔ−ｔ_０）を合成したものである。端部進行波Ｆ_ｄ（ｘ_０、ｔ＋ｔ_０）は、測定位置（ｘ_０）における進行波Ｆ_ｄ（ｘ_０、ｔ）を棒状体端部（ｘ＝０）まで戻したものである。端部後退波Ｆ_ｕ（ｘ_０、ｔ−ｔ_０）は、測定位置（ｘ_０）における後退波Ｆ_ｕ（ｘ_０、ｔ）を棒状体端部（ｘ＝０）まで進めたものである。即ち、棒状体端部（ｘ＝０）から所定距離（ｘ_０）離れた棒状体内部の位置に生じた進行波Ｆ_ｄ（ｘ_０、ｔ）と後退波Ｆ_ｕ（ｘ_０、ｔ）を求め、棒状体端部１１まで進行波を戻した端部進行波Ｆ_ｄ（ｘ_０、ｔ＋ｔ_０）と棒状体端部１１まで後退波を進めた端部後退波Ｆ_ｕ（ｘ_０、ｔ−ｔ_０）とを求め、端部進行波と端部後退波を合成し、式３から棒状体端部（ｘ＝０）の軸方向力Ｆ（０、ｔ）を算出する。
【００２７】
棒状体端部１１のインピーダンスと速度による力の波形は、式４のようにして求められる。ここで、Ｆ_ｄ（ｘ_０、ｔ＋ｔ_０）は、所定距離ｘ_０にある進行波Ｆ_ｄ（ｘ_０、ｔ）を棒状体端部１１に戻した波であり、Ｆ_ｕ（ｘ_０、ｔ−ｔ_０）は、後退波Ｆ_ｕ（ｘ_０、ｔ）を棒状体端部１１に進めた波である。ここで、ｔ_０＝ｘ_０／Ｖ_Ｌであり、Ｖ_Ｌは棒状体１中を伝播する伝播速度である。なお、式３と式４の代わりに、ｔ⇒ｔ＋αとした式５と式６を使用しても良い。ここでαは、任意の値である。
【００２８】
【式３】

【００２９】
【式４】

【００３０】
【式５】

【００３１】
【式６】

【００３２】
＜ホ＞入力波の算出
入力波Ｆ_Ｉ（ｔ）は、棒状体端部（ｘ＝０）に力ｆを作用し、力が棒状体１中に入力したものであり、式７のように、入力波Ｆ_Ｉ（ｔ）は、棒状体端部１１の軸方向力Ｆ（０、ｔ）と等しくなる。これは、棒状体端部１１が自由面であるから、後退波が棒状体端部１１で全反射し進行波となる時に逆位相となり、後退波と進行波が打ち消し合い、棒状体端部１１には、入力波しか存在しなくなる。このようにして、棒状体端部（ｘ＝０）に力ｆが作用し、棒状体端部１１から所定距離（ｘ_０）離れた測定位置における進行波と後退波が求まると、棒状体端部１１から入射した入力波Ｆ_Ｉ（ｔ）を算出することができる。
【００３３】
【式７】

