JP3889344B2 - Analytical method of pile loading test - Google Patents

Description

【０００８】
数式１において、Ｆは杭頭の載荷力、Ｆ_uは地盤の静的抵抗力、αは杭の加速度である。通常、杭の速度ｖ、加速度αは杭頭での測定値が用いられる。スタナミック試験では、Ｆ,ｖ,α,Ｍは既知量であるため、減衰係数Ｃが求まれば静的抵抗力Ｆ_uを得ることができる。
現在一般的に使用されている減衰係数Ｃを求める方法に除荷点法がある。この除荷点とは地盤抵抗力Ｆ_soilと杭変位ｕ関係における最大変位点を指している。すなわち、除荷点では杭の貫入速度はOとなり、この点では動的抵抗力Ｆ_ｖ＝Ｃ・vは0となる。したがって、除荷点では、Ｆ_soil＝Ｆ_uが成り立つ。
以下に除荷点法について説明する。最初に、数式２によってＦ_soilを求める。
【０００９】
【数２】

【００１０】
また、除荷点では数式３の関係が成り立つ。
【００１１】
【数３】

【００１２】
除荷点でのＦ_uは除荷点荷重とよばれ、スタナミック試験における最大静的抵抗力Ｆ_u(max)と考えられている。そして、減衰定数Ｃは、数式４によって決定される。
【００１３】
【数４】

【００１４】
このようにして求めた減衰定数Ｃの値を用いて、各杭変位における地盤の静的抵抗力（静的荷重）Ｆ_uの値は数式５によって求められる。
【００１５】
【数５】

【００１６】
【本発明が解決しようとする課題】
上記した従来の急速載荷試験及びその解析方法にあっては、以下のような問題点がある。
＜イ＞急速載荷試験のデータを除荷点法によって解析しようとしても、除荷点荷重と地盤抵抗力Ｆ_soilの最大値が一致する場合は静的荷重Ｆ_uと変位ｕの関係を推定できない。
＜ロ＞PSPLTなどのスプリング付きハンマの落下による載荷試験では、特別な工夫をしない限り落下したハンマが振幅することによって繰り返し杭頭の打撃がおこなわれ、騒音や振動が繰り返し発生する。また、騒音や衝撃力を抑えるために、杭頭などにクッション材などの緩衝材を配置する方法もあるが、杭に荷重が伝達すると同時に緩衝材による減衰が始まるため、載荷効率が悪くなる。
【００１７】
【本発明の目的】
本発明は上記したような従来の問題を解決するためになされたもので、従来の除荷点法によって解析できない場合にも解析が可能な杭の載荷試験の解析方法を提供することを目的とする。
また、簡便な方法により杭の静的荷重と変位の関係を求めることができる杭の載荷試験の解析方法を提供することを目的とする。
さらに、最初の載荷後に発生する騒音や振動を最小限に抑えることができる載荷試験に適用する杭の載荷試験の解析方法を提供することを目的とする。
本発明は、これらの目的のうち少なくとも一つを達成するものである。
【００１８】
【課題を解決するための手段】
上記のような目的を達成するために、本発明の杭の載荷試験の解析方法は、載荷装置によって杭に載荷したときの計測データを用いて杭の静的荷重と変位の関係を求める杭の載荷試験の解析方法において、前記計測データによる載荷時間と杭頭速度の関係から杭頭速度がほぼ一定になる一定速度区間を抽出し、前記一定速度区間に対応する前記計測データによる載荷荷重と杭頭変位の関係を、杭の載荷初期部分の静的荷重と変位の初期勾配とし、前記載荷初期部分の延長線が、載荷荷重から杭の慣性力を差し引いて計算した地盤抵抗力と変位の関係を示した線に交わった点からは、該地盤抵抗力と変位の関係を静的荷重と変位の関係にすることを特徴とする方法である。この方法によれば、載荷試験によって計測される杭頭の載荷荷重や杭頭の速度等の計測データを使って、簡単に杭の静的荷重と変位の関係を推定することができる。
また、上記に記載した杭の載荷試験の解析方法において、載荷継続時間Ｔと杭長Ｌと杭の縦波の伝播速度ｃによって得られる相対時間ｔ_ｔ＝Ｔ／（２Ｌ／ｃ）が１０より大きく、かつ、載荷開始から最大載荷荷重に到達するまでの時間Ｔ_ｐと地盤バネｋ_ｓと地盤の逸散減衰係数ｃ_ｒによって得られる相対緩和時間Ｒ_Ｔ＝Ｔ_ｐ／（ｃ_ｒ／ｋ_ｓ）が１０より大きい場合にのみ解析をおこなうことができる。ここで、地盤バネｋ_ｓ、地盤の逸散減衰係数ｃ_ｒは、土質試験などによって求めることができる。
さらに、上記した杭の載荷試験の解析方法において、前記載荷装置としてハンマと、該ハンマの下面に並列に配置した２本のバネ材と、一方のバネ材の下部に配置した減衰装置からなる載荷装置を使用することができる。
【００１９】
