JP4104944B2 - Prediction method of displacement behavior of structures in underpinning - Google Patents

Description

ここに、Ｋv：杭の鉛直方向複合ばねのばね定数（kN/m）
Ｋr：杭の回転方向複合ばねのばね定数（kN・m/rad）
ｋp：杭の弾性変形を評価するばねのばね定数（kN/m）
ｋv：杭先端の地盤反力を評価するばねのばね定数（kN/m）
ｋsv：杭周面の鉛直方向せん断地盤反力を評価するばねのばね定数（kN/m）
ｋint：杭周面における既設杭と新設杭との相互作用を評価するばねのばね定数（kN/m）
Ｉy：ｙ軸回りの杭群の２次モーメント（m²）
【００２２】
式（1a）が本発明で提案する複合ばねのばね定数であり、杭の鉛直方向のばねのばね定数を総合的に評価するものである。すなわち、前記複合ばねは、杭の軸心に作用する杭の弾性変形を評価するばねｋpと、杭先端の地盤反力を評価するばねｋvと、杭周面の地盤反力を評価するばねｋsvと、既設杭と新設杭との相互作用を評価するばねｋintとから構成され、杭の軸心に作用する杭の弾性変形を評価するばねｋpと杭先端の地盤反力を評価するばねｋvとを直列に連結させた鉛直方向のばねに、杭の周面に作用する杭周面の鉛直方向せん断地盤反力を評価するばねｋsvと、既設杭と新設杭との相互作用を評価するばねｋintとを並列に連結したものである。
【００２３】
また式（1b）は構造物の基礎の構造に応じて考慮すべき回転方向の複合ばねであり、鉄道系構造物の規準類（▲１▼土木学会：国鉄建造物設計標準解説、基礎構造物抗土圧構造物、技報堂、1986.3.▲２▼運輸省監修、鉄道総合技術研究所編：鉄道構造物等設計標準・同解説（基礎構造物・抗土圧構造物）、丸善、1997.3.）などに示されるものである。構造物のフーチングが杭群により支持されている場合、図４に示すようにｘ軸とｙ軸を決定すれば、そのｙ軸回りの２次モーメントＩyはｙ軸から各杭までの距離ｘiの二乗和により求められ、これから杭群の杭頭部における回転方向の回転ばねのばね定数Ｋrを決定する。
【００２４】
以下、前記複合ばねを構成する各ばねのばね定数を算定する方法を具体的に述べる。
【００２５】
(1)杭の弾性変形を評価するばねのばね定数の算定
杭の弾性変形を評価するばねのばね定数ｋpは次式(2)により与えられる。
【００２６】
【数２】

ここに、Ｅp：新設杭の弾性係数（kN/m²）
Ａp：新設杭の軸部の断面積（m²）
Ｌp：新設杭の長さ（m）
【００２７】
(2)杭先端の地盤反力を評価するばねのばね定数の算定
杭先端の地盤反力を評価するばねのばね定数ｋvは次式(3a)(3b)により与える。
【００２８】
【数３】

ここに、 ｋv^*：新設杭の先端部の鉛直方向地盤反力係数（kN/m³）
Ａpv：新設杭の先端部の断面積（m²）
α：Ｅsの算定方法および荷重条件に対する補正係数
Ｅs：地盤の変形係数（kN/m²）
Ｄ：新設杭の先端部の直径（m）
【００２９】
なお、式(3b)および以下に示す式(4b)の地盤反力係数ｋv^*、ｋsvi^*の算定には、鉄道系構造物の規準類（▲１▼土木学会：国鉄建造物設計標準解説、基礎構造物抗土圧構造物、技報堂、1986.3.▲２▼運輸省監修、鉄道総合技術研究所編：鉄道構造物等設計標準・同解説（基礎構造物・抗土圧構造物）、丸善、1997.3.）に示される方法を用いた。また式(3b)および式(4b)中の地盤の変形係数Ｅsは、孔内水平載荷試験と室内土質試験の結果から決定している。
【００３０】
(3)杭周面の地盤反力を評価するばねｋsvのばね定数の算定
杭周面の鉛直方向せん断地盤反力を評価するばねのばね定数ｋsvは次式(4a)(4b)により算定する。
【００３１】
【数４】

ここに、ｋsvi^*：地層ごとの杭周面の鉛直方向せん断地盤反力係数(kN/m³)
Ｕi：各地層に位置する杭の周面積（m²）
ｎ：地層の数
【００３２】
(4)杭と杭との相互作用を考慮するばねのばね定数の算定
応力導入時に既設杭は建物の挙動に伴い鉛直上向きに変位し、新設杭の沈下量を相殺する。すなわち、既設杭の周面から周辺地盤に伝わる荷重は地盤をせん断変形させることにより、新設杭を仮の単純沈下位置から相対的に隆起させるものと考えられる。従来のアンダーピニングにおける構造物の変位予測は、この杭と杭との相互作用を考慮していないためあまり良い一致を示さない。本研究では、この杭と杭との相互作用を、半無限弾性地盤において集中荷重が作用する場合に任意点の応力と変位を与えるMindlinの解（R. D. Mindlin：Force at a point i-n the interior of a semi-infinite solid、Physics、vol 7、pp.195-202、1936.）を用いて評価することにした。
【００３３】
(a)Mindlin解の特性
地盤内応力の計算に用いる基本的な弾性理論解は、集中荷重が地表面に鉛直に作用する場合のBoussinesq解、同じく水平に作用する場合のCerruti解などがありそれらがよく用いられているが、アンダーピニングにおける杭と杭との相互作用の問題では、その荷重の作用位置を考えれば地盤内部に集中荷重が作用する場合のMindlin解を用いるのが適当である。
【００３４】
図５に示す円柱座標系（ｒ、θ、ｚ）において、半無限弾性地盤内に鉛直集中荷重Ｐが作用する場合の地中の応力解と変位解、すなわちMindlinの応力解と変位解は次式(5a)(5b)で与えられる。
【００３５】
【数５】

