JP2004245691A - Seismic response analysis method - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a seismic response analysis method capable of providing a simple and accurate seismic response of a ground-pile-building compound system in consideration of a difference in excess clearance hydraulic pressure between a free ground and an inter-pile ground. <P>SOLUTION: The shearing force K<SB>p</SB>(Γ<SB>p</SB>) of the ground spring of the inter-pile ground is obtained by using the inter-layer displacement Γp of a pile, the shearing stress τ<SB>p</SB>of the inter-pile ground is obtained by using the shearing force K<SB>p</SB>(Γ<SB>p</SB>), a cumulative degree of damage D<SB>p</SB>of the inter-pile ground is obtained by using the shearing stress τ<SB>p</SB>, and an excess clearance hydraulic pressure rate R<SB>u_p</SB>is obtained by using the cumulative degree of damage D<SB>p</SB>. The effective stress σ<SB>m_p</SB>of the inter-pile ground is obtained by using the excess clearance hydraulic pressure rate R<SB>u_p</SB>, the initial rigidity K<SB>pfo</SB>of the inter-pile ground spring is obtained by using the effective stress σ<SB>m_p</SB>, and an interacting force K<SB>pf</SB>(Γ<SB>pf</SB>) between the inter-pile ground and the free ground is obtained (steps S20 to S27). <P>COPYRIGHT: (C)2004,JPO&NCIPI

Description

【００３０】
なお、図４に示すように杭間地盤２８のｉ層の節点２６の変位をｕ_ｐ＿ｉ、自由地盤３１のｉ層の節点３２の変位をｕ_ｆ＿ｉとした場合、その相対変位δは次式で表される。
【００３１】
δ＝ｕ_ｐ＿ｉ―ｕ_ｆ＿ｉ …（２）
また、杭間地盤２８の層間変位Γ_ｐは次式で表される。
【００３２】
Γ_ｐ＝ｕ_ｐ＿ｉ―ｕ_{ｐ＿ｉ−１} …（３）
また、自由地盤３１の層間変位Γ_ｆは次式で表される。
【００３３】
Γ_ｆ＝ｕ_ｆ＿ｉ―ｕ_{ｆ＿ｉ−１} …（４）
また、杭間地盤２８の層間変位と自由地盤３１の層間変位の相対変位Γ_ｐｆは次式で表される。
【００３４】
Γ_ｐｆ＝（ｕ_ｐ＿ｉ―ｕ_ｆ＿ｉ）−（ｕ_{ｐ＿ｉ−１}―ｕ_{ｆ＿ｉ−１}）＝Γ_ｐ−Γ_ｆ …（５）
次に、第１実施形態の作用として、演算部１６で実行される制御ルーチンについて図５、６に示すフローチャートを参照して説明する。
【００３５】
まず、図５に示すステップＳ１では、オペレータが表示部１８に表示されたメニューに従って操作部１２を操作し、地震応答解析を行うべき解析モデルのパラメータを指定すると、演算部１６では、指定された解析モデルに関するデータを記憶部１４から読み込む。
【００３６】
この解析モデルに関するデータには、例えば解析対象の建物、杭基礎、杭・自由地盤間の地層、自由地盤の地層（例えば上から何番目の地層かを表すデータ）、材料定数、時間積分定数がある。
【００３７】
次のステップＳ２では、以下の地震応答を求める演算において用いる各種データの初期値の設定を行う。このデータには、例えば加速度、速度、変位、せん断応力、せん断ひずみ、上記（１）式における質量行列Ｍ、剛性行列Ｋ、減衰行列Ｃなどがある。演算部１６では、これらのデータに初期値を設定する。
【００３８】
次に、ステップＳ３において、ｔ＋Δｔ時刻の各節点の応答変位、応答速度、応答加速度の予測値ｕ^＊を下記（６）式により算出する。なお、Δｔは計算時間間隔、すなわち時刻歴ループの実行間隔であり、一定の値でもよいし、計算毎に変化させてもよい。
【００３９】
ｕ^＊＝Ａｕ（ｔ）＋ＢΛ …（６）
ここで、Ａは予測オペレーター行列、Ｂは修正オペレーター行列、Λは未知数である修正値ベクトルである。
【００４０】
そして、各節点の変位の予測値から上記（２）〜（５）式により層間変位や相対変位を算出する。これらの値は記憶部１４に記憶される。
【００４１】
次に、ステップＳ４において、外力Ｆ（ｔ＋Δｔ）、粘性力Ｆ_Ｃ、慣性力Ｆ_Ｍの算出を行う。外力は上記（１）式の右辺の算出を（ｔ＋Δｔ）時刻について行うことにより得られる。粘性力Ｆ_Ｃは例えば下記（７）式により、慣性力Ｆ_Ｍは下記（８）式により算出することができる。
【００４２】
【数２】

【００４３】
そして、次のステップＳ５において、ステップＳ３で算出した予測値ｕ^＊から建屋２０、杭２４、杭間地盤２８、杭・自由地盤間の地盤（水平地盤３５）、及び自由地盤３１等に関する内力Ｒを算出する。
【００４４】
このうち、図６には、杭間地盤２８と自由地盤３１の相互作用力を内力として算出する処理ルーチンを示した。図６に示す処理ルーチンでは、杭間地盤２８の累積損傷度Ｄ、過剰間隙水圧比ｒ_ｕ等から、杭間地盤２８と自由地盤３１との力−変位骨格・履歴曲線（関数）Ｋ_ｐｆ（Γ_ｐｆ）を求め、この骨格・履歴曲線により杭間地盤２８と自由地盤３１とに関する地盤ばねの相互作用力（内力Ｒ_ｐｆ）を算出する。
【００４５】
なお、建物や杭に関する内力Ｒについては、質点モデルにおける公知の種々の方法により求めることができる。
【００４６】
具体的には、図６に示すように、まずステップＳ２０において、ｔ＋Δｔ時刻の杭２４の層間変位、すなわち質点２６間の変位Γ_Ｐを記憶部１４から読み込む。
【００４７】
次のステップＳ２１では、変位Γ_ｐに対応するせん断地盤ばねの作用力をＫ_ｐ（Γ_ｐ）より算出する。
【００４８】
次のステップＳ２２では、杭間地盤２８のせん断応力τ_Ｐを次式により算出する。
【００４９】
τ_Ｐ＝Ｋ_Ｐ（Γ_Ｐ）／Ａｓ …（９）
ここで、Ａｓは図７に示すように杭間地盤２８の等価土柱面積、すなわち有効せん断面積である。
【００５０】
また、杭間地盤の力−変位骨格・履歴曲線Ｋ_ｐ（Γ_ｐ）は次式で算出することができる。
【００５１】
【数３】

【００５２】
ここで、Ｋ_ｐ０は、初期平均応力σ_ｍ０の時のせん断ばね剛性、Ｆσ（σ_ｍ／σ_ｍ０）は有効拘束圧に依存する微少ひずみ時の剛性の低減係数（剛性低下率）で経験式（関数）として得られ、下記（１１）式で表される。ｇ（Γ_ｐ、Γ_ｐ５０）は微少ひずみ時の剛性で基準化されたせん断応力−せん断ひずみ曲線で主にせん断ひずみに依存する経験式である。Γ_ｐ５０はせん断ばね剛性が半分になるせん断ひずみの値であり、下記（１２）式で表される。現在の有効応力σ_ｍは、応力評価点の初期平均応力σ_ｍ０に（１−過剰間隙水圧比＝１−ｒ_ｕ＿ｐ）を掛けた値である。
【００５３】
【数４】