また、本発明の杭の載荷試験の解析方法は、載荷装置によって杭に載荷したときの計測データを用いて杭の静的荷重と変位の関係を求める杭の載荷試験の解析方法において、ハンマと、該ハンマの下面に並列に配置した２本のバネ材と、一方のバネ材の下部に配置した減衰装置からなる載荷装置を、該ハンマを剛体質点とすることでモデル化し、杭を複数の区間に分割して一次元の弾性棒でモデル化し、地盤を前記杭の分割節点に接続する地盤バネとダッシュポットでモデル化し、前記載荷装置のモデルに対しては差分解析をおこない、前記杭モデルの応力伝播については特性曲線法に基づく一次元波動伝播解析をおこなうことを特徴とする方法である。
【００２０】
また、載荷装置によって杭に載荷したときの計測データを用いて杭の静的荷重と変位の関係を求める杭の載荷試験の解析方法において、ハンマと、該ハンマの下面に並列に配置した２本のバネ材と、一方のバネ材の下部に配置した減衰装置からなる載荷装置を、該ハンマを剛体質点としてモデル化し、杭を剛体質点としてモデル化し、地盤を前記剛体杭モデルに接続する地盤バネとダッシュポットでモデル化し、２質点系の運動方程式を差分近似して解析をおこなうことを特徴とする杭の載荷試験の解析方法である。
【００２１】
【本発明の実施の形態１】
以下、図面を参照しながら、本発明の実施の形態１について説明する。
【００２２】
＜イ＞載荷試験装置（図１）
載荷装置１は、荷重を付加するものをいい、自由落下させたり油圧式又はディーゼル式で稼動させたりするハンマ４や、特殊な推進剤を燃焼させて反力体を打ち上げて反力を与える装置などがある。
ここでは、ハンマ４と、ハンマ４の下面に並列配置した複数のバネ材２１，２２と、バネ材２２に直列に連結した減衰装置３で構成する載荷装置１について説明する。バネ材２１，２２は、鋼材などを巻いたり曲げたりして強い弾性力を持たせた材料をいい、必要に応じて任意の本数のバネ材を並列に配置することができる。バネ材を使用する本数を増やせば、最大荷重及び載荷時間を大きな範囲でコントロールすることができる。
図１には、２本のバネ材２１，２２を並列に配置した実施例を示した。また、バネ材２１，２２のバネ定数（Ｋ_H1、Ｋ_H2）は、ハンマ４の質量、所望する載荷時間などに応じて任意に調整することができる。例えば、バネ材２１のバネ定数の４倍のバネ定数を有するバネを、バネ材２２に使用することができる。
そして、一方のバネ材２２には、減衰装置３を直列に連結する。減衰装置３を連結するバネ材は、一本に限定されるものではなく、任意に選択することができる。また、必要に応じてすべてのバネ材に減衰装置３を連結してもよい。
減衰装置３は、ハンマ４の移動速度や振幅を減少させるために用いる装置である。減衰装置３は、載荷方向（図１のＡ方向）と除荷方向（Ｂ方向）で減衰定数の異なる装置を使用するのが好ましい。すなわち、載荷方向に移動するときはできるだけハンマ４による載荷荷重を減少させないように減衰定数を０又は低い値とし、ハンマ４が跳ね上がる除荷方向に移動するときは移動速度や振幅を減少させるために減衰定数を高い値に設定した非線形の減衰装置３を使用する。
減衰装置３は、通常、ダンパー又はショックアブソーバとよばれる装置であり、移動方向や変位量などに応じて減衰定数が変化する非線形の減衰装置３はアクティブダンパーとも呼ばれる。減衰装置３にはオイルダンパーやエアダンパー等が使用できる。
【００２３】
＜ロ＞適用条件
後述する簡便な杭の静的荷重と変位の関係を求める方法は、すべての載荷試験に適用できるものではない。
本発明の適用範囲は、次に説明する相対時間（relative duration）と相対緩和時間（relative relaxation time）という２つの指標によって確認することができる。
相対時間ｔ_ｔ＝Ｔ／（２Ｌ／ｃ）は、載荷継続時間Ｔと杭長Ｌと杭の縦波の伝播速度ｃによって求めることができる。相対時間ｔ_ｔの大きさによって、杭中の波動伝播の影響を無視できるか否かを判別することができる。
また、相対緩和時間Ｒ_Ｔ＝Ｔ_ｐ／（ｃ_ｒ／ｋ_ｓ）は、載荷開始から最大載荷荷重に到達するまでの時間Ｔ_ｐと地盤バネｋ_ｓと地盤の逸散減衰係数（radiation damping）ｃ_ｒによって求めることができる。相対緩和時間Ｒ_Ｔは、急速載荷試験の範疇に入るか否かの指標として使用することができる。ここで、地盤バネｋ_ｓ、地盤の逸散減衰係数ｃ_ｒは、土質試験などによって求めることができる。
そして、おおよそ相対時間ｔ_ｔ＞１０、かつ、相対緩和時間Ｒ_Ｔ＞１０の場合に後述する簡便な杭の静的荷重と変位の関係を求める方法が適用できる。通常、動的載荷試験の載荷時間（０．００５〜０．０３秒）の１０倍程度の載荷時間を確保でき、動的載荷試験と静的載荷試験の中間に位置付けられる急速載荷試験は、相対時間ｔ_ｔ＞１０、かつ、相対緩和時間Ｒ_Ｔ＞１０の条件に適合する。
【００２４】
＜ハ＞簡便な杭の静的荷重と変位の関係を求める方法
載荷試験に使用する杭のデータを表１に示す。
【００２５】
【表１】