ここに、σ_z：鉛直方向応力
Ｐ：集中荷重
ν：ポアソン比
z、D、R1、R2：図５を参照
u：鉛直方向変位
Ｇ：せん断弾性係数
【００３６】
(b) Mindlin解の相互作用問題への適用性の検討
杭と杭との相互作用に関する研究は、群杭基礎の分野で多く見受けられる。弾性理論による方法では、山肩・八尾（マサツ群杭基礎の沈下に関する理論解について、第９回土質工学研究発表会、pp.481-484、1974.6.）が、粘性土地盤中に打設された群杭基礎が鉛直荷重を受ける場合の抵抗とその沈下機構について考察している。Mindlin解を用いた変位影響係数により、群杭基礎はその中心部において杭の荷重分担率や杭周辺の摩擦抵抗が小さくなり（地盤が杭とともに沈下するため）、その結果として群杭効率が低下することを説明している。山本・冨永・山肩（杭の相互作用問題における地中変位の評価方法、構造工学論文集、vol 32B、pp.29-38、1986.3.）は、変位影響係数にMindlin解を適用するにあたり、地盤と杭本体との剛性の違いによる影響は加力点の近傍のみで生じることを示している。これらに共通している事象は、任意点の変位を求める変位影響係数にMindlin解を用いこれにより相互作用を評価することであり、ばねを用いた相互作用の評価は見受けられない。
【００３７】
一方、Mindlin解は半無限弾性地盤中の集中荷重によるものであるため、その適用においては注意が必要である。
【００３８】
まず地盤の変形特性に関する問題は、Mindlin解がポアソン比を含んでいるため、この影響を検討する必要がある。平山（杭基礎の圧密沈下解析、土と基礎、pp.15-17、1997.2.）は応力解に関してポアソン比の影響はさほど大きくないことを明らかにしている。ここでは、変位解における地盤特性の影響について考察する。
【００３９】
図６はポアソン比をパラメーターとして地中の変位分布を示したものである。図中、δvはMindlin解により求まる地中の鉛直方向の変位、Ｐiは杭の中心位置に鉛直上向きに作用する荷重、Ｅsは地盤の変形係数、ｚは地中の深さ、Ｌは杭の長さ、ｒは杭の中心からの水平距離、Ｄは杭の直径である。この図から、変位解におけるポアソン比の影響は、ｒ/Ｄ＞10程度の領域においてもさほど小さくならないことがわかる。このことから、アンダーピニング周辺部の地盤が複雑な互層地盤の場合には、図７に示すような方法を用いて相互作用ばねのばね定数ｋ-int^n-1を算出できるものと考えた。すなわち、n-1層の下層にあたるn層の既設杭の周面摩擦応力ｆnによる層境の地中応力σz^n-1を求め、これとn-1層の周面摩擦応力ｆn-1による弾性解の和からn-1層の相互作用ばねのばね定数ｋint^n-1が評価できるという考えである。
【００４０】
【数６】

ここに、ｋint^n-1：n-1層の相互作用ばねのばね定数
ｋint^n-1(σ_zn-1)：n-1層の地盤内応力の影響による相互作用ばねのばね定数
ｋint^n-1(ｆ_n-1)：n-1層の杭の周辺摩擦応力の影響による相互作用ばねのばね定数
【００４１】
次に集中荷重に関する問題であるが、これは集中荷重をそれと等価な分散荷重に置換することで対応できる。しかしながら、その計算は繁雑になるので、載荷点とある程度の距離を有する場合は、集中荷重から直接相互作用の影響を評価しても良いと思われる。
【００４２】
(c)相互作用を評価するばねのばね定数の算定
以上のことを踏まえ、既設杭と新設杭との相互作用を評価するばねのばね定数ｋintは、次に述べるような方法で求められる。
【００４３】
新設杭の周面には、既設杭の周面から地盤に伝達される力により鉛直上向きの力が作用する。いま、図８に示すように杭周面の微小面積dAを想定すれば、それにはτ_rz ^r=aなる力が作用すると考えられる。杭の軸方向の微小長さdzの区間では、下式(7)の力が作用している。
【００４４】
【数７】