【００３４】
＜ヘ＞入力波算出システムの構成
入力波算出システムは、例えば図２に示すように、歪みセンサ２２からの信号を受信する歪み形アンプ５２と、加速度センサ２１からの信号を受信する加速度アンプ５１と、これらのアンプをＡ／Ｄ変換するＡ／Ｄ変換器５３、５４、これらＡ／Ｄ変換器からのデータをデータライン５５を介してＦＩＦＯメモリ５７又はＦＰＧＡロジック５８に入れ、ＣＰＵ５９でデータ処理する算出装置５を備えている。算出装置５は、測定された進行波を測定位置から棒状体端部１１付近まで戻した端部進行波と、測定された後退波を測定位置から棒状体端部１１付近まで進めた端部後退波とを求め、該端部進行波と該端部後退波を合成して棒状体端部１１の入力波を算出する。
【００３５】
＜ト＞入力波算出プログラムと記録媒体
入力波算出プログラムは、算出装置で入力波を算出するものであり、例えば図３に示すように、杭を例に取ると、杭頭から下方の位置ｘ_０で測定した歪みと加速度からＦ（ｘ_０、ｔ）とＺ・Ｖ（ｘ_０、ｔ）を求める（Ｓ１）。Ｆ（ｘ_０、ｔ）とＺ・Ｖ（ｘ_０、ｔ）から進行波Ｆ_ｄ（ｘ_０、ｔ）と後退波Ｆ_ｕ（ｘ_０、ｔ）の分離を行う（Ｓ２）。これから杭頭から位置ｘ_０の測定後退波Ｆ_ｄ（ｘ_０、ｔ）を求める（Ｓ３）。また、入力波Ｆ_Ｉ（ｔ）を求める（Ｓ４）。杭仕様、杭長、断面積、ヤング係数などを入力する（Ｓ１１）。杭体のモデル化を行う（Ｓ１２）。地盤条件を入力する（Ｓ１３）。地盤のモデル化を行う（Ｓ１４）。杭−地盤系のモデル化を行う（Ｓ１５）。測定入力波と杭−地盤系のモデルにより、波動伝播計算を行う（Ｓ１６）。杭頭から位置ｘ_０の計算後退波Ｆ’_ｕ（ｘ_０、ｔ）を求める（Ｓ１７）。測定後退波Ｆ_ｄ（ｘ_０、ｔ）と計算後退波Ｆ’_ｕ（ｘ_０、ｔ）の波形を比較する（Ｓ１８）。一致しない場合、地盤パラメータを修正し（Ｓ１９）、ステップＳ１６に飛ぶ。一致すると、静的抵抗成分を評価する（Ｓ２０）。静的な荷重変位量曲線を求める（Ｓ２１）。杭の差分モデルは、例えば図４のようなモデルとする。この入力波算出プログラムをＣＤ、ハードディスク、メモリカードなどの記録媒体に記録する。このモデルは、動的抵抗成分をダッシュポット３２で、また、静的抵抗成分をばね３３とスライダ３４で、モデル化したものである。なお、図３のフローチャートにおいて、本発明は、ステップＳ４の測定入力波として、Ｆ_Ｉ（ｔ）を使用する。それに対して、従来の「測定点の軸方向力の進行波を入力波として評価する方法（地盤工学会の基準）」では、Ｆ（ｘ_０、ｔ）を使用し、従来の「測定点の軸方向力を入力波と評価する方法」では、Ｆ_ｄ（ｘ_０、ｔ）を使用する点で本発明と相違している。
【００３６】
以下、杭における入力波算出の実施例を説明する。
【００３７】
＜イ＞測定条件
杭頭（棒状体端部）に力ｆを付与して、杭に発生する進行波と後退波、及び杭頭に発生した入力波を確認するために、図５に示すようにシンプルなモデルを製作した。杭３の周面を自由面とするために、地盤４中に先端を閉鎖した鋼管４１をソイルセメント埋設工法で打設し、その中に杭３を立て込んだ。杭３と鋼管４１の間には空洞４２が形成されている。杭頭に力ｆを付与する衝撃装置には、重錘３ｋＮのものを用い、落下高さは８００ｍｍとした。また、杭３は杭長８ｍのＢ種の直杭（Φ４００）を用い、歪センサ２２と加速度センサ２１のセンサ２の配置は杭頭から８００ｍｍ（ｘ_０）離れた位置とした。センサ２からの測定信号は、アンプ５１、５２に入力され、Ａ／Ｄ変換器５３、５４を介してＣＰＵ５９で処理され、進行波、後退波及び入力波が求められた。
【００３８】
＜ロ＞後退波と進行波の算出
後退波と進行波の算出は、歪センサ２２と加速度センサ２１による測定値から軸方向力Ｆ（ｘ_０、ｔ）と速度Ｖ（ｘ_０、ｔ）を求める。この測定値から式１、式２のようにして進行波（下降波）と後退波（上昇波）を算出する。直接測定できない杭頭の軸方向力は、杭頭の位置での進行波と後退波を足し合わせたもので、式３のようにして求められる。杭頭の入力波Ｆ_Ｉ（ｔ）は、杭頭の軸方向力Ｆ（０、ｔ）と等しいので、式７から求めることができる。
【００３９】
＜ハ＞測定波形
測定位置ｘ_０で測定した波形を図６に示す。測定した軸方向力Ｆ（ｘ_０、ｔ）は、図６（Ａ）に示す。分離した進行波Ｆ_ｄ（ｘ_０、ｔ）は、図６（Ｂ）に示す。分離した後退波Ｆ_ｕ（ｘ_０、ｔ）は、図６（Ｃ）に示す。杭頭の入力波Ｆ_Ｉ（ｔ）は、図６（Ｄ）に示す。
【００４０】
＜ニ＞波形マッチング解析
波形マッチング解析は、杭と地盤をモデル化し、波動理論に基づいて算出した計算波形が測定波形と一致するように解析の入力定数を同定し、杭先端や周囲の抵抗などを求める解析方法である。この波動理論に入力波Ｆ_Ｉ（ｔ）を入れて求めた計算後退波を図６（Ｅ）の実線に示す。測定位置（ｘ_０）における測定後退波形を図６（Ｅ）の破線で示す。この図６（Ｅ）から、計算後退波と測定後退波（図６（Ｅ）の破線）とを比較すると、殆ど完全に一致していることが示されている。この結果から、測定値から算出した杭頭の入力波は、正確な値であると考えられる。
【００４１】
＜ホ＞波形マッチングの参考例
従来の二通りの評価方法（「測定点の軸方向力の進行波を入力波として評価する方法」と「測定点の軸方向力を入力波と評価する方法」）で得られた入力波を用いてマッチングを行った例を示す。
【００４２】
１つは、「測定点の軸方向力の進行波を入力波として評価する方法（地盤工学会の基準）」であり、測定位置（ｘ_０）での進行波を入力波と評価する方法であり、この入力波から計算した計算後退波を図７（Ａ）に示す。この図のように、計算後退波は、時間の経過と共に波形が大きくなり、測定後退波とマッチングさせることができない。その理由は、入力波として反射して戻ってくる波を含めた図６（Ｂ）の波を使用していることによる。それに対して、本発明は、入力波として図６（Ｄ）の一波を利用している。
【００４３】
他の１つは、「測定点の軸方向力を入力波と評価する方法」であり、この入力波から計算した計算後退波を図７（Ｂ）に示す。この図でも、計算後退波は、時間の経過と共に波形が大きくなり、測定後退波とマッチングさせることができない。その理由は、上記と同様に、入力波として反射して戻ってくる波を含めた図６（Ａ）の波を使用していることによる。
【００４４】
それに対して、本発明は、図６（Ｅ）に示すように、複数の山と谷でマッチングが取れており、従来の衝撃載荷試験においてマッチングが取れなかった原因が解明できた。
【００４５】
＜ヘ＞杭を地中に埋設した際の波形
本発明の実施例では、図５に示すようにシンプルなモデルを用いたので、測定波形が図６や図７のように明確になるが、実際には、測定波が図８のように明確にならない。このように、実際の図８の波形を見ただけでは、マッチングが合っているように見えていた。図８（Ａ）は、地中に埋設した杭を本発明の方法で測定して求めた入力波Ｆ_Ｉ（ｔ）であり、本発明の実施例の測定波である図６（Ｄ）に対応する。図８（Ｂ）は、地中に埋設した杭を従来の測定点の軸力の進行波を打撃力として評価する方法（地盤工学会の基準）で使用する入力波Ｆ_ｄ（ｘ_０、ｔ）であり、本発明の実施例の測定波である図７（Ａ）に対応する。
【００４６】
このように、１回しか打撃しない場合でも、従来の方法では、入力波に反射して戻ってきた波が加わり、図８（Ｂ）の波形になっていると考えられる。これを明確にするために図５のシンプルなモデルで実験を行った。
【００４７】
図８で使用した杭は、節杭（Φ６００−４５０、Ｌ＝７ｍ）をソイルセメント埋設工法で打設したものである。杭頭は衝撃装置で打撃して、杭に入力波を付与している。
【００４８】
従来の図８（Ｂ）の入力波の曲線Ｆ_ｄ（ｘ_０、ｔ）は、０．０２秒付近で、かなり大きな負の値になっており、引張力が働いていることを示している。しかし、入力波は、杭頭を打撃して得られたものであるので、引張力が働くことは不自然である。それに対して、本発明の図８（Ａ）の入力波の曲線Ｆ_Ｉ（ｔ）は、常に正であり、自然法則に合っていると考えられる。
【００４９】
【発明の効果】
本発明は、次のような効果を得ることができる。
＜イ＞本発明は、棒状体に付与された入力波を正確に求めることができる。
＜ロ＞また、本発明は、棒状体に付与された入力波を正確に求めるシステム、又は方法を提供することができる。
＜ハ＞また、本発明は、杭に入力された入力波を正確に求めることができる。
【図面の簡単な説明】
【図１】入力波の測定の原理図
【図２】入力波算出システムの説明図
【図３】入力波算出プログラムの説明図
【図４】杭の差分モデルの説明図
【図５】杭のモデルによる入力波の測定図
【図６】杭のモデルにおける波形図
【図７】従来の入力波と測定波のマッチングの説明図
【図８】参考ための本発明と従来の実際の入力波の対比説明図
【符号の説明】
１・・・棒状体
１１・・棒状体端部
２・・・センサ
２１・・加速度センサ
２２・・歪みセンサ
３・・・杭
３１・・杭頭
４・・・地盤
４１・・鋼管
４２・・空洞
５・・・算出装置
５１・・加速度アンプ
５２・・歪み計アンプ
５３、５４・・Ａ／Ｄ変換器
５９・・ＣＰＵ[0001]
BACKGROUND OF THE INVENTION
The present invention relates to an input wave generated in a rod-shaped body when a force is applied to a rod-shaped body such as a pile. In particular, the present invention relates to an input wave used for a loading test for a foundation pile, a soundness test for a foundation pile and a structure, and the like.
[0002]
[Prior art]
Conventionally, the vertical loading test of a pile is a method of confirming the vertical bearing capacity of the pile from the experiment. The “Pile vertical loading test method / comment (May 2002)” of the Japan Geotechnical Society, 6) A) indentation test method, B) tip loading test method, C) pull-out test method, D) lead orthogonal load loading test method, E) rapid loading test method, F) impact loading test method are specified. ing. Among these, A) to D) are static test methods, and E) and F) are dynamic loading test methods.