【００２６】
地盤のデータを表２に示す。
【００２７】
【表２】

【００２８】
載荷装置１のデータを表３に示す。
【００２９】
【表３】

【００３０】
図２（ａ）に経過時間と載荷荷重の関係を、図２（ｂ）に経過時間と杭頭変位の関係を、図２（ｃ）に経過時間と杭頭速度の関係を示す。これらの関係は載荷試験の計測データより得ることができる。
この実施例においては、載荷継続時間Ｔは0.237秒、載荷開始から最大載荷荷重に到達するまでの時間Ｔ_ｐは0.108秒であり、相対時間ｔ_ｔ＝Ｔ／（２Ｌ／ｃ）＝48、相対緩和時間Ｒ_Ｔ＝12.1となった。ここで、地盤バネｋ_ｓ＝10864kN/m³、地盤の逸散減衰係数ｃ_ｒ＝144kNs/m³である。
図３に載荷荷重Ｆ、地盤抵抗力Ｆ_soil、静的荷重Ｆ_uの各荷重と杭頭変位の関係を示す。ここで地盤抵抗力Ｆ_soilは、載荷荷重Ｆから杭の慣性力Ｆ_aを差し引いて計算することができる。この地盤抵抗力Ｆ_soilの最大値は静的荷重Ｆ_uの最大値（すなわち杭の極限支持力）に一致し、杭が極限支持力に達するまでの杭の慣性力Ｆ_aは非常に小さい。このため、この間の載荷荷重Ｆと地盤抵抗力Ｆ_soilはほぼ一致している。しかし、杭の貫入速度に依存する地盤の逸散減衰係数（radiation damping）ｃ_ｒの影響を受けているため地盤抵抗力Ｆ_soilは地盤の静的荷重Ｆ_uを過大に評価しているといえる。この実施例では、除荷点荷重と地盤抵抗力Ｆ_soilの最大値が一致しているため、従来の除荷点法によっては静的荷重Ｆ_uと変位ｕの関係を推定することはできない。
このような場合に対して、次のような新しい静的荷重Ｆ_uと変位ｕの関係を簡便に推定する方法を示す。
【００３１】
杭が極限支持力に達するまでには、図２（ｃ）に示されるように、杭頭速度ｖがほぼ一定になる一定速度区間が現れる。杭頭速度ｖが一定となっている区間に対応する静的荷重Ｆ_uと杭頭変位ｕの区間を図３に示す。この区間の勾配は、ほぼ静的載荷試験の初期勾配に一致する。このことは杭頭速度ｖが一定になる区間が現れた他の実施例でも同様であった。
そこで、杭頭速度ｖが一定となっている区間に対応する載荷荷重Ｆと杭頭変位ｕの関係を、杭の載荷初期部分の静的荷重Ｆ_uと杭頭変位ｕの初期勾配とする。そして、この初期勾配の延長線が地盤抵抗力Ｆ_soilと杭頭変位ｕの関係を示した線に交わった点からは、地盤抵抗力Ｆ_soilと杭頭変位の関係を静的荷重Ｆ_uと杭頭変位ｕの関係にすることで全体的な静的荷重Ｆ_uと杭頭変位ｕを近似することができる。ここで、経過時間ｔ、杭頭速度ｖ、載荷荷重Ｆ、杭頭変位ｕは計測データによって得ることができる。
【００３２】
＜ニ＞減衰装置を考慮した試験結果
バネ材を備えたハンマ４の落下による載荷試験では、特別な工夫をしない限り落下したハンマ４が跳ね上がり、杭頭の打撃を繰り返す。そのため、騒音、振動の観点から実務での使用上の問題点となる場合がある。
そこで、非線形の減衰装置３を使用することで、載荷効率を低下させることなく載荷後のハンマ４の跳ね上がりを低減することができることを説明する。
図４には、減衰装置を稼動させない場合のハンマ速度と経過時間の関係及びハンマ変位と経過時間の関係を示す。ここで、バネ材２１のバネ定数は３１５８．３（kN/m）、バネ材２２のバネ定数は０．０（kN/m）、減衰定数は常に０．０（kN s/m）である。
また、図５には、非線形の減衰装置３を使用した場合のハンマ速度と経過時間の関係及びハンマ変位と経過時間の関係を示す。ここで、非線形の減衰装置３は、載荷荷重（すなわち、バネ材の縮み量）が最大値に達するまでは、減衰係数Ｃ_Hが０、載荷荷重が最大値に達すると減衰係数Ｃ_Hが発揮されるようにしたアクティブダンパー機能を有する。すなわち、杭５の受ける荷重が最大値に達するまでは減衰定数が０．０（kN s/m）であり、最大荷重に達した後は減衰定数が１２５．７（kN s/m）となるように設定した。また、バネ材２１のバネ定数は０．０（kN/m）、バネ材２２のバネ定数は３１５８．３（kN/m）とした。
なお、減衰装置を稼動させない場合と非線形の減衰装置３を使用した場合では、減衰装置３の設定以外は同じ条件である。
【００３３】
図５（ａ）は非線形の減衰装置３を使用した場合の結果であるが、図４（ａ）と比べると、載荷荷重が最大値に達する（ハンマ４の速度が０となる）まではハンマ４の速度が一致していることがわかる。しかし、除荷が始まると、図４（ａ）の速度が載荷時と同じように速度を増すのに比べて、図５（ａ）のハンマ４の速度はほとんど増加せずに低い値で収束することがわかる。これは、バネ材に蓄えられた力が減衰装置３によって吸収されるためである。最終的に図４（ａ）のハンマ４の跳ね上がり速度は３．８（m/s）になるのに対して、図５（ａ）のハンマ４の跳ね上がり速度は１．４（m/s）で留まることになる。ここで、ハンマ４の速度は、図１のＡ方向に移動するときに正となり、Ｂ方向に移動するときに負となる。
【００３４】
また、図４（ｂ）のハンマ４の変位は、放物線を描き、載荷が始まった位置よりも上方に跳ね上がることが図からわかる。これに対して図５（ｂ）のハンマ４の変位は最大変位に達するまでは図４（ｂ）と一致した動きを示すが、除荷が始まると図５（ｂ）のハンマ４の戻りは鈍くなり、図４（ｂ）が最初の位置に戻った時間に達しても、０．１５ｍ程度しか戻らないことがわかる。この結果、非線形の減衰装置３を使用すれば、載荷荷重を減少させることなく早期に振幅を減少させることができるといえる。
【００３５】
【本発明の実施の形態２】
上記の実施の形態１で説明した簡便な杭の載荷試験の解析方法の他に、載荷試験の計測データと載荷試験モデルによる解析結果とから杭の静的荷重と変位の関係を求めることができる。
【００３６】
載荷装置１モデルを含めた載荷試験モデルＮｏ．１を図６に示す。ここで、載荷装置１のモデル化は、ハンマ４は剛体質点としてモデル化し、バネ材２１のバネ定数をＫ_H1とし、バネ材２２のバネ定数をＫ_H2とし、減衰装置３の減衰定数をＣ_Hとしておこなう。
杭５は複数の分割杭５１に分割し、断面積Ａ_p、密度ρ_p、ヤング率Ｅ_p、縦波の伝播速度ｃ_pを有する一次元の弾性棒でモデル化する。ここで、ｃ_pはヤング率Ｅ_pを密度ρ_pで割った値を平方根して求めることができる。幾つかの区間に分割した分割杭５１ａ，５１ｂ，・・・の各杭節点には、地盤バネ（ｋ_s）６１とダッシュポット（ｃ_s）６２でモデル化した地盤抵抗モデルが連結される。
載荷試験モデルＮｏ．１においては、載荷装置１モデルについては差分解析をし、杭中の応力波伝播については特性曲線法に基づく一次元波動伝播解析を行う、ハイブリッド解析を適用する。
【００３７】
図７には載荷装置１をモデル化した図を示す。ここで、ｕ^Hはハンマ変位を示し、ｕ^Pは杭頭変位を示す。また、バネ材２１のバネに蓄えられる力をＦ^H1、バネ材２２のバネに蓄えられる力をＦ^H2とする。
載荷試験モデルＮｏ．１の支配方程式を数式６に示す。
【００３８】
【数６】

【００３９】
載荷装置１モデルの差分解析は、数式７に従っておこなう。
【００４０】
【数７】

【００４１】
ここで、数式７の‘ｊ’は、時間間隔Δｔで計算するときの計算ステップを表す。係数A₂〜A₅と、B₂〜B₄は数式８で求められる。
【００４２】
【数８】