【００４５】
一方、杭周面の地盤は、既設杭の周面から地盤に伝達される力により鉛直上向きの力により、鉛直上向きにδ_ziだけ変位する。杭周面部において杭と地盤との間に相対変位が生じないと仮定すれば、鉛直上向きの変位δ_ziは相殺される新設杭の沈下量である。このような現象を新設杭の沈下の抵抗とすれば、これをばねで評価するのが都合よく、このばねのばね定数は新設杭の周面に作用する鉛直上向きの力と新設杭の鉛直上向きの変位量との比で表すことができる。
【００４６】
既設杭と新設杭との相互作用を評価するばねのばね定数ｋintは、図８を参考にして次式(8a)(8b)から算定することにした。
【００４７】
【数８】

ここに、τ_rzi：Mindlinの第１解による応力解(kN/m²)
δ_zi：Mindlinの第１解による変位解(m)
Ｉ_p：杭の形状による影響を表す係数（ここでは1.0とした）
n：対象とした新設杭に影響を与える既設杭の本数
l：地盤中にある新設杭の長さ(m)
ａ：新設杭の半径(m)
【００４８】
(5)受替版下の地盤反力を評価するばねのばね定数の算定
受替版下の地盤ばねのばね定数ｋsは次式(9a)(9b)により算定する。なお、地盤反力係数の推定には鉄道系構造物の規準類に示される方法を用いた。
【００４９】
【数９】

ここに、Ａ_v0：受替版底部の単位面積(m²)
ｋs^*：受替版底部の鉛直方向の地盤反力係数(kN/m³)
ｋs0^*：土質試験より求めた変形係数より推定する地盤反力係数(kN/m³)（下式(10)により求める。)
【００５０】
【数１０】

α：Ｅsの算定方法および荷重条件に対する補正係数
Ｅs：地盤の変形係数(kN/m²)
Ｂs：基礎の換算載荷幅(m)
【００５１】
(6)既設構造物の挙動を評価するばねのばね定数の算定
一般に、アンダーピニングの対象が比較的規模の大きい建物などの場合、その一部分を多点支持により受替える事例が多い。このため、建物を３次元のラーメン構造などで評価した構造モデルに荷重または変位を作用させ、任意点の変位量を算出するのが望ましいと考える。しかしながら、建物の剛性は地中梁や基礎スラブの剛性だけではなく上部の梁、壁、柱などの剛性の影響を受けているため、構造の適正なモデル化は困難である。さらに、老朽化した建物の剛性を適正に評価することも難しい。
【００５２】
これらのことから、建物の変位は次式(11a)(11b)により算定することとした。
【００５３】
【数１１】

ここに、δi：既設杭の杭頭の鉛直変位(m)
Pi：応力導入荷重(kN)
Ｋ_v ^u：既設杭の挙動を評価する鉛直方向の複合ばねのばね定数(kN/m)
【００５４】
図９に示すように、式(11a)により各既設杭の杭頭の鉛直変位δiを算出し、これを建物の当該点の変位とした。この方法による建物変位の予測値は、建物の剛性を考慮していない。したがって、建物の各点に不等変位を生じる場合には、予測値が実測値よりも若干大きく算出されると推察できる。
【００５５】
また式(11b)に示した既設杭の変位を算出するときの鉛直方向のばね定数Ｋ_v ^uが式(1a)に示す複合ばねのばね定数と異なるのは、右辺第１項中のｋvtと右辺第３項のｋint^uの２か所である。次に、これに関して考察を加える。
【００５６】
(a)杭先端部付近の地盤の主働的な挙動を評価するばねのばね定数の算定
シールドトンネル覆工の設計を例とした木村・小泉(地盤と覆工の相互作用を考慮したシールドトンネルの設計法について、土木学会論文集、No.624/III-47、pp.123-134、1999.6.）の研究によれば、覆工がトンネル外側に変形し地盤が受働的挙動を示す場合と、覆工がトンネル内空側に変形し地盤が主働的挙動を示す場合とでは、それぞれの変形特性が異なるとしている。これらの挙動を弾性ばねでモデル化する場合、主働的挙動を評価するばねのばね定数は、受働的挙動を評価するそれの半分程度であることを模型実験から求めている。図１０はその概念を模式的に表した図であり、状態a)は土柱に土の重量のみが作用している状態である。状態b)は、建物荷重などを受けて土柱が状態a)よりも縮んでいる状態であり、受替える前の状態がこれにあたる。状態c)は、状態b)に新たな荷重が作用して土柱がさらに圧縮される状態であり、応力導入時の新設杭の先端部における地盤の受働的な挙動を表している。状態d)は、状態b)からある程度の荷重が減少して土柱が伸張する状態であり、応力導入時の既設杭の先端部における地盤の主働的な挙動を表している。
【００５７】
このことから、既設杭の先端部の地盤の主働的な挙動を評価するばねのばね定数ｋvtは次式により算定することとした。
【００５８】
【数１２】

ここに、ｋvt：圧縮領域において地盤が主働的な挙動を示すときの地盤反力を評価するばねのばね定数
ｋv：地盤が受働的な挙動を示すときの地盤反力を評価するばねのばね定数である。
【００５９】
(7)受替版と既設杭との相互作用を評価するばねのばね定数の算定
受替版下の地山を残した状態で応力を導入する本施工手順のアンダーピニングの場合、既設杭における相互作用は、既設杭と新設杭との間、および既設杭と受替版底面との間に生じる。荷重の作用位置との距離を考えれば後者の方が支配的であると思われる。したがって、ここでは既設杭と受替版との間の相互作用を評価することにした。
【００６０】
この相互作用を評価するばねのばね定数ｋint^ｕは次式(13a)(13b)により算定する。なお、ばね定数の算定の概念は数式(8)と同様である。ただし、荷重が作用する状態を勘案して、地中の応力伝播はBoussinesq解により評価している。また、この時の作用荷重は、ジャッキ軸芯上に作用する受替荷重とした。
【００６１】
【数１３】