[0003]
Procedure shock loading test the F) particularly relevant to the present invention, a) the axial force of the x ₀ away from the pile head seek (axial force) and speed (particle velocity), b) an axial force F (X ₀ , t) is separated into traveling wave F _d (x ₀ , t) and backward wave F _u (x ₀ , t), c) waveform matching is performed from the backward wave of axial force, Identify the resistance and calculate the bearing capacity of the pile.
[0004]
The above-mentioned waveform matching models the pile and the ground, identifies the resistance and damping constant of the ground so that the calculated waveform calculated based on the wave theory matches the measured waveform, and determines the bearing capacity of the pile tip and peripheral surface. It is a method to seek. Compared to other test methods, the impact load test method is a load test method that is easy to prepare for an experiment, is inexpensive, and can be easily performed.
[0005]
References are listed below.
1) Geotechnical Society: Pile vertical loading test method and explanation, pp. 227-244, 2002.5.
2) Matsumoto, J .: Theoretical background in the application of wave theory to piles, pile driveability, and application of wave theory to piles.
Proceedings of symposium presentations, Geotechnical Society, pp. 7-21, 1989.
3) Tomoaki Sakai: Basics of wave theory-pile driving analysis program-Proceedings of symposium on pile driveability and application of wave theory to piles, Geotechnical Society, pp. 23-33, 1989.
4) Shinji Nishimura: Requirements for signal matching analysis in impact loading test, Proceedings of the 36th Geotechnical Research Conference, pp. 1645-1646, 2001.
5) Eiji Kojima, Tomoko Futami, Yusuke Honma, Junichi Kuwayama, Motohiro Watanabe: Fundamental study of impact loading test applicable to piles with longitudinal cross-sectional changes, Part 1 to Part 3, 38th Geotechnical Engineering Presentation Posted in the conference lecture collection, 2003.
[0006]
Conventionally, there are mainly two methods for evaluating an input wave (blowing force) in an impact loading test. Neither of these methods yielded satisfactory results.
[0007]
(1) Method of evaluating the traveling wave of the axial force at the measurement point as an input wave In the dynamic loading system (FPDS-3) of the Dutch Institute of Applied Science (TNO), the axial force at the measurement point Were separated into traveling waves and backward waves, and traveling waves were evaluated as input waves. The method of the Geotechnical Society (see Reference 1) employs this method (see Reference 4).
[0008]
(2) Method for Evaluating Axial Force at Measurement Point as Input Wave In the dynamic loading system dWAVE (manufactured by Soft Prime), the axial force at the measurement point is evaluated as an input wave. Since the strain and acceleration of the pile head cannot be measured, it is considered from engineering judgment that the axial force at a distance slightly below the pile head is not much different as input waves for piles of several meters or tens of meters. It was.
[0009]
In the conventional impact loading test, the vibration equation is solved based on the input wave generated at the pile head, but the input wave at the core pile head cannot be measured for the following reason. i) The load distribution is not uniform at the pile head. ii) The sensor cannot be attached (the strain gauge cannot be attached, and the accelerometer may be destroyed). Accordingly, the measuring point a point a predetermined distance x ₀ from the pile head. According to the standards of the Society of Geotechnical Engineers, it is recommended that the measurement point should be at a distance of 1.5 times the pile diameter from the pile head.
[0010]
[Problems to be solved by the invention]
<A> The present invention is to accurately obtain an input wave applied to a rod-shaped body.
<B> The present invention also provides a system or method for accurately obtaining an input wave applied to a rod-shaped body.
<C> Further, the present invention is to accurately obtain an input wave input to a pile.
[0011]
The present invention relates to an input wave calculation system that calculates an input wave generated by a force applied to a rod-shaped body, and includes a sensor and a calculation device, the sensor is attached at a position away from the end of the rod-shaped body by a predetermined distance, The traveling wave and the backward wave are obtained from the measured value of the sensor generated by the force applied to the end of the rod-shaped body, the traveling wave is returned from the sensor position to the vicinity of the rod-shaped body end , and the backward traveling wave The end receding wave which is advanced from the sensor position to the vicinity of the end of the rod-shaped body, and the input wave at the end of the rod-shaped body is calculated by synthesizing the end traveling wave and the end receding wave. In the input wave calculation system.