【００５４】
また、Γ_ｐ５０は、過剰間隙水圧比との関係から次式を用いて求めることが出来る。
【００５５】
【数５】

【００５６】
ここで、（Γ_ｐ５０）_ｒｅｆはσ_ｒｅｆでのΓ_ｐ５０である．
なお、力−変位骨格・履歴曲線は、一般に図１０に示すような形をしている。中心にある曲線を骨格曲線、それを囲んでいる曲線を履歴曲線という。そして、ゼロ点からプラスまたはマイナス側に大きくなるときには、骨格曲線を用い、変位が折り返してゼロに向かいはじめたら履歴曲線を用いる。骨格曲線が決まれば、履歴曲線は自動的に決定される。たとえば骨格曲線をｇ_ｐ（Γ_ｐ）とした場合、履歴曲線は例えばｇ_ｐ（（Γ−Γ_Ｒ）／２）のように定義することができる。ここで、Γ_Ｒは折り返し点の杭間変位である。一般に骨格曲線としては、Ｈａｒｄｉｎ−ＤｒｎｅｖｉｃｈモデルやＲａｍｂｅｒｇ−Ｏｓｇｏｏｄモデル等を用いることができる。本実施形態では、骨格曲線及び履歴曲線を合わせて力−変位骨格・履歴曲線とし、Ｋ_ｐ（Γ_ｐ）やＫ_ｐｆ（Γ_ｐｆ）で表す。ここで、Ｋ_ｐ（Γ_ｐ）は杭間地盤の地盤ばね、Ｋ_ｐｆ（Γ_ｐｆ）は杭間地盤と自由地盤の相互地盤ばねである。
【００５７】
ステップＳ２３では、せん断応力τ_ｐから杭間地盤２８の累積損傷度Ｄ_Ｐを算出し、ステップ２４では、過剰間隙水圧比ｒ_ｕ＿Ｐを求める。
【００５８】
累積損傷度Ｄ_Ｐ及び過剰間隙水圧比ｒ_ｕ＿Ｐは、図８に示すような▲１▼〜▲４▼の関係を用いて求める。
【００５９】
図８に示す▲１▼は、時々刻々と変化する杭間地盤のせん断応力τ_ｐを示している。
【００６０】
図８に示す▲２▼は、液状化強度曲線を示している。なお、▲２▼の横軸は液状化するときの繰り返し回数Ｎ、縦軸は応力比τ_ｐ／σ_ｍ０である。この液状化強度曲線は、地盤調査における動的非排水変形試験により得られたものを用いることができる。ここで、σ_ｍ０は応力評価点の初期平均応力である。
【００６１】
図８の▲１▼、▲２▼に示すように、せん断応力τ_ｐから応力比τ_ｐ／σ_ｍ０を求め、この応力比τ_ｐ／σ_ｍ０から繰り返し回数Ｎを求めることができる。さらに、求めた繰り返し回数Ｎから、累積損傷度の増分ΔＤを求めることができる。累積損傷度の増分ΔＤは、次式で示される。
【００６２】
ΔＤ＝１／２Ｎ …（１３）
また、図８の▲３▼に示すように、累積損傷度の増分ΔＤから累積損傷度Ｄ_ｐを求めることができる。
【００６３】
図８に示す▲４▼は、累積損傷度Ｄと過剰間隙水圧比Ｒ_ｕとの関係を示しており、累積損傷度Ｄ_ｐから過剰間隙水圧比Ｒ_ｕ＿Ｐを求めることができる。この累積損傷度Ｄ_ｐと過剰間隙水圧比Ｒ_ｕ＿Ｐとの関係は、実験により得ることができるが、公知の次式を用いて算出してもよく、Ｒ_ｕ＿Ｐ＝Ｄ_ｐとしてもよい。
【００６４】
【数６】