ここに、τ_rzi：Boussinesqによる応力解(kN/m²)
δ_zi：Boussinesqによる変位解(m)
Ｉp：杭の形状による影響を表す係数（ここでは1.0とした）
ｎ：対象とした既設杭に影響を与えるジャッキ受け台座の数
【００６２】
なお、図１１に示す円柱座標系（ｒ，θ，ｚ）において，地表面に鉛直集中荷重が作用する場合の地中の応力解と変位解、すなわちBoussinesqの応力解と変位解は次式(14a)(14b)で与えられる。
【００６３】
【数１４】

ここに、σz：鉛直方向応力
Ｐ：集中荷重
z、R、r：図１１を参照
ν：ポアソン比
Ｇ：せん断弾性係数
【００６４】
【実施例】
次いで、本実施例では、前記複合ばねモデルによる変位予測手法の妥当性を実際のアンダーピニング工事で得られた建物各点の変位の計測結果から検証した。
【００６５】
(1)アンダーピニング工事の概要
対象とした工事は、臨海副都心線２期工事の第１広町トンネル工区における建物３棟のアンダーピニングである。大井町駅と大崎駅との間に位置する第１広町トンネルは、シールド工法により建設される外径7100mmの鉄道単線断面トンネルである。この路線上には、ＲＣ造１２階建のJR広町社宅２棟（６号棟及び３号棟）と、ＲＣ造８階建の品川区防災センターの計３棟の建物が位置し、それらの建物の基礎杭の一部がトンネル掘削の支障となるため、アンダーピニングを実施した。
【００６６】
受替えは下受け梁方式とし、表１に示されるように、建物の総重量618MNの内152.8MNを受替えるものである。また、３棟すべてにおいて、前述したように、工期短縮を目的とした先行応力導入（受替版下の地盤を残した状態でプレロードを行う）を実施している。
【００６７】
【表１】

【００６８】
土質は地表から1.8m程度まで埋土層が分布しており、その下にN値30程度の武蔵野礫層が3.4m程度の厚さで分布している。さらにN値10程度の東京粘土層（一部東京砂層が介在）が16m程度分布し、その下に周辺構造物の支持層であるＮ値50以上の東京礫層が分布している。この東京礫層には水が豊富に存在する。透水係数はk=10^-1〜10^-2cm/secの範囲にあり、かつ20m程度の被圧水頭を持っている。このため、受替杭の造成および既設杭撤去の支障とならないように、事前に受替範囲の全体にわたって二重管複相式注入工法による地盤改良を行っている。
【００６９】
また、表２に示すように、撤去杭は直径φ800〜φ2000の計５３本で、このうち防災センターのみが拡底杭となっている。受替杭は直径φ2000〜φ2200の計３７本で、すべて拡底杭を採用している。図１２〜図１５はその受替えの状況を示したものである。
【００７０】
【表２】

【００７１】
(2)実測値と予測値との比較およびその考察
(a)建物と受替版の挙動
図１６と図１７は、JR社宅２棟（６号棟、３号棟）における応力導入時の建物と受替版の変位挙動を示したものである。図中、黒丸は実測値を、白三角は従来の手法による予測値を、白菱形は本発明に係る複合ばねモデルによる予測値を表している。ここで用いた従来の手法は、杭の挙動を評価するばねのばね定数を「土木学会：国鉄建造物設計指針、基礎構造物杭土圧構造物、pp.182-183、1986.3.」に基づき算定したものである。また、上半のプラス側が建物各点の隆起量を、下半のマイナス側が受替版各点の沈下量を示している。
【００７２】
これらの図から複合ばねモデルによる予測値は、従来の手法による予測値と比較して、実測値とより良い一致を示していることがわかる。図１６(d)に示すE-6点や図１７(b)に示すB-3点における建物の変位の予測値は、実測値と若干の相違があるが、これは非受替部の影響によるものと考えられる。すなわち、予測計算の対象範囲外にある建物の地中梁、基礎スラブおよび柱、壁、上部梁などの剛性の影響、あるいはその部分の基礎杭の周面摩擦などの影響が他の点と比べ大きいため、当該点の変位が抑制されたものと思われる。これは建物のレベリングなどに関連して、このような非受替部に隣接する箇所をジャッキアップする必要が生じた場合には、設計荷重に対して十分な余力を持つジャッキを配置しておくことが必要であることを示している。
【００７３】
図１８は、品川区防災センターの建物と受替版の挙動を示したものである。この図から複合ばねモデルによる予測値は、従来の手法による予測値と比較して、実測値をより良く説明していることがわかる。しかしながら、建物の変位（図中、上半側に示す変位）についてはあまり良い一致を示しておらず、これは防災センターの既設杭が拡底杭であることによると思われる。拡底杭は杭の先端部が下方に向かって広がるテーパー形状になっているため、杭に鉛直上向きの荷重が作用した場合に、このテーパー部が地盤に押し付けられる方向に挙動することが考えられ、実際の変位量が小さくなったものと考えられる。
【００７４】
上式(13b)中の杭の形状を評価する係数Ｉpを、予測値と実測値が一致するように逆算すれば、本拡底杭の場合にはＩp=６〜７程度になる。形状係数Ｉpは杭の種別、拡底部の形状、周辺地盤の変形特性などの要因を考慮して決定されるべきであり、この結果を他の工事にそのまま適用することはできない。しかしながら、複合ばねモデルによる予測値は、実測値と同様の変位の分布形状になること、その値は従来の手法と比較してより良い一致を示すことなどから、杭間の相対変位が特に重要である非受替部の近傍においても、建物の健全性の照査に十分適用可能であると思われる。
【００７５】
(b)複合ばねモデルの適合性の定量評価
複合ばねモデルによる予測値は、従来法と比べて格段に実測値との適合性が良いことがわかった。また、建物の変位は、非受替部の近傍において、建物本体の剛性の影響を受ける可能性が示された。ここでは非受替部からの位置を指標にして、複合ばねモデルの適合性を定量的に評価することを試みる。以下に適合性を評価するための手法を述べる。
【００７６】
建物各点の変位の実測値と予測値をそれぞれｍ_i、ａ_iとし、また、非受替部からの距離が同一な計測点の総数をＮとすると、受替部全体にわたる実測値と予測値との平均的な差は式(15)で表される。式(15)中のＳ^２を便宜上分散と呼び、この分散Ｓ^２の値が小さいものほど適合性が高いと判断することにした。
【００７７】
【数１５】