[0012]
Further, the present invention provides an input wave calculation method for calculating an input wave generated by a force applied to a rod-shaped body , in which a sensor is attached at a position away from the end of the rod-shaped body by a predetermined distance .
Determining a retraction wave traveling wave from the measured values of the sensor caused depending on the force applied to the rod-like body end, end traveling wave and the backward wave returned to the traveling wave from the position of the sensor to the rod-like body end A step of calculating an end receding wave from the sensor position to the end of the rod-shaped body, a step of combining the end traveling wave and the end receding wave, and calculating an input wave of the end of the rod-shaped body; The input wave calculation method is characterized by comprising:
[0013]
DETAILED DESCRIPTION OF THE INVENTION
Hereinafter, embodiments of the present invention will be described with reference to the drawings.
[0014]
<I> Input wave calculation system or input wave calculation method The input wave calculation system or input wave calculation method is a force input to a rod-shaped body when a force is applied to the rod-shaped body such as a pile, a column, or a concrete structure, That is, a system or method that includes a device that can determine an input wave. The direction of the force applied to the rod-shaped body includes an axial direction of the rod-shaped body, a direction orthogonal to the axial direction, a bending direction of the rod-shaped body, or a twisting direction of the rod-shaped body. In the case of the axial direction, a longitudinal wave is generated in the rod-shaped body, and in the case of a direction orthogonal to the axial direction, a transverse wave is generated in the rod-shaped body. The bending direction of the rod-shaped body is a direction in which the axis is bent by applying a force in a direction orthogonal to the axial direction. The twisting direction of the rod-shaped body is a direction in which the rod-shaped body is twisted by rotating the shaft. The type of force applied to the rod-shaped body may be any as long as an input wave is generated in the rod-shaped body, such as impact force, impact force, tensile force, blasting force due to blasting, and repeating force by a vibrator.
[0015]
The input wave calculation system or the input wave calculation method may be anything as long as the input wave input to the rod-like body can be obtained. The input wave calculation system or the input wave calculation method can be applied to, for example, an analysis such as an impact loading test, a rapid loading test, or a soundness test of a structure such as a foundation pile. Examples of this analysis include a finite element method, a thin layer element method, a boundary element method, a difference analysis method, a wave propagation analysis method based on a characteristic curve, a frame analysis method, and a numerical analysis method such as a mass system.
[0016]
In addition to the input wave calculation system or the input wave calculation method, the present invention can be expressed by a program and implemented by a computer. The program can be stored in a recording medium and distributed.
[0017]
<B> An example in which the force f is applied in the axial direction at the end of the measuring rod 1 by the measuring device is shown in FIG. The input wave F _I (t) generated at the action position (x = 0) of the rod-like body end portion 11 where the force f is applied cannot be directly measured because the force distribution is not uniform. Therefore, a wave generated at a position (x ₀ ) where the force distribution is almost uniform at a position away from the position where the force is applied is measured. This wave, a traveling wave F _d away the middle rod-shaped body 1 from the operating position, there is a backward wave F _u Back to the operative position. Here, the force distribution is substantially uniform, the degree of uniformity varies depending on the measurement accuracy, but the force distribution (the direction of the force and the direction of the force) (Size) is almost complete.
[0018]