【００６５】
なお、せん断応力から累積損傷度を求め、この累積損傷度から過剰間隙水圧比を求める方法は、上記の方法に限らず、特願２００３−３５３９０号に記載された方法や特開２００１−２０８６４１号公報に記載された方法、及び他の公知の方法を用いることができる。
【００６６】
次のステップＳ２５では、杭間地盤２８の有効応力σ_ｍ＿Ｐを次式により算出する。
【００６７】
σ_ｍ＿Ｐ＝（１−Ｒ_ｕ＿Ｐ）σ_ｍ０ …（１５）
ここで、σ_ｍ０は応力評価点の初期平均応力である。
【００６８】
ステップＳ２６では、杭間地盤２８の地盤ばねの初期せん断ばね剛性Ｋ_ｐｆ０を次式により更新する。
【００６９】
Ｋ_ｐｆ０＝Ｋ^’ _ｐｆ０×（σ_ｍ＿Ｐ／σ_ｍ０）^ｎ …（１６）
ここで、Ｋ^’ _ｐｆ０は前回のステップで算出した初期せん断ばね剛性Ｋ_ｐｆ０である。
【００７０】
このように、初期せん断ばね剛性Ｋ_ｐｆ０を更新することにより、図９に示すような力−変位骨格・履歴曲線Ｋ_ｐｆ（Γ_ｐｆ）が得られる。
【００７１】
ステップＳ２７では、杭間地盤２８の層間変位と自由地盤３１の層間変位の相対変位Γ_ｐｆを記憶部１４から読み出し、この相対変位Γ_ｐｆに対応する、杭間地盤２８と自由地盤３１に関する相互作用力、すなわち内力Ｒ_ｐｆを力−変位骨格・履歴曲線Ｋ_ｐｆ（Γ_ｐｆ）により算出する。
【００７２】
ここで、Ｋ_ｐｆ（Γ_ｐｆ）は上記（１０）〜（１２）式と同様に求めることができ、各式において‘ｐ’を‘ｐｆ’に置き換えることにより求めることができる。
【００７３】
このように、本実施形態では、杭間地盤の骨格・履歴曲線と自由地盤の骨格・履歴曲線は本来異なるものであるため、杭間地盤２８の層間変位と自由地盤３１の層間変位の相対変位Γ_ｐｆから杭間地盤２８と自由地盤３１に関する相互作用力をＫ_ｐｆ（Γ_ｐｆ）より算出する。
【００７４】
次に、図５のステップＳ６において、外部から作用する外力Ｆ、粘性力Ｆ_Ｃ、慣性力Ｆ_Ｍ、内力Ｒの不釣り合い力（残差力）ΔＲを求める。不釣り合い力ΔＲは次式により求めることができる。
【００７５】
ΔＲ＝Ｆ−Ｆ_Ｍ−Ｆ_Ｃ−Ｒ …（１７）
次に、ステップＳ７において、建物、杭、杭間地盤ばね、自由地盤のそれぞれの接線剛性から修正値を計算するための全体修正剛性行列（動的解析用全体行列）Ｋ^＊を算出する。動的解析用全体行列Ｋ^＊は次式で示される。
【００７６】
Ｋ^＊＝Ｍ＋γΔｔＣ＋βΔｔ^２Ｋ …（１８）
ここで、β、γは、Ｎｅｗｍａｒｋ−β法における係数（一定）である。また、Ｋは接線剛性である。
【００７７】
次に、ステップＳ８において、不釣り合い力ΔＲより（ｔ＋Δｔ）時刻の修正値Λを下記（２０）式により算出する。
【００７８】
Λ＝Ｋ^＊−１ΔＲ …（１９）
次に、ステップＳ９において，この修正値Λにより予測値ｕ^＊を修正し、（ｔ＋Δｔ）時刻の応答変位、応答速度、応答加速度を求める。
【００７９】
次に、ステップＳ１０において、修正された応答変位、応答速度、応答加速度のもとでステップＳ４と同様に外力Ｆ（ｔ＋Δｔ）、粘性力Ｆ_Ｃ、慣性力Ｆ_Ｍの算出を行う。
【００８０】
次に、ステップＳ１１において、ステップＳ５と同様に、建物、杭、杭間地盤、杭・自由地盤間の地盤、及び自由地盤の内力Ｒを算出する
次に、ステップＳ１２において、ステップＳ６と同様に、外部から作用する外力Ｆ、粘性力Ｆ_Ｃ、慣性力Ｆ_Ｍ、内力Ｒの不釣り合い力ΔＲを求める。
【００８１】
次に、ステップＳ１３において、この不釣り合い力ΔＲが収束したか否か、すなわち許容値以下であるか否かを判断する。そして、不釣り合い力ΔＲが許容値を越えている場合には、ステップＳ７へ戻って上記と同様の計算を行う。一方、不釣り合い力ΔＲが許容値以下であれば、次のステップＳ１４へ移行する。
【００８２】
ステップＳ１４では、変位、速度、加速度を更新する。すなわち、不釣り合い力ΔＲが収束したときの変位、速度、加速度をその時点の変位、速度、加速度とする。
【００８３】
このようにして、地震時間全体についてステップＳ３〜Ｓ１４までの処理（時刻歴ループ）を行い、各時刻毎の各応答値を算出する。
【００８４】
そして、時刻歴ループが終了すると、ステップＳ１５において、時刻歴ループにおいて算出した各応答値や各応答値の最大値などを表示部１８や記憶部１４に出力する。
【００８５】
このように、本実施形態では、杭間地盤の過剰間隙水圧から杭間地盤のせん断ばねを評価し、これに基づいて杭間地盤と自由地盤との相互作用力を求めるので、従来のように自由地盤の過剰間隙水圧を用いて杭間地盤の液状化を考慮していた地震応答計算法よりもより精度の高い評価が可能となる。
【００８６】
（第２実施形態）
次に、本発明の第２実施形態について説明する。なお、第１実施形態と同一部分には同一符号を付し、その詳細な説明は省略する。
【００８７】
第１実施形態では、図６のステップＳ２７において杭間地盤の層間変位及び自由地盤の層間変位の相対変位Γ_ｐｆから杭間地盤と自由地盤との相互作用力を骨格・履歴曲線ｋ_ｐｆ（Γ_ｐｆ）より求めていたが、第２実施形態では、杭間地盤の層間変位Γ_ｐからその作用力を図６と同様の処理によりＫ_ｐ（Γ_ｐ）より算出すると共に、自由地盤の層間変位Γ_ｆからその作用力をＫ_ｆ（Γ_ｆ）より算出する。
【００８８】
そして、杭間地盤と自由地盤との相互作用力、すなわち内力Ｒ_ｐｆを次式により求める。
【００８９】
Ｒ_ｐｆ＝Ｋ_ｐ（Γ_ｐ）−Ｋ_ｆ（Γ_ｆ） …（２０）
すなわち、図１１に示すように、杭間地盤の作用力と自由地盤の作用力とをそれぞれの層間変位から独立に求め、それぞれの作用力の差を相互作用力とするので、杭間地盤及び自由地盤の時々刻々の非線形材料特性を忠実に評価することができる。
【００９０】
【実施例】
次に、本発明の実施例について図面を参照して説明する。
【００９１】
図１２には、本発明を適用した液状化模型振動試験に用いた模型４０の概略構成を示した。図１２（Ａ）は模型４０の断面図を、図１２（Ｂ）には平面図を示した。
【００９２】
この液状化模型振動試験は、図１２に示すようにせん断箱４２に液状化層４４及び及び非液状化層４６の２つの材料特性の異なる砂層からなる地層と複数（５×５＝２５本）の杭４８を基礎に持つ建屋５０の模型を設置し、このせん断箱４２を振動台５２で水平方向に加振することにより液状化について測定する試験である。なお、入力地震動には実記録の地震動を用いた。
【００９３】
図１２（Ａ）に示すように、模型４０の挙動を計測するために地中には加速度計５４、間隙水圧計５６を、杭４８にはひずみゲージ５８を配置した。
【００９４】
これを本発明で提案した質点−ばねモデルでモデル化を行い、試験を行った。モデル化に用いた地盤の材料諸元は、２層の地層に対して以下の表１に示す値を用いた。
【００９５】
【表１】