なお、品川区防災センターの計測点は、すべて非受替部からの距離が同一なため、ここでは除外している。また、非受替部の位置は式(16)により無次元化したものを指標にしている（図１９参照）。
【００７８】
【数１６】

ここに、Ｌx、Ｌy：建物全体の幅と奥行きの長さ(m)
Ｌx^u、Ｌy^u、：受替部の幅と奥行きの長さ(m)
Ｌxⁱ：非受替部から計測点までの距離(m)
【００７９】
図２０に従来の手法による予測値と複合ばねモデルによる予測値とを比較した結果を示す。この図から複合ばねモデルによる予測値は、従来の予測手法による予測値と比較して、定量的にみて実測値との適合性が高いことがわかる。また、非受替部からの無次元化した位置が０．２以内の範囲では、分散が大きくなっている。すなわち、予測精度が低下していることがわかる。
【００８０】
アンダーピニング工事の挙動予測において、必要となる精度は受替えの対象である既設構造物の種類やその重要度などにより異なる。JR社宅６号棟を例にすれば、杭間の相対変位で4.20mm、杭の絶対変位で10.00mmの１次管理値に対して、従来の手法による予測値は平均4.18mmの誤差を、複合ばねモデルによる予測値は平均0.48mmの誤差を生じていることが図１６よりわかる。隣接する杭部の予測値が互いに危険側の値となるケースを想定すれば、本工事の場合、最低でも2.00mm程度以内の予測精度が必要と思われる。
【００８１】
(3)周辺部が複雑な互層地盤となっているアンダーピニング工事例への複合ばねモデルの適用性の検討
以上の結果より複合ばねモデルは、２層もしくは３層程度の層状地盤において適用性を有することがわかった。次に、より複雑な地盤条件下におけるアンダーピニングを対象に変位挙動の予測を行い、互層地盤においても複合ばねモデルが適用できるか否かに検討を加えることとした。複合ばねモデル中の相互作用ばねはMindlin解に基づいて算定される。すでに述べたようにMindlin解は半無限弾性地盤を対象にしているため、これを互層地盤にそのまま適用することはできない。そこでこの検討事例では式(6)に示したような分散荷重による弾性解の和から評価することにした。
【００８２】
(a)アンダーピニング工事の概要
対象とした検証事例は、昭和６０年に施工された営団地下鉄１１号線人形町工区におけるナンヤビルのアンダーピニング工事である。ナンヤビルはSRC造８階建の構造物であり、計１０本の場所打ち杭（φ1500＝８本、φ1000＝２本）により支持されている。建物の総重量は31MNでこのうち26.3MNを受替えるものである（図２１参照）。
【００８３】
土質は杭頭部から4.5m程度が軟弱な地層であり、Ｎ値が0〜1程度の細砂と砂混じりシルトの互層が分布している。その下にはＮ値８の粘土層が8.0m程度、さらにＮ値30の細砂層が3.0m程度、そしてＮ値10の粘土層が5.0m程度分布している。
【００８４】
(b)実測値と予測値との比較およびその考察
図２２にナンヤビルにおける応力導入時の建物と受替版の変位挙動の実測値と予測値とを示す。この図をみると、複合ばねモデルによる予測値は、従来の手法による予測値と比較して実測値と良い一致を示していることがわかる。
【００８５】
図２３はナンヤビルとJR社宅６号棟の場合の分散Ｓ^２を比較したものである。図中の横軸は受替版端部からの距離を表しているが、ナンヤビルのアンダーピニングは非受替部が存在しないため、それには工学的な意味はない。また、JR社宅６号棟については、非受替部の影響を受けている範囲は除外して示した。
【００８６】
この図から、ナンヤビルの変位挙動の予測値は、JR社宅６号棟のそれと比較して分散の幅が大きく、推定精度が落ちることがわかる。しかしながら、分散の平方根Ｓは、平均で0.60mmであり受替えの規模や杭のスパンなどを併せて考えれば、実用上の予測精度は十分高いと考えられ、本研究で提示した複合ばねモデルが互層地盤におけるアンダーピニング工事にも適用できることがわかる。
【００８７】
【発明の効果】
以上詳説のとおり本発明によれば、アンダーピニング工事において、応力導入時（受替時）における既設構造物又は受替構造物等の構造物の変位挙動を予測するに当たり、予測値と実測値とが精度良く一致する予測手法を提案することが可能となり、もって受替初期の建物の健全性、受替荷重、最終的な建物と受替構造物の健全性を適性に評価することが可能となる。
【図面の簡単な説明】
【図１】本形態例におけるアンダーピニングの施工手順図である。
【図２】従来のアンダーピニング施工手順図である。
【図３】本発明に係る複合ばねモデルの概念図である。
【図４】杭群の回転ばねのばね定数の算定方法説明図である。
【図５】 Mindlin解の座標系を示す図である。
【図６】 Mindlinによる変位解と地盤特性の関係図である。
【図７】互層地盤における相互作用ばねの算出方法の説明図である。
【図８】 Mindlin解による相互作用ばねのばね定数の算定方法の説明図である。
【図９】建物変位の算出方法の説明図である。
【図１０】圧縮領域において地盤が主働土圧的挙動を示す時の地盤反力を評価するばねの説明図である。
【図１１】 Boussinesq解の座標系を示す図である。
【図１２】実施例におけるJR社宅６号棟のアンダーピニング例（その１）である。
【図１３】実施例におけるJR社宅３号棟のアンダーピニング例（その２）である。
【図１４】実施例における品川区防災センターのアンダーピニング例（その３）である。
【図１５】その受替状況断面図である。
【図１６】アンダーピニング例（その１）の実測値と予測値との比較図である。
【図１７】アンダーピニング例（その２）の実測値と予測値との比較図である。
【図１８】アンダーピニング例（その３）の実測値と予測値との比較図である。
【図１９】解析モデルの定量評価に用いた非受替部からの位置を無次元化した指標図である。
【図２０】解析モデルの定量評価図である。
【図２１】ナンヤビルの受替状況図である。
【図２２】ナンヤビルにおける実測値と予測値との比較図である。
【図２３】ナンヤビルとJR６号棟の建物変位の予測値の分散Ｓ^２の比較図である。[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a prediction method for predicting the displacement behavior of a structure such as an existing structure or a replacement structure so that a predicted value and an actual measurement value coincide with each other accurately in underpinning work.
[0002]
[Prior art]
In urban areas such as Tokyo and Osaka, overcrowding and agglomeration accompanying rapid economic growth are intense. Underground is no exception, and facilities such as railways, sewers, electric power, and communications are congested under the road, and the underground areas up to the middle and shallow are already full. Under these circumstances, the construction of new underground facilities such as railways is increasingly being carried out in the remaining deep areas and private underground areas.
[0003]
In tunnel construction, the shield construction method is often used because it has little impact on the above-ground facilities and underground facilities. However, high-rise buildings are located on private land, and bridge piers such as elevated railways and elevated roads are located on the road, and the foundation piles become an obstacle when shields dig under them. For this reason, underpinning is often required to replace a part or all of the existing structure with a new foundation.
[0004]
In recent years, with the increase in such special construction conditions, underpinning has been increasing in scale as the number of achievements has increased dramatically. In underpinning, it is extremely important to predict the displacement behavior of existing buildings and replacement structures from the viewpoints of ensuring the soundness of existing buildings and evaluating replacement loads during stress introduction (preload). It becomes.
[0005]
As shown in the following Non-Patent Documents 1 to 3 (Prior Art 1), the current displacement behavior prediction method uses the pile foundation design technique to calculate the vertical displacement of existing buildings and replacement structures. It was common. Non-Patent Document 4 (Prior Art 2) below proposes a method for calculating the vertical displacement of the pile head using a displacement transfer function that takes into account the interaction between the existing pile and the new pile. This method is based on the research of the following non-patent document 5 that considers the behavior of group piles. From the result of the finite element method, the relationship between the unit load acting on an arbitrary point in the ground and the displacement of the arbitrary point is shown. The evaluation is performed using a displacement transfer function that represents.