The rod-shaped body 1 is an object in which the propagation of force does not spread radially but propagates in a substantially constant direction, such as a columnar body, a hollow cylindrical body, and a columnar body having a large number of holes. is there. The cross section of the rod-like body 1 may have any shape, for example, a circle, an ellipse, a square, a polygon or the like. Further, the material of the rod-like body 1 may be any material as long as the force can be propagated, such as concrete, steel, plastic, inorganic material, or an object in which these are mixed.
[0019]
There are various measurement methods for measuring the traveling wave _Fd and the backward wave _Fu , and the same type of measuring device such as an accelerometer, an accelerometer, a speedometer, a displacement meter, a strain accelerometer, a strain speedometer, and a strain meter. These can be combined or a plurality of types can be combined. For example, there is a combination of a strain measuring device such as a strain sensor and a speed measuring device such as a velocity sensor, a combination of a strain measuring device and an acceleration measuring device such as an acceleration sensor, or a combination of strain measuring devices that measure strain at a plurality of locations. . Examples of the measuring device include a device that is directly attached to the rod-shaped body 1 for measurement and a device that is indirectly measured after being separated from the rod-shaped body 1.
[0020]
As an example of a combination of measuring devices, there are a case where a plurality of measuring devices of the same type are combined and a case where a plurality of measuring devices are combined. When a plurality of measuring devices of the same type are combined, the plurality of measuring devices are arranged at predetermined intervals along the axial direction of the rod-shaped body 1, and are preferably arranged on the same line parallel to the axis. Alternatively, when a plurality of types of measuring devices are combined, the plurality of types of measuring devices are arranged at the same distance from the rod-like body end portion 11, preferably in the vicinity thereof.
[0021]
When a plurality of measuring devices of the same type are combined, a plurality of measuring devices of the same type are preferably arranged at the same distance from the rod-like body end portion 11. These measuring devices of the same type are preferably arranged at equal intervals around the rod-shaped body 1. For example, two measuring devices of the same type are arranged at positions symmetrical with respect to the axis of the rod-shaped body 1. The measured values of these measuring devices are averaged.
[0022]
In the case of combining a plurality of types of measuring devices, preferably, the plurality of the same types of measuring devices are arranged at equal intervals around the rod-shaped body 1 having the same distance from the rod-shaped body end portion 11. For example, two measuring devices of the same type are arranged at positions symmetrical with respect to the axis of the rod-shaped body 1. The measured values of these measuring devices are averaged.
[0023]
<C> Calculation of traveling wave and backward wave As an example of the measurement of the traveling wave and backward wave when force f is applied in the axial direction at the end 11 of the rod-like body, a strain measuring device and an acceleration measuring device are used. In order to calculate the traveling wave and the backward wave, first, (I) a force f is applied to the end 11 of the rod-shaped body. (II) in the measurement position of the rod-shaped body 1 (e.g., spaced from the rod-like body end by a predetermined distance x ₀ position), the axial force F (x _{0, t)} by the distortion measuring device _{= A p · E · ε (} x ₀ , t), an acceleration α is obtained by an acceleration measuring device, and the acceleration α is integrated to obtain a velocity V (x ₀ , t). (III) From the axial force F (x ₀ , t) obtained by measurement and Z · V (x ₀ , t), the traveling wave F _d (x ₀ , t) and the backward movement are obtained as shown in equations 1 and 2. The wave F _u (x ₀ , t) is calculated. A _p in the formula represents a cross-sectional area of the rod-like body at the measurement position, E is shows the Young's modulus of the rod-shaped body 1 at the measurement _position, ε (x 0, _t) represents the distortion at the measurement position, Z Indicates impedance. Note that in this specification, vector notation such as force and speed is preferably vector notation, but is represented as one-dimensional in order to simplify the notation. In the case of imparting a force f perpendicular to the axial direction in the rod-like body end 11, directed force _F (x 0, t) which is perpendicular to the axial direction _{= A p · G · ε (} x 0, t) to be. Here, G is a shear elastic modulus.
[0024]
[Formula 1]