【００４３】
杭頭変位ｕ^Pに起因する杭頭速度は、杭について特性曲線法に基づく一次元波動伝播解析をおこなった結果を基に、数式７によって導くことができる。この杭頭速度の計算は本願の発明者の松本らが開発した公知のKWAVEプログラム（1991）によって計算することができる。
【００４４】
また、地盤バネとダッシュポットでモデル化した地盤モデルは、Randolph and Simons (1986).によって提案された軸抵抗モデルによって計算することができる。このモデルでは、ダッシュポットを粘性に起因するｃ_vと、杭から遠く離れた地盤に逸散して減衰される逸散減衰係数ｃ_ｒに分けて取り扱う。ここでは、軸バネのバネ定数を地盤バネｋ_ｓとする。数式９に地盤バネｋ_ｓと逸散減衰係数ｃ_ｒを求める式を示す。
【００４５】
【数９】

【００４６】
ここで、Ｇはせん断係数、Ｖ_sは杭の周辺地盤のせん断波速度、r₀は杭の半径を示す。
なお、載荷試験モデルＮｏ．１の計算は、数式１０を初期条件として計算することができる。
【００４７】
【数１０】

【００４８】
以上に示した数式に計測データを入力し、地盤抵抗を仮定して計算を繰り返すことによって、杭の静的荷重と変位の関係を求めることができる。
【００４９】
【本発明の実施の形態３】
上記の実施の形態２とは別の載荷試験モデルを使用して杭の静的荷重と変位の関係を求めることができる。
【００５０】
載荷装置１モデルを含めた載荷試験モデルＮｏ．２を図８に示す。
載荷装置１のモデル化は載荷試験モデルＮｏ．１と同様にしておこなう（図７参照）。
そして、杭は質量Ｍ_pを有する剛体質点でモデル化する。また、地盤も地盤バネＫ_sとダッシュポットＣ_sでモデル化した地盤抵抗モデルを使用する。
載荷試験モデルＮｏ．２では、２質点系の運動方程式を差分近似して解析を行う。載荷試験モデルＮｏ．２の支配方程式を数式１１に示す。
【００５１】
【数１１】

【００５２】
２質点系の運動方程式の差分近似は、数式１２によって導く。
【００５３】
【数１２】

【００５４】
なお、載荷試験モデルＮｏ．２の計算も載荷試験モデルＮｏ．１と同様に、数式１０を初期条件として計測データを入力し、地盤抵抗を仮定して計算を繰り返すことによって、杭の静的荷重と変位の関係を求めることができる。
【００５５】
【本発明の効果】
本発明の杭の載荷試験の解析方法は以上説明したようになるから、次のような効果を得ることができる。
＜イ＞従来の除荷点法によって解析できない場合にも、静的荷重と変位の関係を杭の載荷試験の結果から推定することができる。
＜ロ＞載荷試験の計測データを用いて簡便な方法により杭の静的荷重と変位の関係を求めることができる。
＜ハ＞載荷荷重が最大値に達した後に、効果的にハンマの速度や振幅を減衰させることができる試験装置を使用することで、最初の載荷後に発生する騒音や振動を最小限に抑えることができる載荷試験を実施し、その載荷試験の結果を解析することができる。
【図面の簡単な説明】
【図１】本発明の載荷試験の実施例の説明図。
【図２】（ａ）経過時間と載荷荷重の関係図。（ｂ）経過時間と杭頭変位の関係図。（ｃ）経過時間と杭頭速度の関係図。
【図３】載荷荷重Ｆ、地盤抵抗力Ｆ_soil、静的荷重Ｆ_uの各荷重と杭頭変位の関係図。
【図４】（ａ）減衰装置を稼動させない場合の経過時間とハンマ速度の関係図。（ｂ）減衰装置を稼動させない場合のハンマ変位と経過時間の関係図。
【図５】（ａ）非線形の減衰装置を使用した場合の経過時間とハンマ速度の関係図。（ｂ）非線形の減衰装置を使用した場合のハンマ変位と経過時間の関係図。
【図６】載荷試験モデルＮｏ．１のモデルを表した説明図。
【図７】載荷装置モデルを表した説明図。
【図８】載荷試験モデルＮｏ．２のモデルを表した説明図。
【図９】従来の除荷点法で使用する載荷試験モデルの説明図。
【符号の説明】
１・・・載荷装置
２１・・バネ材
２２・・バネ材
３・・・減衰装置
４・・・ハンマ
５・・・杭
５１・・分割杭[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a pile loading test analysis method for obtaining a relationship between a static load and a displacement of a pile from measurement data when loaded on the pile by a loading device in a pile loading test.
[0002]
[Prior art]
In designing pile foundation structures that receive vertical loads, a method is generally used to predict the vertical load-deformation relation of the entire pile foundation structure based on the vertical load-subsidence relation of a single pile that is a structural member. . Since the vertical load-settlement characteristics of piles are greatly influenced by the construction method in addition to the ground conditions, it is often difficult to evaluate this with high accuracy only by an analytical method.
Therefore, as a method for evaluating the vertical load-settlement characteristics of a single pile, a static loading test has been widely used so far. This is due to the recognition that the load-settlement relationship in the static loading test is most reliable. However, since static loading tests require a relatively large amount of time and cost, dynamic loading tests have been used in practice since the 1960s. However, in the load-settlement relationship estimation by signal matching based on the one-dimensional wave theory, the accuracy of the analysis depends on the skill level of the analysis, and differences in the analysis results occur due to differences in the ground model used for signal matching analysis. Issues such as are left.
[0003]
Furthermore, in the case of driven piles in saturated ground, it is widely known that the so-called setup effect improves the load-sinking characteristics after standing compared to the load-sinking characteristics at the time of initial impact. In order to correctly evaluate the load-settlement characteristics after being left, a re-hitting test is necessary, but it is often not easy to carry out the re-hitting test in an actual site.
[0004]
Currently, when carrying out static loading tests, the reaction force pile method is mostly adopted, but the problem with the static loading test method using the reaction force pile method is that the initial pile head stiffness is overestimated. It is to underestimate pile peripheral friction, and to overestimate pile tip bearing capacity. In the vertical loading test method of piles and the explanation (Geotechnical Society, 2002), the distance between the center of the test pile and the reaction force pile is more than 3 times the diameter of the pile so that the influence of the reaction force pile can be ignored. The distance between the reaction force piles is specified to be 3 times or more of the pile diameter, and the distance between the reference point and the center of the test pile is specified to be 5 times or more of the pile diameter. However, in order to be able to ignore the influence of the reaction force pile, there is also a knowledge that the distance between the test pile and the reaction force pile needs to be about 10 times or more the pile diameter. However, it is very difficult to satisfy such a condition at an actual site.
[0005]
Therefore, the first method proposed to give a loading duration that can ignore the effect of wave propagation in the pile without using the reaction pile is the Dynatest by Gonineta1 (I984). . This dynatest is a method of applying a loading force to a pile head by dropping a weight through a spring installed on the pile head. In addition, a method called “Statnamic test” was proposed, in which the force of launching the anti-Kamas installed on the pile head by gas pressure is used as the loading force as well as the reaction force. Thereafter, Pseudo-static pi1e load test (hereinafter abbreviated as PSPLT) is proposed by Sche11ingerhout & Revoort (1996), in which a loading test is performed by dropping a weight with a spring attached to the bottom.
These test methods are monotonically increasing and monotonically decreasing loading durations of 80 ms to 150 ms, and can be loaded on the pile head. These methods are intermediate between the static loading test method and the dynamic loading test method. It is positioned as a rapid loading test method with unique properties. The load capacity of Dynatest and PSPLT is about 4MN. On the other hand, in the static test, loading up to 30MN is possible. One of the advantages of Dynatest and PSPLT compared to the static test is the short test time including test preparation time. Therefore, in dynatest and PSPLT, it is possible to test 10 or more piles per day.
[0006]
In addition, when simple interpretation of rapid loading test data is performed, it is assumed that pile a can ignore the effect of wave propagation in the pile, and pile a is modeled with a rigid mass point, and ground is modeled with ground spring b and dashpot c. The method of doing is performed conventionally (refer FIG. 9). In this case it represents the applied load d in loading force F, pile a is modeled with rigid mass point mass M, the static resistance of the ground with a force F _u by ground spring b, dynamic resistance of the ground F _v = C · v is represented by a dashpot c having a damping coefficient C and a penetration speed v of the pile a.
Several simple methods for estimating the static load-settlement relationship have been proposed based on the above model, and each method uses a force balance equation given by Equation 1.
[0007]
[Expression 1]