[0006]
[Non-Patent Document 1]
Noboru Yamada, Hitoshi Kiyoji, Koyoshi Saiki “Behavior of Underpinning Support Structures-Prediction and Results”, 55th Annual Conference of Japan Society of Civil Engineers, September 2000, VI-259
[Non-Patent Document 2]
Seibu Nishibayashi, Shuichi Yazaki “Underpinning of high-rise buildings, tunnel and underground”, March 1990, Vol. 21, No. 3, p.7-16
[Non-Patent Document 3]
Jiro Hayashi, Naotake Nishimura, Seto Matsuo, Hiroshi Koyama “Design and Practice in Underpinning Construction of Subway at Katafuku Connection Line Minamimorimachi Construction”, Basic Engineering, March 1996, p.86-94
[Non-Patent Document 4]
Jiro Hirose, Joji Konishi, Yuji Nakamura “Behavior of Underpinning of Buildings Supported by Pile Foundation”, Proceedings of Japan Society of Civil Engineers, September 1991, No.435 / VI-15, p.43-50
[Non-Patent Document 5]
Motohiro Murata, Yuji Nakamura, Susumu Mizutani “Calculation method and application example for vertical load of group pile using axisymmetric finite element method”, Abstracts of the 40th Annual Conference of the Japan Society of Civil Engineers, September 1985 Moon, III-60
[0007]
[Problems to be solved by the invention]
However, in the case of the prior art 1, it has been reported in many cases that the predicted value obtained by calculation is several times larger than the actual measurement value, and it is difficult to say that the behavior is sufficiently evaluated. . For this reason, a method of correcting the ground deformation coefficient and adapting it to the actual displacement at the time of stress introduction is adopted at the site, and the final displacement amount of the building and the subsidence amount of the replacement structure are estimated using this correction value. It is the actual situation. Therefore, since the evaluation of the replacement load is not sufficient, in the construction management at the time of initial stress introduction, the soundness of the building has been lacking in rationality, for example, the post-judgment must be made by the measuring worker.
[0008]
Moreover, in the case of the said prior art 2, this calculation method is applicable, for example, that an existing structure and a new structure are each substantially symmetrical structures, and that a replacement load is transmitted to the ground only through a pile. There are no practical examples because the conditions are very limited and the calculation involves a lot of effort. In addition, it is difficult to apply this method when stress is introduced in a state where the construction procedure shown in the present embodiment described later, that is, the ground under the replacement plate is left as the construction procedure.
[0009]
Therefore, the main problem of the present invention is that in predicting the displacement behavior of an existing structure or a structure such as a replacement structure when stress is introduced (replacement) in underpinning work, the predicted value and the actual measurement value are accurate. By proposing a well-matched prediction method, it is possible to appropriately evaluate the soundness of the building at the beginning of replacement, the replacement load, and the soundness of the final building and replacement structure.
[0010]
[Means for Solving the Problems]
  In the underpinning in which part or all of an existing structure including a pile foundation is replaced by a replacement structure including a pile foundation newly provided in the basement as the present invention according to claim 1 to solve the above problem. A prediction method for predicting the displacement behavior of the existing structure or replacement structure,
  When the existing structure and the replacement structure are modeled with a frame structure, the surrounding ground is interposed.AlreadyA method for predicting the displacement behavior of a structure in underpinning, characterized by setting a model with a composite spring that takes into account the spring that evaluates the interaction between the installed pile and the new pile, and analyzing the displacement behavior at the time of replacement Is provided.
[0011]
  When a replacement load is applied at the time of stress introduction and the structure is jacked up, a vertical upward force is applied to the existing pile, and a vertical downward force is applied to the new pile. The upward force of the existing piles will affect the new piles through the surrounding ground, and it is thought that a phenomenon will occur that offsets part of the settlement. Since the conventional displacement prediction method does not consider the interaction between the piles and the piles, the predicted value and the actually measured value do not show a good match. Therefore, in the present invention described in claim 1, when modeling with a frame structure, the surrounding ground is interposed.AlreadyA model with a composite spring was established in consideration of the spring to evaluate the interaction between the installed pile and the new pile. As will be described later in the examples, the predicted value and the actually measured value coincide with each other accurately by considering a spring for evaluating the interaction between the existing pile and the new pile.