【００９６】
図１３には、これらの地層のせん断ひずみに対する剛性低下率Ｇ／Ｇ_０及び減衰定数ｈの増加率の関係を示した。なお、設定値とは、測定値を式で近似したものである。また、図１４には、液状化強度曲線、すなわち繰り返し回数Ｎに対するせん断応力比の関係を示した。
【００９７】
図１５には過剰間隙水圧の最大値の深度分布について、観測記録、既存解析法によるシミュレーション結果（既往例）、本発明の解析法によるシミュレーション結果をそれぞれ示した。なお、既存解析法は、液状化の上昇を自由地盤の挙動から算出しており、本解析法では、杭間地盤から算出している。
【００９８】
図１５に示すように、観測値の過剰間隙水圧比は地表面付近まで１．０近くまで上昇しており、本発明の解析方法による解析結果は既存解析法の解析結果よりも、観測値により近い値となっている。これは本解析方法が、本実験で観測された「自由地盤よりも杭間地盤の方が液状化がやや進んだ」結果を再現しており、理論的に忠実に現象を再現していることを確認することができた。
【００９９】
また、図１６には、過剰間隙水圧の上昇過程を実験の観測記録とともに示した。図１６から明らかなように、本解析法による解析結果は観測記録とよく対応していることを確認することができた。
【０１００】
【発明の効果】
以上説明したように、本発明によれば、自由地盤と杭間地盤との過剰間隙水圧の違いを考慮した簡便且つ精度のよい地盤−杭−建屋連成系の地震応答を得ることができる、いう効果を有する。
【図面の簡単な説明】
【図１】地震応答解析装置の概略ブロック図である。
【図２】解析対象のモデル図である。
【図３】杭及び杭間地盤の変形について説明するための図である。
【図４】杭間地盤及び自由地盤の変形について説明するための図である。
【図５】演算部で実行されるメインルーチンのフローチャートである。
【図６】演算部で実行される内力算出ルーチンのフローチャートである。
【図７】杭間地盤の作用力等について説明するための図である。
【図８】過剰間隙水圧比の算出について説明するための図である。
【図９】力−変位骨格・履歴曲線について説明するための図である。
【図１０】力−変位骨格・履歴曲線を示す図である。
【図１１】杭間地盤と自由地盤との相互作用力について説明するための図である。
【図１２】実施例に係る試験装置の概略構成図である。
【図１３】実施例に係るせん断ひずみと剛性低下率との関係を示すグラフである。
【図１４】実施例に係る繰り返し回数とせん断応力比との関係を示すグラフである。
【図１５】実施例に係る過剰間隙水圧比の最大値の深度分布を示す図である。
【図１６】実施例に係る過剰間隙水圧比の上昇過程を示す線図である。
【符号の説明】
１０ 地震応答解析装置
１２ 操作部
１４ 記憶部
１６ 演算部
１８ 表示部[0001]
TECHNICAL FIELD OF THE INVENTION
The present invention relates to a method for analyzing seismic response, and more particularly to a method for analyzing seismic response of a coupled soil-pile-building system in consideration of liquefaction of the ground.
[0002]
[Prior art]
Conventionally, as a ground-pile-building coupled system analysis method, a ground, a pile supporting a building, and a building are modeled using a finite element method or the like, and a method of evaluating each response, for example, a Penzien type model There is a method in which the ground is replaced by an equivalent ground spring using a mass point model such as the above, and the response of the pile and the building is evaluated (for example, see Non-Patent Document 1).
[0003]
However, in the former method using the finite element method or the like, it is difficult to directly obtain a coefficient for determining a method for determining a decrease in ground stiffness (referred to as a stress-strain relationship or a constitutive equation) from the ground constant, and modeling is difficult. In addition, there is a problem that it takes a long time to calculate. At present, the correct natural law for earthquakes is not known.However, although many simulation methods have been proposed, evaluation methods have not been standardized for random phenomena such as earthquakes. There has been a problem that the analysis results are significantly different.
[0004]
In the latter method using the mass model, the excess pore water pressure generated on the ground surrounded by piles supporting the building (hereinafter referred to as the “pile between piles”) is used to replace the ground with an equivalent ground spring. Cannot be evaluated. For this reason, the excess pore water pressure generated in the ground having no structure in the vicinity (hereinafter referred to as “free ground”) must be separately obtained by analysis and used as the excess pore water pressure in the pile ground. Actually, since the deformation state of the free ground and the ground between the piles are different, the excess pore water pressure generated in the ground during an earthquake, that is, the degree of liquefaction is also different. Therefore, in the latter method using the mass point model, there is a problem that the analysis result may be far different from the actual result.
[0005]
[Non-patent document 1]
Yuji Miyamoto, Yuji Sakai, Eiji Kitamura, Kenji Miura, "Study on Seismic Response Characteristics of Pile Foundation in Nonlinear, Liquefied Ground", Journal of Structural Engineering, Architectural Institute of Japan, May 1995, No. 471, p. 41-50
[0006]
[Problems to be solved by the invention]
The present invention has been made in order to solve the above problems, and provides a simple and accurate ground-pile-building coupled seismic response in consideration of the difference in excess pore water pressure between free ground and pile ground. An object of the present invention is to provide a seismic response analysis method that can be obtained.
[0007]
[Means for Solving the Problems]
In order to solve the above-mentioned problem, the invention according to claim 1 is characterized in that a structure including a building and a pile, and a ground between piles around the pile and a ground including free ground separated from the structure by a predetermined distance or more are used. Mass information of the analysis target model modeled by the model, stiffness information, damping information, and obtain the displacement information of the analysis target model that changes every moment using the equation of motion based on the input earthquake information, based on the displacement information, In the seismic response analysis method of obtaining a time characteristic of a response value related to at least a strain that changes from moment to moment, an interlayer displacement of the ground between piles and an interlayer displacement of the free ground are calculated based on the displacement information, and the ground displacement of the ground between piles is calculated. From the interlayer displacement and the interlayer displacement of the free ground, the relative displacement between the interlayer displacement of the ground between the piles and the interlayer displacement of the free ground is calculated, and the interlayer displacement of the ground between the piles and Calculating the shear stress of the ground between the piles based on the force-displacement skeleton / history curve of the ground between the piles, calculating the cumulative damage degree of the ground between the piles based on the shear stress of the ground between the piles, Calculate the excess pore water pressure ratio of the ground between the piles based on the cumulative damage degree of the ground between the piles, calculate the effective stress of the ground between the piles based on the excess pore water pressure ratio of the ground between the piles, and calculate the effective stress of the ground between the piles. The initial shear spring stiffness of the ground between piles is calculated based on the effective stress, and the force-displacement skeleton / history curve relating to the interaction force between the ground between the piles and the free ground is updated using the initial shear spring rigidity. Then, the process of calculating the interaction force based on the updated force-displacement skeleton / history curve and the relative displacement is repeated every predetermined time.
[0008]
The present invention is directed to an analysis target model obtained by modeling a structure including a building and a pile, and a ground between piles around the pile and a ground including a free ground at a predetermined distance or more from the structure using a mass point model. is there. Then, mass information, stiffness information, damping information, and using the equation of motion based on the input earthquake information to determine the displacement information of the analysis target model that changes from moment to moment, based on this displacement information, at least regarding the strain that changes from moment to moment. Find the time characteristic of the response value.
[0009]
In the present invention, first, the interlayer displacement of the ground between piles and the interlayer displacement of the free ground are calculated based on the displacement information. Next, the relative displacement of the interlayer displacement of the pile-to-pile ground and the interlayer displacement of the free ground is calculated from the interlayer displacement of the pile-to-pile ground and the interlayer displacement of the free ground.・ Calculate the shear stress of the ground between piles based on the hysteresis curve.
[0010]
Then, the cumulative damage degree of the ground between the piles is calculated based on the shear stress of the ground between the piles. For example, the cumulative damage can be determined from the shear stress, the stress ratio is determined, the number of repetitions corresponding to the stress ratio is determined, the increment of the cumulative damage corresponding to the number of repetitions is determined, and the increment of the cumulative damage can be determined. .
[0011]
Then, the excess pore water pressure ratio of the pile-to-pile ground is calculated based on the accumulated damage degree of the pile-to-pile ground, and the effective stress of the pile-to-pile ground is calculated based on the excess pore-water pressure ratio of the pile-to-pile ground. The initial shear spring stiffness of the ground between piles is calculated based on the stress, and the force-displacement skeleton / history curve relating to the interaction force between the ground between the piles and the free ground is updated using the initial shear spring stiffness. The interaction force is calculated based on the force-displacement skeleton / history curve and the relative displacement.
[0012]
The time history of the earthquake response can be obtained by repeating such processing every predetermined time.
[0013]
As described above, in the present invention, the effective stress of the ground between piles is evaluated from the excess pore water pressure of the ground between piles, and the interaction force between the ground between the piles and the free ground is determined based on this. It is possible to evaluate with higher accuracy than when considering the liquefaction of the ground between piles using excess pore water pressure of free ground.
[0014]
In addition, as described in claim 2, a structure including a building and a pile, and a ground between piles around the pile and a ground including free ground separated from the structure by a predetermined distance or more are modeled by a mass point model. Mass information, rigidity information, damping information, and the displacement information of the analysis target model, which changes every moment using the equation of motion based on the input earthquake information, are calculated based on the displacement information. In the seismic response analysis method for obtaining a time characteristic of a response value related to at least a strain, the interlayer displacement of the ground between the piles and the interlayer displacement of the free ground are calculated based on the displacement information, and the interlayer displacement of the ground between the piles and the Based on the force-displacement skeleton / history curve of the ground between piles, the shear stress of the ground between piles is calculated, and the interlayer displacement of the free ground and the force-change of the free ground are calculated. The shear stress of the free ground is calculated based on a skeleton / history curve, and the cumulative damage degree of the ground between the piles is calculated based on the shear stress of the ground between the piles, and based on the shear stress of the free ground. Calculate the cumulative damage degree of the free ground, calculate the excess pore water pressure ratio of the ground between the piles based on the cumulative damage degree of the ground between the piles, and calculate the excess pore pressure ratio of the free ground based on the cumulative damage degree of the free ground. Calculate the pore water pressure ratio, calculate the effective stress of the ground between the piles based on the excess pore water pressure ratio of the ground between the piles, and calculate the effective stress of the free ground based on the excess pore water pressure ratio of the free ground. Calculating the initial shear spring rigidity of the ground between the piles based on the effective stress of the ground between the piles, and calculating the initial shear spring rigidity of the free ground based on the effective stress of the free ground, Using the initial shear spring stiffness of the ground, the force-displacement skeleton / history curve relating to the acting force of the ground between the piles is updated, and based on the updated force-displacement skeleton / history curve and the interlayer displacement of the ground between the piles. While calculating the acting force of the ground between the piles, the force-displacement skeleton / history curve relating to the acting force of the free ground is updated using the initial shear spring stiffness of the free ground, and the updated force-displacement skeleton Calculate the acting force of the free ground based on a hysteresis curve and the interlayer displacement of the free ground, and calculate the acting force of the inter-pile ground and the free ground based on the acting force of the inter-pile ground and the acting force of the free ground. The process of calculating the interaction force may be repeated every predetermined time.
[0015]
That is, the acting force of the ground between the piles and the acting force of the free ground are obtained independently from the respective interlayer displacements, and the difference between the acting forces is defined as the interaction force. As a result, the non-linear material properties of the pile-to-pile ground and the free ground can be faithfully evaluated every moment.
[0016]
BEST MODE FOR CARRYING OUT THE INVENTION
(1st Embodiment)
Hereinafter, a first embodiment of the present invention will be described with reference to the drawings.
[0017]
FIG. 1 shows an earthquake response analysis device 10. The earthquake response analysis device 10 includes an operation unit 12, a storage unit 14, a calculation unit 16, and a display unit 18.
[0018]
The operation unit 12 is used by an operator to specify an instruction for causing the arithmetic unit 16 to execute an earthquake response analysis on a desired analysis model in accordance with a menu displayed on the display unit 18 and to specify necessary parameters. The storage unit 14 stores various analysis model parameters and various arithmetic expressions necessary for earthquake response analysis in the arithmetic unit 16. The storage unit 14 stores the analysis result of the earthquake response analysis performed by the calculation unit 16.
[0019]
The arithmetic unit 16 reads necessary data from the storage unit 14 in accordance with an instruction from the operation unit 12, performs an earthquake response analysis, stores the output result in the storage unit 14, and outputs the output result to the display unit 18.
[0020]
The calculation unit 16 performs an earthquake response analysis on the building, the pile, and the ground to be analyzed in consideration of the liquefaction of the ground between the piles.
[0021]
The seismic response analysis is generally performed as follows. That is, for the portion related to the ground, the cumulative damage degree is obtained from the time history of the shear stress, the excess pore water pressure is obtained from the cumulative damage degree, and the shear rigidity reduction rate due to liquefaction is obtained from the effective stress obtained thereby. Further, using the stress-strain relationship (non-linear stiffness) obtained in consideration of the shear stiffness reduction rate, a time history response for finding a shear stress depending on the shear strain every moment, that is, an earthquake response analysis is performed. For buildings and piles, response analysis using a conventional elastic or plastic model is performed.
[0022]
As a model for the seismic response analysis of the ground, piles, and building (building), a mass point model as shown in FIG. 2 is used. In this model, the ground, piles, and building are each represented by a spring (shear spring, horizontal ground spring, etc.) connecting the mass points. In addition, the ground is divided into a free ground located far from the building and a ground between piles located immediately below the building.
[0023]
As shown in FIG. 2, the building 20 is represented by a mass point 22. As shown in FIG. 3, the plurality of piles 24 supporting the building 20 are integrated into one pile 24A on the assumption that they are integrally deformed. The pile 24A in which the plurality of piles 24 are aggregated is represented by a plurality of mass points 26 as shown in FIG.
[0024]
The ground 28 between the piles existing between the piles 24 shown in FIG. 3 is represented by a ground spring 30 connecting the mass points 26 as shown in FIG. As described above, since it is assumed that the plurality of piles 24 are integrally deformed, as shown in FIG. 3, the deformation (shear strain) γ of the piles 24 is performed._pIs the deformation of the ground between piles γ_sIs the same as
[0025]
The free ground 31 is represented by mass points 32 and a ground spring 34 connecting the mass points 32. The pile 24 and the free ground 31 transmit force via the horizontal ground spring 36 and the ground spring 30 of the horizontal ground 35 between the pile 24 and the free ground 31.
[0026]
The seismic response analysis includes a method of integrally analyzing these models, and a method of first performing analysis of free ground and acting as an external force on seismic response analysis of ground-pile-pile-building between piles.
[0027]
In the present invention, when calculating the acting force and rigidity of the horizontal ground spring and the ground between piles in consideration of liquefaction, conventionally, only the liquefaction of the free ground is considered in the pile ground, the horizontal ground, and the free ground. On the other hand, considering the liquefaction of the pile-pile ground for the pile-pile ground and the liquefaction of the free ground for the horizontal ground and the free ground, it has made it possible to perform simple and accurate seismic response analysis. It is.
[0028]
The response value at the time of the earthquake can be obtained by solving the equation of motion for the ground between piles, the horizontal ground, and the free ground by the following equation using time integration. In the present embodiment, a generally well-known time integration method for a dynamic nonlinear problem can be used for time integration. In the present embodiment, as an example, the incremental method based on the Newmark-β method is used.
[0029]
(Equation 1)