[0025]
[Formula 2]

[0026]
<D> Calculation of the axial force at the end of the rod-shaped body The axial force F (0, t) at the end of the rod-shaped body 11 is the traveling wave F _d (x ₀ , t + t ₀ ) at the end of the rod-shaped body (x = 0). ) And the backward wave F _u (x ₀ , t−t ₀ ). The end traveling wave F _d (x ₀ , t + t ₀ ) is obtained by returning the traveling wave F _d (x ₀ , t) at the measurement position (x ₀ ) to the end of the rod-shaped body (x = 0). The end receding wave F _u (x ₀ , t−t ₀ ) is obtained by advancing the receding wave F _u (x ₀ , t) at the measurement position (x ₀ ) to the end of the rod-shaped body (x = 0). . That is, the traveling wave F _d (x ₀ , t) and the backward wave F _u (x ₀ , t) generated at a position inside the rod-shaped body that is a predetermined distance (x ₀ ) away from the end of the rod-shaped body (x = 0). The end traveling wave F _d (x ₀ , t + t ₀ ) obtained by returning the traveling wave to the rod end 11 and the end receding wave F _u (x ₀ , t −) that advanced the receding wave to the rod end 11 are obtained. t ₀ ) is calculated, and the end traveling wave and the end retreating wave are combined, and the axial force F (0, t) at the end of the rod-shaped body (x = 0) is calculated from Equation 3.
[0027]
The waveform of the force due to the impedance and speed of the rod-like body end portion 11 is obtained as shown in Equation 4. Here, F _d (x ₀ , t + t ₀ ) is a wave obtained by returning the traveling wave F _d (x ₀ , t) at the predetermined distance x ₀ to the rod-like body end portion 11, and F _u (x ₀ , t -T ₀ ) is a wave obtained by advancing the backward wave F _u (x ₀ , t) to the rod-shaped body end portion 11. Here, t ₀ = x ₀ / V _L , and V _L is a propagation velocity that propagates through the rod-shaped body 1. Instead of Equation 3 and Equation 4, Equation 5 and Equation 6 where t⇒t + α may be used. Here, α is an arbitrary value.
[0028]
[Formula 3]