[0012]
As the present invention according to claim 2, the composite spring model includes a spring for evaluating the elastic deformation of the pile, a spring for evaluating the ground reaction force at the tip of the pile, and a spring for evaluating the ground reaction force of the circumferential surface of the pile, It consists of a spring that evaluates the interaction between the existing pile and the new pile. Of these, the spring that acts on the axis of the pile is connected in series, and the spring that acts on the peripheral surface of the pile is connected in parallel. The method for predicting the displacement behavior of a structure in underpinning according to claim 1, wherein the behavior between the pile and the ground is evaluated in a composite manner.
[0013]
According to a third aspect of the present invention, there is provided a method for predicting the displacement behavior of a structure in underpinning according to the second aspect, wherein a composite spring in the direction of rotation of the pile is set according to the structure of the foundation.
[0014]
  As the present invention according to claim 4, in calculating the spring constant of a spring for evaluating the interaction between an existing pile and a new pile, Mindlin gives stress and displacement at an arbitrary point when concentrated load acts on a semi-infinite elastic ground. The prediction method of the displacement behavior of the structure in the underpinning in any one of Claims 1-3 using the solution of this is provided.
[0015]
DETAILED DESCRIPTION OF THE INVENTION
Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.
[0016]
(Underpinning construction procedure)
The underpinning handled in this embodiment is different in construction procedure from the conventional general construction procedure for the purpose of shortening the construction period. In conventional underpinning using a general under-beam method, as shown in FIG. 2, there are many cases where the ground under the replacement plate is excavated prior to the introduction of stress. This is to avoid factors that complicate the prediction of displacement behavior and control of replacement, such as deformation due to the dead weight of the replacement plate, ground reaction force under the replacement plate, and rebound of the ground due to excavation (hereinafter hereafter). This is called advanced excavation).
[0017]
However, when adopting underpinning by the preceding excavation, after excavating to the depth required for the construction of the new pile, it is necessary to create a new pile that takes into account the additional pile, backfill, and build a replacement version At the same time, it is necessary to introduce stress through re-excavation of laid sand. For this reason, it was an uneconomical process because the three steps of increasing piles, backfilling with sand and excavation were reworked. In addition, the existing and new piles stand under the underpinned building, so re-excavation under the replacement plate is performed in a confined space and large heavy machinery cannot be carried in, resulting in reduced construction efficiency. There were problems such as being forced to do so.
[0018]
Therefore, in the underpinning work in this embodiment, the reworking process is omitted to shorten the work period. That is, as shown in Fig. 1, the lower end of the replacement plate is used as the primary flooring machine, and the construction of the new pile and construction of the replacement plate are performed from there, and stress is introduced with the ground below the replacement plate remaining. Decided to do. The construction process can be shortened by omitting the three steps of pile pile, backfilling and excavation, and the introduction of stress prior to excavation under the replacement plate. The excavation under the replacement version can be performed in parallel. In addition, since the space for loading large heavy machinery can be secured at an early stage, the process has a good progress rate.
[0019]
(Structural analysis model)
When a replacement load is applied at the time of stress introduction and the structure is jacked up, a vertical upward force is applied to the existing pile, and a vertical downward force is applied to the new pile. The upward force of the existing piles will affect the new piles through the surrounding ground, and it is thought that a phenomenon will occur that offsets part of the settlement.
[0020]
Therefore, in the present invention, when modeling the existing structure and the replacement structure with a framework structure, as shown in FIG. 3, a spring for evaluating the interaction between the existing pile and the new pile via the surrounding ground A model having a composite spring in consideration of That is, the replacement plate is modeled with a frame structure or the like, and this is supported by the composite spring. The spring constants Kv and Kr of this composite spring are expressed by the following equations (1a) and (1b).
[0021]
[Expression 1]