[0030]
In addition, as shown in FIG. 4, the displacement of the node 26 of the i-layer_{p_i}, The displacement of the node 32 of the i layer of the free ground 31 is u_{f_i}, The relative displacement δ is expressed by the following equation.
[0031]
δ = u_{p_i}-U_{f_i}    … (2)
In addition, the interlayer displacement of the ground 28 between the piles Γ_pIs represented by the following equation.
[0032]
Γ_p= U_{p_i}-U_{p_i-1}        … (3)
In addition, the interlayer displacement of the free ground 31 Γ_fIs represented by the following equation.
[0033]
Γ_f= U_{f_i}-U_{f_i-1}        … (4)
In addition, the relative displacement Γ between the interlayer displacement of the pile-to-pile ground 28 and the interlayer displacement of the free ground 31._pfIs represented by the following equation.
[0034]
Γ_pf= (U_{p_i}-U_{f_i})-(U_{p_i-1}-U_{f_i-1}) = Γ_p−Γ_f    … (5)
Next, as an operation of the first embodiment, a control routine executed by the arithmetic unit 16 will be described with reference to flowcharts shown in FIGS.
[0035]
First, in step S1 shown in FIG. 5, the operator operates the operation unit 12 according to the menu displayed on the display unit 18 to specify parameters of an analysis model to be subjected to an earthquake response analysis. Data relating to the analysis model is read from the storage unit 14.
[0036]
The data related to this analysis model includes, for example, a building to be analyzed, a pile foundation, a stratum between piles and free ground, a stratum of free ground (for example, data indicating a stratum from the top), a material constant, and a time integration constant. is there.
[0037]
In the next step S2, initial values of various data used in the following calculation for obtaining an earthquake response are set. The data includes, for example, acceleration, velocity, displacement, shear stress, shear strain, mass matrix M, stiffness matrix K, and damping matrix C in the above equation (1). The calculation unit 16 sets initial values for these data.
[0038]
Next, in step S3, the predicted value u of the response displacement, response speed, and response acceleration of each node at time t + Δt^*Is calculated by the following equation (6). Note that Δt is a calculation time interval, that is, an execution interval of a time history loop, and may be a constant value or may be changed for each calculation.
[0039]
u^*= Au (t) + BΛ (6)
Here, A is a prediction operator matrix, B is a correction operator matrix, and Λ is a correction value vector that is an unknown number.
[0040]
Then, from the predicted value of the displacement of each node, the interlayer displacement and the relative displacement are calculated by the above equations (2) to (5). These values are stored in the storage unit 14.
[0041]
Next, in step S4, the external force F (t + Δt), the viscous force F_C, Inertial force F_MIs calculated. The external force is obtained by calculating the right side of the above equation (1) for the time (t + Δt). Viscous force F_CIs, for example, by the following equation (7),_MCan be calculated by the following equation (8).
[0042]
(Equation 2)