[0008]
In Equation 1, F is loading force of the pile head, the F _u static resistance of the ground, alpha is the acceleration of the pile. Usually, the measured value at the pile head is used for the velocity v and acceleration α of the pile. In Sutanamikku test, F, v, alpha, M is for a known amount, it is possible to obtain the static resistance force F _u If the damping coefficient C is Motomare.
There is an unloading point method as a method for obtaining the damping coefficient C generally used at present. This unloading point refers to the maximum displacement point in the relationship between the ground resistance force F _soil and the pile displacement u. That is, the pile penetration speed is O at the unloading point, and the dynamic resistance force F _v = C · v is 0 at this point. Therefore, in the unloading point, F _soil = F _u holds.
The unloading point method will be described below. First, F _soil is obtained by Equation 2.
[0009]
[Expression 2]

[0010]
Moreover, the relationship of Formula 3 is established at the unloading point.
[0011]
[Equation 3]

[0012]
F _u at unloading point called unloading point load are considered as the maximum static resistance force F _u (max) in Sutanamikku test. The attenuation constant C is determined by Equation 4.
[0013]
[Expression 4]

[0014]
In this way, using the value of the damping constant C was calculated, the value of the static resistance (static load) F _u of soil in each pile displacement is determined by Equation 5.
[0015]
[Equation 5]