[0029]
[Formula 4]

[0030]
[Formula 5]

[0031]
[Formula 6]

[0032]
<E> Calculation of Input Wave The input wave F _I (t) is a force f applied to the end of the rod-shaped body (x = 0), and the force is input into the rod-shaped body 1, as shown in Equation 7 The input wave F _I (t) is equal to the axial force F (0, t) of the rod-like body end portion 11. This is because the rod-shaped body end 11 is a free surface, and therefore, when the backward wave is totally reflected by the rod-shaped body end 11 and becomes a traveling wave, the phase is reversed, the backward wave and the traveling wave cancel each other, and the rod-shaped body end 11 Only has an input wave. In this way, when the force f acts on the rod-like body end portion (x = 0) and the traveling wave and the backward wave at the measurement position away from the rod-like body end portion 11 by a predetermined distance (x ₀ ) are obtained, The input wave F _I (t) incident from the unit 11 can be calculated.
[0033]
[Formula 7]

[0034]
<F> Configuration of Input Wave Calculation System The input wave calculation system includes, for example, a distortion amplifier 52 that receives a signal from the strain sensor 22 and an acceleration amplifier 51 that receives a signal from the acceleration sensor 21, as shown in FIG. A / D converters 53 and 54 for A / D converting these amplifiers, and data from these A / D converters are input to the FIFO memory 57 or the FPGA logic 58 via the data line 55, and data processing is performed by the CPU 59. The calculating device 5 is provided. The calculation device 5 includes an end traveling wave in which the measured traveling wave is returned from the measurement position to the vicinity of the rod-shaped body end 11, and an end retreat in which the measured backward wave is advanced from the measurement position to the vicinity of the rod-shaped body end 11. A wave is obtained, and the end traveling wave and the end receding wave are combined to calculate the input wave of the rod end 11.
[0035]
<G> The input wave calculation program and the recording medium input wave calculation program calculate an input wave by a calculation device. For example, as shown in FIG. ₀ distortion and the acceleration measured in F _(x 0, t) and determining the _{Z · V (x 0, t} ) (S1). The traveling wave F _d (x ₀ , t) and the backward wave F _u (x ₀ , t) are separated from F (x ₀ , t) and Z · V (x ₀ , t) (S2). From this, the measured backward wave F _d (x ₀ , t) at the position x ₀ is obtained from the pile head (S3). Further, an input wave F _I (t) is obtained (S4). Pile specifications, pile length, cross-sectional area, Young's modulus, etc. are input (S11). The pile body is modeled (S12). A ground condition is input (S13). The ground is modeled (S14). The pile-ground system is modeled (S15). Wave propagation calculation is performed using the measured input wave and the pile-ground model (S16). A calculated backward wave F ′ _u (x ₀ , t) at the position x ₀ is obtained from the pile head (S17). The waveforms of the measured backward wave F _d (x ₀ , t) and the calculated backward wave F ′ _u (x ₀ , t) are compared (S18). If not, the ground parameter is corrected (S19), and the process jumps to step S16. If they match, the static resistance component is evaluated (S20). A static load displacement curve is obtained (S21). The pile difference model is, for example, a model as shown in FIG. This input wave calculation program is recorded on a recording medium such as a CD, a hard disk, or a memory card. In this model, a dynamic resistance component is modeled by a dashpot 32 and a static resistance component is modeled by a spring 33 and a slider 34. In the flowchart of FIG. 3, the present invention uses F _I (t) as the measurement input wave in step S4. On the other hand, in the conventional “method for evaluating the traveling wave of the axial force at the measurement point as an input wave (standard of the Geotechnical Society), F (x ₀ , t) is used, The “method for evaluating axial force as an input wave” differs from the present invention in that F _d (x ₀ , t) is used.
[0036]
Hereinafter, an embodiment of calculating an input wave in a pile will be described.
[0037]
<I> Measurement conditions To apply force f to the pile head (end of rod-like body) and confirm the traveling wave and backward wave generated in the pile and the input wave generated in the pile head, as shown in FIG. Made a simple model. In order to make the peripheral surface of the pile 3 a free surface, a steel pipe 41 whose tip was closed in the ground 4 was placed by a soil cement embedding method, and the pile 3 was stowed therein. A cavity 42 is formed between the pile 3 and the steel pipe 41. As an impact device for applying force f to the pile head, a weight of 3 kN was used, and the drop height was 800 mm. Further, pile 3 with a B type straight pile Kuicho 8m (Φ400), the arrangement of the sensor 2 of the strain sensor 22 and the acceleration sensor 21 is set to 800 mm _{(x 0)} away from the pile. The measurement signal from the sensor 2 was input to the amplifiers 51 and 52 and processed by the CPU 59 via the A / D converters 53 and 54, and a traveling wave, a backward wave and an input wave were obtained.
[0038]
<B> Calculation of Backward Wave and Traveling Wave The backward wave and traveling wave are calculated by calculating the axial force F (x ₀ , t) and velocity V (x ₀ , t) from the measured values by the strain sensor 22 and the acceleration sensor 21. Ask. From this measured value, a traveling wave (downward wave) and a backward wave (upward wave) are calculated as in Expression 1 and Expression 2. The axial force of the pile head that cannot be measured directly is the sum of the traveling wave and the backward wave at the position of the pile head, and is obtained as shown in Equation 3. Since the pile head input wave F _I (t) is equal to the pile head axial force F (0, t), it can be obtained from Equation 7.
[0039]
Shows a waveform measured by <c> measured waveform measurement location x ₀ in FIG. The measured axial force F (x ₀ , t) is shown in FIG. The separated traveling wave F _d (x ₀ , t) is shown in FIG. The separated backward wave F _u (x ₀ , t) is shown in FIG. The input wave F _I (t) of the pile head is shown in FIG.
[0040]
<D> Waveform matching analysis Waveform matching analysis models piles and ground, identifies the input constants of the analysis so that the calculated waveform calculated based on wave theory matches the measured waveform, and the resistance of the pile tip and surroundings, etc. This is an analysis method for obtaining. The calculated backward wave obtained by putting the input wave F _I (t) into this wave theory is shown by the solid line in FIG. A measurement backward waveform at the measurement position (x ₀ ) is indicated by a broken line in FIG. FIG. 6E shows that the calculated backward wave and the measured backward wave (broken line in FIG. 6E) almost completely match. From this result, it is considered that the input wave of the pile head calculated from the measured value is an accurate value.
[0041]
<E> Reference example of waveform matching Two conventional evaluation methods ("Method to evaluate the traveling wave of the axial force at the measurement point as an input wave" and "Method to evaluate the axial force at the measurement point as an input wave" The example which matched using the input wave obtained by () is shown.
[0042]
One is a “method for evaluating the traveling wave of the axial force at the measurement point as an input wave (standard of the Geotechnical Society), and a method for evaluating the traveling wave at the measurement position (x ₀ ) as an input wave. There is a calculated backward wave calculated from this input wave as shown in FIG. As shown in this figure, the calculated backward wave becomes larger with time and cannot be matched with the measured backward wave. The reason is that the waves shown in FIG. 6B including the waves reflected and returned as the input waves are used. On the other hand, the present invention uses one wave of FIG. 6D as an input wave.
[0043]
The other one is “a method for evaluating the axial force at the measurement point as an input wave”, and a calculated backward wave calculated from this input wave is shown in FIG. Also in this figure, the calculated backward wave becomes larger with time and cannot be matched with the measured backward wave. The reason is that, as described above, the waves shown in FIG. 6A including the waves reflected and returned as the input waves are used.
[0044]
On the other hand, as shown in FIG. 6 (E), in the present invention, matching was achieved at a plurality of peaks and valleys, and the cause of failure in matching in the conventional impact loading test could be clarified.
[0045]
<F> Waveform when the pile is buried in the ground In the embodiment of the present invention, since a simple model is used as shown in FIG. 5, the measured waveform becomes clear as shown in FIG. 6 and FIG. Actually, the measurement wave is not clear as shown in FIG. Thus, just looking at the actual waveform of FIG. FIG. 8A is an input wave F _I (t) obtained by measuring a pile buried in the ground by the method of the present invention, and FIG. 6D is a measured wave of the embodiment of the present invention. Correspond. FIG. 8B shows an input wave F _d (x ₀ , t) used in a method of evaluating a traveling wave of an axial force at a conventional measurement point as a striking force for a pile buried in the ground (standard of the Geotechnical Society). And corresponds to FIG. 7A which is a measurement wave of the embodiment of the present invention.
[0046]
In this way, even when hitting only once, it is considered that the conventional method adds a wave reflected and returned to the input wave, resulting in the waveform of FIG. In order to clarify this, an experiment was conducted with the simple model of FIG.
[0047]
The pile used in FIG. 8 is a knot pile (Φ600-450, L = 7 m) placed by a soil cement burying method. The pile head is struck with an impact device to give an input wave to the pile.
[0048]
The curve F _d (x ₀ , t) of the input wave in FIG. 8 (B) in the prior art has a fairly large negative value around 0.02 seconds, indicating that the tensile force is working. . However, since the input wave is obtained by hitting the pile head, it is unnatural that the tensile force works. On the other hand, the curve F _I (t) of the input wave in FIG. 8A of the present invention is always positive and is considered to meet the natural law.
[0049]
【The invention's effect】
The present invention can obtain the following effects.
<A> The present invention can accurately determine the input wave applied to the rod-shaped body.
<B> The present invention can also provide a system or method for accurately obtaining an input wave applied to a rod-shaped body.
<C> In addition, the present invention can accurately determine the input wave input to the pile.
[Brief description of the drawings]
[Fig. 1] Principle of input wave measurement [Fig. 2] Illustration of input wave calculation system [Fig. 3] Illustration of input wave calculation program [Fig. 4] Illustration of differential model of pile [Fig. Fig. 6 Waveform diagram of the pile model. Fig. 7 Explanatory diagram of matching between the conventional input wave and the measured wave. Fig. 8 The present invention for reference and the conventional actual input wave. Comparison diagram [Explanation of symbols]
DESCRIPTION OF SYMBOLS 1 ... Bar-shaped body 11 ... Bar-shaped body edge part 2 ... Sensor 21 ... Acceleration sensor 22 ... Strain sensor 3 ... Pile 31 ... Pile head 4 ... Ground 41 ... Steel pipe 42 ... Cavity 5 ... Calculation device 51..Acceleration amplifier 52..Strain meter amplifier 53, 54..A / D converter 59..CPU