[0043]
Then, in the next step S5, the predicted value u calculated in step S3^*Then, the internal force R relating to the building 20, the pile 24, the ground 28 between the piles, the ground between the pile and the free ground (horizontal ground 35), the free ground 31, and the like is calculated.
[0044]
FIG. 6 shows a processing routine for calculating the interaction force between the ground 28 between the piles and the free ground 31 as an internal force. In the processing routine shown in FIG. 6, the accumulated damage degree D of the pile-to-pile ground 28 and the excess pore water pressure ratio r_uFrom the above, the force-displacement skeleton / history curve (function) K between the pile ground 28 and the free ground 31_pf(Γ_pf), And the interaction force (internal force R) of the ground spring on the ground 28 between the piles and the free ground 31_pf) Is calculated.
[0045]
In addition, the internal force R regarding a building or a pile can be obtained by various known methods in a mass point model.
[0046]
Specifically, as shown in FIG. 6, first, in step S20, the interlayer displacement of the pile 24 at the time t + Δt, that is, the displacement 質 between the mass points 26,_PIs read from the storage unit 14.
[0047]
In the next step S21, the displacement Γ_pThe acting force of the shear ground spring corresponding to_p(Γ_p).
[0048]
In the next step S22, the shear stress τ_PIs calculated by the following equation.
[0049]
τ_P= K_P(Γ_P) / As… (9)
Here, As is an equivalent earth column area of the ground 28 between piles, that is, an effective shear area as shown in FIG.
[0050]
In addition, the force-displacement skeleton / history curve K of the ground between piles_p(Γ_p) Can be calculated by the following equation.
[0051]
(Equation 3)

[0052]
Where K_p0Is the initial average stress σ_m0, The shear spring stiffness at the time of Fσ (σ_m/ Σ_m0) Is a stiffness reduction coefficient (stiffness reduction rate) at the time of micro-strain depending on the effective constraint pressure, which is obtained as an empirical formula (function) and is expressed by the following formula (11). g (Γ_p, Γ_p50) Is an empirical formula that is a shear stress-shear strain curve standardized by the rigidity at the time of micro-strain and mainly depends on the shear strain. Γ_p50Is the value of the shear strain at which the shear spring stiffness is halved, and is expressed by the following equation (12). Current effective stress σ_mIs the initial average stress σ at the stress evaluation point_m0(1-excess pore water pressure ratio = 1-r_{u_p}).
[0053]
(Equation 4)

[0054]
Also, Γ_p50Can be determined from the relationship with the excess pore water pressure ratio using the following equation.
[0055]
(Equation 5)

[0056]
Where (Γ_p50)_refIs σ_refIn_p50.
Note that the force-displacement skeleton / history curve generally has a shape as shown in FIG. The curve at the center is called the skeletal curve, and the curve surrounding it is called the hysteresis curve. When the displacement increases from the zero point to the plus or minus side, the skeletal curve is used, and when the displacement starts to return to zero, the hysteresis curve is used. Once the skeletal curve is determined, the hysteresis curve is automatically determined. For example, skeletal curve is g_p(Γ_p), The hysteresis curve is, for example, g_p((Γ-Γ_R) / 2). Where Γ_RIs the displacement between piles at the turning point. Generally, a Hardin-Drnevic model, a Ramberg-Osgood model, or the like can be used as the skeleton curve. In the present embodiment, the skeleton curve and the hysteresis curve are combined into a force-displacement skeleton / history curve, and K_p(Γ_p) And K_pf(Γ_pf). Where K_p(Γ_p) Is the ground spring of the ground between piles, K_pf(Γ_pf) Is the mutual ground spring between the pile ground and the free ground.
[0057]
In step S23, the shear stress τ_pDamage degree D of pile ground 28_PIn step 24, the excess pore water pressure ratio r_{u_P}Ask for.
[0058]
Cumulative damage degree D_PAnd excess pore water pressure ratio r_{u_P}Is obtained using the relations (1) to (4) as shown in FIG.
[0059]
(1) shown in FIG. 8 is the shear stress τ of the pile-to-pile ground that changes every moment._pIs shown.
[0060]
(2) shown in FIG. 8 indicates a liquefaction strength curve. The horizontal axis of (2) is the number of repetitions N during liquefaction, and the vertical axis is the stress ratio τ._p/ Σ_m0It is. As the liquefaction strength curve, a curve obtained by a dynamic undrained deformation test in a ground survey can be used. Where σ_m0Is the initial average stress at the stress evaluation point.
[0061]
As shown in (1) and (2) in FIG._pTo stress ratio τ_p/ Σ_m0And the stress ratio τ_p/ Σ_m0Can be used to determine the number of repetitions N. Further, the increment ΔD of the cumulative damage degree can be obtained from the obtained number of repetitions N. The increment ΔD of the cumulative damage degree is represented by the following equation.
[0062]
ΔD = １ ／ N (13)
Further, as shown by (3) in FIG. 8, the cumulative damage degree D is calculated from the cumulative damage degree increment ΔD._pCan be requested.
[0063]
(4) shown in FIG. 8 indicates cumulative damage degree D and excess pore water pressure ratio R._uAnd the cumulative damage degree D_pFrom excess pore water pressure ratio R_{u_P}Can be requested. This cumulative damage degree D_pAnd excess pore water pressure ratio R_{u_P}Can be obtained by experiments, but may be calculated using the following known equation._{u_P}= D_pIt may be.
[0064]
(Equation 6)