[0016]
[Problems to be solved by the present invention]
The conventional rapid loading test and the analysis method thereof have the following problems.
<A> Even if trying to analyze the data of the rapid loading test by the unloading point method, if the unloading point load and the maximum value of the ground resistance force F _soil match, the relationship between the static load _Fu and the displacement u cannot be estimated. .
<B> In a loading test by dropping a hammer with a spring such as PSPLT, unless the hammer is specially devised, the pile head is repeatedly hit by the amplitude of the dropped hammer, and noise and vibration are repeatedly generated. Moreover, in order to suppress noise and impact force, there is a method in which a cushioning material such as a cushioning material is arranged on the pile head or the like. However, since the load is transmitted to the pile and the damping by the cushioning material starts at the same time, the loading efficiency is deteriorated.
[0017]
[Object of the present invention]
The present invention was made to solve the conventional problems as described above, and an object thereof is to provide an analysis method for a loading test of a pile that can be analyzed even when the conventional unloading point method cannot be used. To do.
Moreover, it aims at providing the analysis method of the load test of a pile which can obtain | require the relationship between the static load and displacement of a pile by a simple method.
Furthermore, it aims at providing the analysis method of the pile loading test applied to the loading test which can suppress the noise and vibration which generate | occur | produce after the first loading to the minimum.
The present invention achieves at least one of these objects.
[0018]
[Means for Solving the Problems]
In order to achieve the above-described object, the pile loading test analysis method of the present invention uses a measurement data when the pile is loaded by the loading device to obtain a relationship between the static load and the displacement of the pile. In the loading test analysis method, a constant speed section in which the pile head speed is substantially constant is extracted from the relationship between the loading time and the pile head speed based on the measurement data, and the load and pile according to the measurement data corresponding to the constant speed section are extracted. The relationship between the head displacement is the static load and initial displacement gradient of the initial loading portion of the pile, and the extension line of the initial loading portion described above is the relationship between the ground resistance force and displacement calculated by subtracting the inertia force of the pile from the loading load. From the point where the line crosses the line, the relationship between the ground resistance force and the displacement is a relationship between the static load and the displacement. According to this method, it is possible to easily estimate the relationship between the static load and the displacement of the pile by using measurement data such as the pile head loading load and the pile head speed measured by the loading test.
Moreover, in the analysis method of the pile loading test described above, the relative time t _t = T / (2L / c) obtained from the loading duration T, the pile length L, and the propagation velocity c of the longitudinal wave of the pile is 10 large, and the maximum time to reach the applied load _{T p} and ground spring _{k s} and ground relative relaxation time obtained by the escape damping coefficient _{c r} from loading start _{R T = T p / (c} r / k s ) Can only be analyzed if it is greater than 10. Here, the ground spring k _s, escape damping coefficient c _r of the ground can be determined, such as by soil tests.
Furthermore, in the analysis method of the pile loading test described above, a loading comprising a hammer as the above-described loading device, two spring materials arranged in parallel on the lower surface of the hammer, and a damping device arranged at the lower portion of one spring material The device can be used.
[0019]
Further, the pile loading test analysis method of the present invention is a pile loading test analysis method for obtaining a relationship between a static load and displacement of a pile using measurement data when loaded on the pile by a loading device. A loading device composed of two spring members arranged in parallel on the lower surface of the hammer and a damping device arranged under one of the spring materials is modeled by using the hammer as a rigid mass point, and a plurality of piles are formed. Is modeled with a one-dimensional elastic rod, the ground is modeled with a ground spring and a dashpot connected to the split node of the pile, and a differential analysis is performed on the model of the loading device described above. For model stress propagation, a one-dimensional wave propagation analysis based on the characteristic curve method is performed.
[0020]
Moreover, in the analysis method of the pile loading test which calculates | requires the relationship between the static load of a pile and a displacement using the measurement data when loaded on a pile with a loading apparatus, two pieces arranged in parallel on the hammer and the lower surface of the hammer A load device composed of a spring material and a damping device disposed below one of the spring materials, the hammer is modeled as a rigid mass point, the pile is modeled as a rigid mass point, and the ground is connected to the rigid pile model It is an analysis method of a pile loading test characterized by modeling with ground springs and dashpots and performing an analysis by approximating the motion equation of the two mass system.
[0021]
[Embodiment 1 of the present invention]
The first embodiment of the present invention will be described below with reference to the drawings.
[0022]
<I> Loading test equipment (Fig. 1)
The loading device 1 refers to a device that applies a load, such as a hammer 4 that freely drops or operates in a hydraulic or diesel manner, or a device that launches a reaction force body by burning a special propellant to give a reaction force. and so on.
Here, the loading device 1 constituted by the hammer 4, a plurality of spring materials 21 and 22 arranged in parallel on the lower surface of the hammer 4, and the damping device 3 connected in series to the spring material 22 will be described. The spring materials 21 and 22 are materials having a strong elastic force by winding or bending a steel material or the like, and an arbitrary number of spring materials can be arranged in parallel as necessary. If the number of spring materials used is increased, the maximum load and loading time can be controlled in a large range.
FIG. 1 shows an embodiment in which two spring members 21 and 22 are arranged in parallel. Further, the spring constants (K _H1 , K _H2 ) of the spring members 21 and 22 can be arbitrarily adjusted according to the mass of the hammer 4, a desired loading time, and the like. For example, a spring having a spring constant four times the spring constant of the spring material 21 can be used for the spring material 22.
The damping device 3 is connected in series to one spring material 22. The spring material connecting the damping device 3 is not limited to one, and can be arbitrarily selected. Moreover, you may connect the damping device 3 to all the spring materials as needed.
The attenuation device 3 is a device used to reduce the moving speed and amplitude of the hammer 4. The damping device 3 is preferably a device having different damping constants in the loading direction (A direction in FIG. 1) and the unloading direction (B direction). That is, when moving in the loading direction, the damping constant is set to 0 or a low value so as not to reduce the loading load by the hammer 4 as much as possible, and when moving in the unloading direction in which the hammer 4 jumps up, the moving speed and amplitude are decreased. A nonlinear attenuator 3 having a high attenuation constant is used.
The damping device 3 is usually a device called a damper or a shock absorber, and the nonlinear damping device 3 whose damping constant changes according to the moving direction, the amount of displacement, etc. is also called an active damper. An oil damper, an air damper or the like can be used for the damping device 3.
[0023]
<B> Application conditions The simple method of obtaining the relationship between the static load and displacement of a pile, which will be described later, is not applicable to all loading tests.
The application range of the present invention can be confirmed by two indices, a relative duration and a relative relaxation time, which will be described below.
The relative time t _t = T / (2L / c) can be obtained from the loading duration T, the pile length L, and the propagation velocity c of the longitudinal wave of the pile. By the magnitude of the relative time t _t, it is possible to determine whether it is possible to ignore the influence of wave propagation in the pile.
The relative relaxation time R _T = T _p / (c _r / k _s ) is the time T _p from the start of loading until reaching the maximum loaded load, the ground spring k _s, and the ground's dissipation damping coefficient (radiation damping) It can be obtained by _cr . The relative relaxation time _RT can be used as an indicator of whether to enter the category of rapid loading test. Here, the ground spring k _s, escape damping coefficient c _r of the ground can be determined, such as by soil tests.
Then, it roughly and relative time t _t> 10,, a method of determining the relationship between the simple static load and displacement of the pile which will be described later in the case of a relative relaxation time R _T> 10 applies. Usually, the loading time of about 10 times the loading time of the dynamic loading test (0.005 to 0.03 seconds) can be secured, and the rapid loading test positioned between the dynamic loading test and the static loading test is relatively The conditions of time t _t > 10 and relative relaxation time R _T > 10 are met.
[0024]
<C> A simple method for determining the relationship between the static load and displacement of a pile Pile data used in a loading test is shown in Table 1.
[0025]
[Table 1]

[0026]
The ground data is shown in Table 2.
[0027]
[Table 2]

[0028]
Table 3 shows data of the loading device 1.
[0029]
[Table 3]