Claims (5)

In the input wave calculation system for calculating the input wave generated by the force applied to the rod-shaped body,
A sensor and a calculation device,
The sensor is attached at a position away from the end of the rod-shaped body by a predetermined distance,
The calculation device obtains a traveling wave and a backward wave from the measured value of the sensor generated by the force applied to the end of the rod-shaped body, and an end traveling wave that returns the traveling wave from the position of the sensor to the vicinity of the rod-shaped body end; Obtaining an end receding wave that advances the receding wave from the position of the sensor to the vicinity of the end of the rod-shaped body, and combining the end traveling wave and the end receding wave to calculate an input wave at the end of the rod-shaped body An input wave calculation system characterized by In the input wave calculation system according to claim 1 ,
The force applied to the end of the rod-shaped body is the substantially axial direction of the rod-shaped body, the direction substantially perpendicular to the axial direction of the rod-shaped body, the bending direction of the rod-shaped body, or the twisting direction of the rod-shaped body. Wave calculation system. In the input wave calculation method for calculating the input wave generated by the force applied to the rod-shaped body, the sensor is attached at a position away from the end of the rod-shaped body,
Obtaining a traveling wave and a backward wave from the measured value of the sensor generated by the force applied to the end of the rod-shaped body;
Calculating an end traveling wave obtained by returning the traveling wave from the position of the sensor to the end of the rod-shaped body and an end retreating wave obtained by advancing the backward wave from the position of the sensor to the end of the rod-shaped body;
And a step of synthesizing the end traveling wave and the end receding wave to calculate an input wave at the end of the rod-like body. A procedure for obtaining a traveling wave and a backward wave from a measurement value of a sensor attached to a position away from the rod-shaped body end portion by a force generated by a force applied to the rod-shaped body end portion;
A procedure for calculating an end traveling wave in which the traveling wave is returned from the sensor position to the end of the rod-shaped body and an end receding wave in which the backward wave is advanced from the sensor position to the end of the rod-shaped body;
A program for causing a computer to execute a procedure for synthesizing the end traveling wave and the end receding wave to calculate an input wave at the end of the rod-shaped body. A procedure for obtaining a traveling wave and a backward wave from a measured value of a sensor attached to a position away from a rod-shaped body end portion by a force applied to the rod-shaped body end portion,
A procedure for calculating an end traveling wave in which the traveling wave is returned from the sensor position to the end of the rod-shaped body and an end receding wave in which the backward wave is advanced from the sensor position to the end of the rod-shaped body;
A computer-readable recording medium having recorded thereon a program for causing a computer to execute a procedure for synthesizing the edge traveling wave and the edge backward wave to calculate an input wave at the end of the rod-like body.

Images