[0065]
In addition, the method of obtaining the cumulative damage degree from the shear stress and obtaining the excess pore water pressure ratio from the cumulative damage degree is not limited to the method described above, and the method described in Japanese Patent Application No. 2003-35390 or Japanese Patent Application Laid-Open No. 2001-208641. The method described in the gazette and other known methods can be used.
[0066]
In the next step S25, the effective stress σ_{m_P}Is calculated by the following equation.
[0067]
σ_{m_P}= (1-R_{u_P}) Σ_m0    … (15)
Where σ_m0Is the initial average stress at the stress evaluation point.
[0068]
In step S26, the initial shear spring rigidity K of the ground spring on the_pf0Is updated by the following equation.
[0069]
K_pf0= K^' _pf0× (σ_{m_P}/ Σ_m0)ⁿ  … (16)
Where K^' _pf0Is the initial shear spring stiffness K calculated in the previous step_pf0It is.
[0070]
Thus, the initial shear spring stiffness K_pf0Is updated to obtain a force-displacement skeleton / history curve K as shown in FIG._pf(Γ_pf) Is obtained.
[0071]
In step S27, the relative displacement 層 間 between the interlayer displacement of the ground 28 between the piles and the interlayer displacement of the free ground 31 is obtained._pfIs read from the storage unit 14 and the relative displacement Γ_pf, The interaction force between the pile ground 28 and the free ground 31, that is, the internal force R_pfIs the force-displacement skeleton / history curve K_pf(Γ_pf).
[0072]
Where K_pf(Γ_pf) Can be obtained in the same manner as in the above equations (10) to (12), and can be obtained by replacing ‘p’ with ‘pf’ in each equation.
[0073]
As described above, in the present embodiment, since the skeleton / history curve of the ground between piles and the skeleton / history curve of the free ground are originally different, the relative displacement between the interlayer displacement of the pile ground 28 and the interlayer displacement of the free ground 31 is different. Γ_pfFrom the interaction force between the pile ground 28 and the free ground 31_pf(Γ_pf).
[0074]
Next, in step S6 of FIG. 5, the external force F and the viscous force F_C, Inertial force F_M, The unbalanced force (residual force) ΔR of the internal force R is determined. The unbalance force ΔR can be obtained by the following equation.
[0075]
ΔR = FF_M-F_C-R (17)
Next, in step S7, an overall correction stiffness matrix (dynamic analysis overall matrix) K for calculating a correction value from the tangential stiffness of each of the building, the pile, the ground spring between the piles, and the free ground.^*Is calculated. Dynamic analysis whole matrix K^*Is represented by the following equation.
[0076]
K^*= M + γΔtC + βΔt²K ... (18)
Here, β and γ are coefficients (constant) in the Newmark-β method. K is the tangential rigidity.
[0077]
Next, in step S8, a correction value Λ at (t + Δt) time is calculated from the unbalance force ΔR by the following equation (20).
[0078]
Λ = K^{* -1}ΔR (19)
Next, in step S9, the predicted value u^*Is corrected, and the response displacement, response speed, and response acceleration at (t + Δt) time are obtained.
[0079]
Next, in step S10, the external force F (t + Δt) and the viscous force F are obtained based on the corrected response displacement, response speed, and response acceleration, as in step S4._C, Inertial force F_MIs calculated.
[0080]
Next, in step S11, similarly to step S5, the internal force R of the building, the pile, the ground between the piles, the ground between the pile and the free ground, and the free ground are calculated.
Next, in step S12, similarly to step S6, external force F and viscous force F acting from outside are applied._C, Inertial force F_M, The unbalance force ΔR of the internal force R is determined.
[0081]
Next, in step S13, it is determined whether or not the unbalance force ΔR has converged, that is, whether or not the value is equal to or less than an allowable value. If the unbalance force ΔR exceeds the allowable value, the process returns to step S7 and performs the same calculation as above. On the other hand, if the unbalance force ΔR is equal to or less than the allowable value, the process proceeds to the next step S14.
[0082]
In step S14, the displacement, speed, and acceleration are updated. That is, the displacement, speed, and acceleration when the unbalance force ΔR converges are regarded as the displacement, speed, and acceleration at that time.
[0083]
In this way, the processes from step S3 to S14 (time history loop) are performed for the entire earthquake time, and each response value for each time is calculated.
[0084]
When the time history loop ends, in step S15, each response value calculated in the time history loop and the maximum value of each response value are output to the display unit 18 and the storage unit 14.
[0085]
As described above, in the present embodiment, the shear force of the ground between the piles is evaluated from the excess pore water pressure of the ground between the piles, and the interaction force between the ground between the piles and the free ground is obtained based on the evaluation. It is possible to evaluate with higher accuracy than the seismic response calculation method that considered the liquefaction of the ground between piles using excess pore water pressure of free ground.
[0086]
(2nd Embodiment)
Next, a second embodiment of the present invention will be described. The same parts as those in the first embodiment are denoted by the same reference numerals, and detailed description thereof will be omitted.
[0087]
In the first embodiment, in step S27 of FIG. 6, the relative displacement 層 間 of the interlayer displacement of the ground between piles and the interlayer displacement of the free ground._pfThe interaction force between the ground between the piles and the free ground is calculated from the_pf(Γ_pf), In the second embodiment, the interlayer displacement of the ground between piles Γ_pFrom the K force by the same processing as in FIG._p(Γ_p) And the interlayer displacement of the free ground Γ_fFrom its action force_f(Γ_f).
[0088]
And the interaction force between the ground between the piles and the free ground, that is, the internal force R_pfIs determined by the following equation.
[0089]
R_pf= K_p(Γ_p) -K_f(Γ_f…… (20)
That is, as shown in FIG. 11, the acting force of the ground between the piles and the acting force of the free ground are obtained independently from the respective interlayer displacements, and the difference between the acting forces is defined as the interaction force. It is possible to faithfully evaluate the non-linear material characteristics of free ground every moment.
[0090]
【Example】
Next, embodiments of the present invention will be described with reference to the drawings.
[0091]
FIG. 12 shows a schematic configuration of a model 40 used in a liquefaction model vibration test to which the present invention is applied. FIG. 12A is a cross-sectional view of the model 40, and FIG. 12B is a plan view.
[0092]
In this liquefaction model vibration test, as shown in FIG. 12, in the shear box 42, a liquefied layer 44 and a non-liquefied layer 46 composed of two layers (5 × 5 = 25) composed of sand layers having different material properties. This is a test for measuring liquefaction by installing a model of a building 50 having a pile 48 as a foundation and vibrating the shear box 42 in a horizontal direction with a shaking table 52. The actual ground motion was used as the input ground motion.
[0093]
As shown in FIG. 12A, an accelerometer 54 and a pore water pressure gauge 56 were arranged in the ground to measure the behavior of the model 40, and a strain gauge 58 was arranged on the pile 48.
[0094]
This was modeled using a mass-spring model proposed in the present invention, and a test was performed. As the material specifications of the ground used for the modeling, the values shown in Table 1 below were used for the two layers.
[0095]
[Table 1]