[0030]
FIG. 2A shows the relationship between elapsed time and loaded load, FIG. 2B shows the relationship between elapsed time and pile head displacement, and FIG. 2C shows the relationship between elapsed time and pile head speed. These relationships can be obtained from the measurement data of the loading test.
In this embodiment, the loading duration T is 0.237 seconds, the time T _p from the start of loading until reaching the maximum loading load is 0.108 seconds, the relative time t _t = T / (2L / c) = 48, relative The relaxation time R _{T was} 12.1. Here, the ground spring k _s = 10864 kN / m ³ , and the ground dissipation attenuation coefficient c _r = 144 kNs / m ³ .
Applied load F in FIG. 3, the ground resistance F _soil, shows the relationship between the load and pile displacement static load F _u. Here soil resistance force F _soil can be calculated by subtracting the inertial force F _a of piles from applied load F. The maximum value of this soil resistance force F _soil coincides with the maximum value of the static load F _u (i.e. ultimate bearing capacity of the pile), the inertial force F _a pile up pile reaches the ultimate bearing capacity is very small. Therefore, during this time the applied load F and soil resistance force F _soil is almost the same. However, it can be said that the ground resistance F _soil because of the influence of fugitive attenuation coefficient (radiation damping) c _r of the ground which depends on the penetration rate of the pile are overestimated the static load F _u of the ground . In this embodiment, since the unloading point load and the maximum value of the ground resistance force F _soil coincide with each other, the relationship between the static load _Fu and the displacement u cannot be estimated by the conventional unloading point method.
For such a case, a method for simply estimating the relationship between the new static load _Fu and the displacement u will be described.
[0031]
By the time the pile reaches the ultimate support force, as shown in FIG. 2 (c), a constant speed section in which the pile head speed v becomes substantially constant appears. Pile velocity v shown in Figure 3 is the section of the static load F _u and pile displacement u corresponding to the section which is constant. The slope of this section approximately matches the initial slope of the static loading test. This is the same in other examples in which a section where the pile head speed v becomes constant appears.
Therefore, the relationship between the applied load F and pile displacement u corresponding to the section of pile head velocity v is constant, the initial slope of the static load F _u and pile head displacement u of loading initial portion of the pile. Then, from the viewpoint of extension of the initial slope intersects the line showing the relationship of the ground resistance F _soil and the pile head displacement u is a static load F _u relationships of the ground resistance F _soil and pile displacement it is possible to approximate the overall static load F _u and pile head displacement u by the relation of pile head displacement u. Here, the elapsed time t, the pile head speed v, the loading load F, and the pile head displacement u can be obtained from the measurement data.
[0032]
<D> Test Results Considering Damping Device In the loading test by dropping the hammer 4 provided with the spring material, the dropped hammer 4 jumps up and repeats the hitting of the pile head unless special measures are taken. Therefore, it may become a problem in practical use from the viewpoint of noise and vibration.
Therefore, it will be described that the use of the nonlinear damping device 3 can reduce the jumping of the hammer 4 after loading without reducing the loading efficiency.
FIG. 4 shows the relationship between the hammer speed and the elapsed time and the relationship between the hammer displacement and the elapsed time when the damping device is not operated. Here, the spring constant of the spring member 21 is 3158.3 (kN / m), the spring constant of the spring member 22 is 0.0 (kN / m), and the damping constant is always 0.0 (kN s / m). .
FIG. 5 shows the relationship between the hammer speed and the elapsed time and the relationship between the hammer displacement and the elapsed time when the nonlinear damping device 3 is used. Here, the nonlinear damping device 3 exhibits a damping coefficient C _H of 0 until the load load (that is, the amount of contraction of the spring material) reaches the maximum value, and exhibits the damping coefficient C _H when the load load reaches the maximum value. It has an active damper function. That is, the damping constant is 0.0 (kN s / m) until the load received by the pile 5 reaches the maximum value, and after reaching the maximum load, the damping constant becomes 125.7 (kN s / m). Was set as follows. The spring constant of the spring member 21 was 0.0 (kN / m), and the spring constant of the spring member 22 was 3158.3 (kN / m).
It should be noted that, when the attenuation device is not operated and when the nonlinear attenuation device 3 is used, the conditions are the same except for the setting of the attenuation device 3.
[0033]
FIG. 5A shows the result when the nonlinear damping device 3 is used. Compared with FIG. 4A, the load load reaches the maximum value (the speed of the hammer 4 becomes 0). It can be seen that the speeds of 4 match. However, when unloading starts, the speed of the hammer 4 in FIG. 5 (a) hardly increases and converges at a low value compared to the speed in FIG. I understand that This is because the force stored in the spring material is absorbed by the damping device 3. Finally, the jumping speed of the hammer 4 in FIG. 4A is 3.8 (m / s), whereas the jumping speed of the hammer 4 in FIG. 5A is 1.4 (m / s). Will stay at. Here, the speed of the hammer 4 is positive when moving in the A direction in FIG. 1 and negative when moving in the B direction.
[0034]
Moreover, it can be seen from the figure that the displacement of the hammer 4 in FIG. 4B draws a parabola and jumps upward from the position where loading has started. On the other hand, the displacement of the hammer 4 in FIG. 5B shows the same movement as in FIG. 4B until the maximum displacement is reached, but when the unloading starts, the return of the hammer 4 in FIG. It turns out that even if it reaches the time when FIG. 4B returns to the initial position, it returns only about 0.15 m. As a result, if the nonlinear damping device 3 is used, it can be said that the amplitude can be reduced at an early stage without reducing the loaded load.
[0035]
[Embodiment 2 of the present invention]
In addition to the simple pile loading test analysis method described in the first embodiment, the relationship between the static load and displacement of the pile can be obtained from the measurement data of the loading test and the analysis result of the loading test model. .
[0036]
Loading test model No. including loading device 1 model. 1 is shown in FIG. Here, the loading device 1 is modeled by modeling the hammer 4 as a rigid mass point, the spring constant of the spring material 21 as K _H1 , the spring constant of the spring material 22 as K _H2, and the damping constant of the damping device 3. performed as C _H.
The pile 5 is divided into a plurality of divided piles 51 and is modeled by a one-dimensional elastic bar having a cross-sectional area A _p , a density ρ _p , a Young's modulus E _p , and a longitudinal wave propagation velocity c _p . Here, c _p can be obtained by square root of a value obtained by dividing Young's modulus E _p by density ρ _p . A ground resistance model modeled by a ground spring (k _s ) 61 and a dash pot (c _s ) 62 is connected to each pile node of the divided piles 51 a, 51 b,... Divided into several sections.
Loading test model No. In 1, the differential analysis is applied to the loading device 1 model, and the hybrid analysis is applied to the one-dimensional wave propagation analysis based on the characteristic curve method for the stress wave propagation in the pile.
[0037]
FIG. 7 shows a model of the loading device 1. Here, u ^H denotes the hammer displacement, u ^P denotes the pile head displacement. The force stored in the spring of the spring material 21 is F ^H1 , and the force stored in the spring of the spring material 22 is F ^H2 .
Loading test model No. The governing equation of 1 is shown in Equation 6.
[0038]
[Formula 6]

[0039]
The differential analysis of the loading device 1 model is performed according to Equation 7.
[0040]
[Expression 7]

[0041]
Here, “j” in Expression 7 represents a calculation step when calculating at the time interval Δt. The coefficient _{A 2 ~A 5, B 2 ~B} 4 is obtained by the equation 8.
[0042]
[Equation 8]