[0096]
FIG. 13 shows the stiffness reduction rate G / G with respect to the shear strain of these formations.₀And the relationship between the rate of increase of the damping constant h. Note that the set value is obtained by approximating the measured value by an equation. FIG. 14 shows the liquefaction strength curve, that is, the relationship between the shear stress ratio and the number of repetitions N.
[0097]
FIG. 15 shows the depth distribution of the maximum value of the excess pore water pressure, the observation record, the simulation result by the existing analysis method (an existing example), and the simulation result by the analysis method of the present invention. In addition, in the existing analysis method, the rise of liquefaction is calculated from the behavior of the free ground, and in this analysis method, it is calculated from the ground between piles.
[0098]
As shown in FIG. 15, the excess pore water pressure ratio of the observed value has increased to near 1.0 near the ground surface, and the analysis result by the analysis method of the present invention is larger than the analysis result of the existing analysis method. The values are close. This means that the analysis method reproduces the result observed in this experiment that "the liquefaction was slightly more in the pile ground than in the free ground", and reproduced the phenomenon faithfully in theory Could be confirmed.
[0099]
FIG. 16 shows the process of increasing the excess pore water pressure together with the observation record of the experiment. As is clear from FIG. 16, it was confirmed that the analysis results obtained by the present analysis method corresponded well with the observation records.
[0100]
【The invention's effect】
As described above, according to the present invention, it is possible to obtain a simple and accurate ground-pile-building-coupled seismic response in consideration of a difference in excess pore water pressure between free ground and pile ground, This has the effect of
[Brief description of the drawings]
FIG. 1 is a schematic block diagram of an earthquake response analysis device.
FIG. 2 is a model diagram of an analysis target.
FIG. 3 is a diagram for explaining deformation of a pile and ground between piles.
FIG. 4 is a diagram for explaining deformation of a ground between piles and a free ground.
FIG. 5 is a flowchart of a main routine executed by a calculation unit.
FIG. 6 is a flowchart of an internal force calculation routine executed by a calculation unit.
FIG. 7 is a diagram for explaining the acting force and the like of the ground between piles.
FIG. 8 is a diagram for explaining calculation of an excess pore water pressure ratio.
FIG. 9 is a diagram for describing a force-displacement skeleton / history curve.
FIG. 10 is a diagram showing a force-displacement skeleton / history curve.
FIG. 11 is a diagram for explaining the interaction force between the pile ground and the free ground.
FIG. 12 is a schematic configuration diagram of a test apparatus according to an example.
FIG. 13 is a graph showing a relationship between a shear strain and a stiffness reduction rate according to an example.
FIG. 14 is a graph showing the relationship between the number of repetitions and the shear stress ratio according to the example.
FIG. 15 is a diagram illustrating the depth distribution of the maximum value of the excess pore water pressure ratio according to the example.
FIG. 16 is a diagram showing a process of increasing the excess pore water pressure ratio according to the example.
[Explanation of symbols]
10 Seismic response analyzer
12 Operation section
14 Storage unit
16 Operation part
18 Display

Claims (2)

Mass information, rigidity information of an analysis target model in which a structure including a building and a pile, and a ground between piles around the pile and a free ground separated from the structure by a predetermined distance or more, and a mass model, Using the damping information and the equation of motion based on the input earthquake information, the displacement information of the model to be analyzed that changes every moment is obtained, and based on the displacement information, the time characteristic of at least the response value regarding the strain that changes every moment is obtained. In the seismic response analysis method,
Based on the displacement information, calculate the interlayer displacement of the ground between the piles and the interlayer displacement of the free ground,
From the interlayer displacement of the pile ground and the interlayer displacement of the free ground, calculate the relative displacement of the interlayer displacement of the pile ground and the interlayer displacement of the free ground,
Calculating the shear stress of the ground between the piles based on the interlayer displacement of the ground between the piles and the force-displacement skeleton / history curve of the ground between the piles,
Calculating the cumulative damage degree of the pile ground based on the shear stress of the pile ground,
Calculate the excess pore water pressure ratio of the pile ground based on the cumulative damage degree of the pile ground,
Calculate the effective stress of the ground between the piles based on the excess pore water pressure ratio of the ground between the piles,
Calculating the initial shear spring stiffness of the ground between the piles based on the effective stress of the ground between the piles,
Using the initial shear spring stiffness, the force-displacement skeleton / history curve relating to the interaction force between the ground between the piles and the free ground is updated, and based on the updated force-displacement skeleton / history curve and the relative displacement. A process of calculating the interaction force by repeating at predetermined intervals a predetermined time. Mass information, rigidity information of an analysis target model in which a structure including a building and a pile, and a ground between piles around the pile and a free ground separated from the structure by a predetermined distance or more, and a mass model, Using the damping information and the equation of motion based on the input earthquake information, the displacement information of the model to be analyzed that changes every moment is obtained, and based on the displacement information, the time characteristic of at least the response value regarding the strain that changes every moment is obtained. In the seismic response analysis method,
Based on the displacement information, calculate the interlayer displacement of the ground between the piles and the interlayer displacement of the free ground,
The shear stress of the ground between the piles is calculated based on the interlayer displacement of the ground between the piles and the force-displacement skeleton / history curve of the ground between the piles, and the interlayer displacement of the free ground and the force-displacement skeleton of the free ground are calculated. Calculating a shear stress of the free ground based on a hysteresis curve,
Calculating the cumulative damage degree of the ground between the piles based on the shear stress of the ground between the piles, and calculating the cumulative damage degree of the free ground based on the shear stress of the free ground,
While calculating the excess pore water pressure ratio of the pile ground based on the cumulative damage degree of the pile ground, calculating the excess pore water pressure ratio of the free ground based on the cumulative damage degree of the free ground,
Calculating the effective stress of the ground between the piles based on the excess pore water pressure ratio of the ground between the piles, and calculating the effective stress of the free ground based on the excess pore water pressure ratio of the free ground,
Calculating the initial shear spring stiffness of the ground between the piles based on the effective stress of the ground between the piles, and calculating the initial shear spring stiffness of the free ground based on the effective stress of the free ground,
Using the initial shear spring stiffness of the ground between the piles, the force-displacement skeleton / history curve related to the acting force of the ground between the piles is updated, and the updated force-displacement skeleton / history curve and the interlayer displacement of the ground between the piles Calculating the acting force of the ground between the piles on the basis of, and using the initial shear spring stiffness of the free ground, updating the force-displacement skeleton / history curve relating to the acting force of the free ground, and updating the updated force- Calculate the acting force of the free ground based on the displacement skeleton / history curve and the interlayer displacement of the free ground,
The process of calculating the interaction force between the pile ground and the free ground based on the acting force of the ground between the piles and the acting force of the free ground is repeated every predetermined time. Seismic response analysis method.

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