[0043]
The pile head speed resulting from the pile head displacement u ^P can be derived from Equation 7 based on the result of one-dimensional wave propagation analysis based on the characteristic curve method for the pile. This pile head speed can be calculated by a known KWAVE program (1991) developed by Matsumoto et al.
[0044]
The ground model modeled by ground springs and dashpots can be calculated by the axial resistance model proposed by Randolph and Simons (1986). In this model, the c _v caused a dashpot viscous and handled separately in dissipation damping coefficient c _r is attenuated by escape to the remote ground from the pile. Here, the spring constant of the shaft spring and ground spring k _s. Shows the equation for determining the ground spring k _s and dissipation damping coefficient c _r in Equation 9.
[0045]
[Equation 9]

[0046]
Here, G is the shear coefficient, V _s is the shear wave velocity of the ground around the pile, and r ₀ is the radius of the pile.
The loading test model No. The calculation of 1 can be performed using Equation 10 as an initial condition.
[0047]
[Expression 10]

[0048]
The relationship between the static load and displacement of the pile can be obtained by inputting measurement data into the above formula and repeating the calculation assuming ground resistance.
[0049]
[Embodiment 3 of the present invention]
The relationship between the static load and the displacement of the pile can be obtained using a loading test model different from that of the second embodiment.
[0050]
Loading test model No. including loading device 1 model. 2 is shown in FIG.
The loading device 1 is modeled by a loading test model No. 1 is performed (see FIG. 7).
The pile is modeled with a rigid mass point having mass M _p . The ground also uses a ground resistance model modeled by ground spring K _s and dash pot C _s .
Loading test model No. In 2, analysis is performed with a difference approximation of the motion equation of the two mass system. Loading test model No. The governing equation of 2 is shown in Formula 11.
[0051]
[Expression 11]

[0052]
The difference approximation of the equation of motion of the two mass point system is derived by Equation 12.
[0053]
[Expression 12]

[0054]
The loading test model No. In the calculation of No. 2, the load test model No. Similar to 1, the measurement data is input using Equation 10 as an initial condition, and the relationship between the static load and the displacement of the pile can be obtained by repeating the calculation assuming ground resistance.
[0055]
[Effect of the present invention]
Since the analysis method of the pile loading test of the present invention is as described above, the following effects can be obtained.
<A> Even when the conventional unloading point method cannot be used for analysis, the relationship between the static load and the displacement can be estimated from the results of the pile loading test.
<B> The relationship between the static load and displacement of the pile can be obtained by a simple method using the measurement data of the loading test.
<C> Minimize noise and vibration generated after the initial loading by using a test device that can effectively attenuate the hammer speed and amplitude after the loading load reaches the maximum value. It is possible to perform a loading test that can be performed and analyze the result of the loading test.
[Brief description of the drawings]
FIG. 1 is an explanatory diagram of an embodiment of a loading test according to the present invention.
FIG. 2A is a relationship diagram of elapsed time and loaded load. (B) Relationship diagram between elapsed time and pile head displacement. (C) Relationship diagram between elapsed time and pile head speed.
[Figure 3] applied load F, soil resistance force F _soil, relationship diagram of the load and pile displacement of static load F _u.
FIG. 4A is a relationship diagram between elapsed time and hammer speed when the damping device is not operated. (B) Relationship diagram between hammer displacement and elapsed time when the damping device is not operated.
FIG. 5A is a diagram showing the relationship between elapsed time and hammer speed when using a non-linear damping device. (B) Relationship diagram between hammer displacement and elapsed time when a non-linear damping device is used.
6 is a load test model no. Explanatory drawing showing the model of 1. FIG.
FIG. 7 is an explanatory diagram showing a loading device model.
[Fig. 8] Loading test model no. Explanatory drawing showing the model of 2. FIG.
FIG. 9 is an explanatory diagram of a loading test model used in a conventional unloading point method.
[Explanation of symbols]
DESCRIPTION OF SYMBOLS 1 ... Loading apparatus 21 ... Spring material 22 ... Spring material 3 ... Damping device 4 ... Hammer 5 ... Pile 51 ... Divided pile

Claims (5)

In the analysis method of the pile loading test to obtain the relationship between the static load and displacement of the pile using the measurement data when loaded on the pile by the loading device,
From the relationship between the loading time and the pile head speed according to the measurement data, extract a constant speed section where the pile head speed is almost constant,
The relationship between the loading load and the pile head displacement according to the measurement data corresponding to the constant speed section, the static load and the initial gradient of the displacement of the initial loading portion of the pile,
From the point where the extension line of the initial part of the load mentioned above intersects the line showing the relationship between the ground resistance and displacement calculated by subtracting the inertia force of the pile from the load, the relationship between the ground resistance and displacement is static. It is characterized by the relationship between load and displacement,
Pile loading test analysis method. In the pile loading test analysis method according to claim 1,
The relative time t _t = T / (2L / c) obtained by the loading duration T, the pile length L and the propagation velocity c of the longitudinal wave of the pile is greater than 10, and from the start of loading until the maximum loading load is reached. The analysis is performed only when the relative relaxation time R _T = T _p / (c _r / k _s ) obtained by the time T _p , the ground spring k _s, and the ground dissipation coefficient c _r is larger than 10. To
Pile loading test analysis method. In the analysis method of the load test of the pile according to claim 1 or 2,
The loading device is characterized by using a loading device comprising a hammer, two spring materials arranged in parallel on the lower surface of the hammer, and a damping device arranged under one of the spring materials,
Pile loading test analysis method. In the analysis method of the pile loading test to obtain the relationship between the static load and displacement of the pile using the measurement data when loaded on the pile by the loading device,
A loading device composed of a hammer, two spring members arranged in parallel on the lower surface of the hammer, and a damping device arranged at the lower part of one of the spring materials is modeled by using the hammer as a rigid mass point.
The pile is divided into multiple sections and modeled with a one-dimensional elastic bar,
Model the ground with ground springs and dashpots that connect the split nodes of the pile,
The differential analysis is performed for the model of the loading device described above, and the one-dimensional wave propagation analysis based on the characteristic curve method is performed for the stress propagation of the pile model,
Pile loading test analysis method. In the analysis method of the pile loading test to obtain the relationship between the static load and displacement of the pile using the measurement data when loaded on the pile by the loading device,
A loading device consisting of a hammer, two spring members arranged in parallel on the lower surface of the hammer, and a damping device arranged at the lower part of one of the spring materials is modeled with the hammer as a rigid mass point,
Model the pile as a rigid mass point,
Model the ground with ground springs and dashpots that connect to the rigid pile model,
It is characterized by performing a differential approximation on the equation of motion of a two-mass system and performing analysis.
Pile loading test analysis method.

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