Where, Kv: Spring constant of the vertical composite spring of the pile (kN / m)
Kr: Spring constant of compound spring in the direction of pile rotation (kN · m / rad)
kp: Spring constant of the spring for evaluating the elastic deformation of the pile (kN / m)
kv: Spring constant of the spring to evaluate the ground reaction force at the tip of the pile (kN / m)
ksv: Spring constant (kN / m) of the spring that evaluates the vertical shear ground reaction force on the circumference of the pile
kint: Spring constant (kN / m) of the spring that evaluates the interaction between the existing pile and the new pile on the circumference of the pile
Iy: Second moment of pile group around y axis (m²)
[0022]
Equation (1a) is the spring constant of the composite spring proposed in the present invention, and comprehensively evaluates the spring constant of the spring in the vertical direction of the pile. That is, the composite spring includes a spring kp for evaluating the elastic deformation of the pile acting on the axis of the pile, a spring kv for evaluating the ground reaction force at the tip of the pile, and a spring ksv for evaluating the ground reaction force on the circumferential surface of the pile. A spring kint for evaluating the interaction between the existing pile and the new pile, and a spring kv for evaluating the elastic deformation of the pile acting on the axis of the pile and a spring kv for evaluating the ground reaction force at the tip of the pile A spring ksv that evaluates the vertical shear ground reaction force of the pile peripheral surface acting on the peripheral surface of the pile and a spring kint that evaluates the interaction between the existing pile and the new pile Are connected in parallel.
[0023]
Formula (1b) is a composite spring in the rotating direction that should be considered according to the structure of the foundation of the structure. Standards for railway structures (▲ 1) Japan Society of Civil Engineers: National Railway Building Design Standards Explanation, Foundation Structure Anti-earth pressure structure, Gihodo, March 1986. (2) Supervised by the Ministry of Transport, Railway Technical Research Institute: Railway structure design standards and explanation (foundation structure / anti-earth pressure structure), Maruzen, March. 1997.) And so on. When the footing of the structure is supported by the pile group, if the x axis and the y axis are determined as shown in FIG. 4, the secondary moment Iy around the y axis is the distance xi from the y axis to each pile. The spring constant Kr of the rotational spring in the rotational direction at the pile head of the pile group is determined from the sum of squares.
[0024]
Hereinafter, a method for calculating the spring constant of each spring constituting the composite spring will be specifically described.
[0025]
(1) Calculation of spring constant of spring to evaluate elastic deformation of pile
The spring constant kp of the spring for evaluating the elastic deformation of the pile is given by the following equation (2).
[0026]
[Expression 2]

Where Ep is the elastic modulus of the new pile (kN / m²)
Ap: sectional area of the shaft of the new pile (m²)
Lp: Length of new pile (m)
[0027]
(2) Calculation of spring constant of spring to evaluate ground reaction force at the tip of pile
The spring constant kv of the spring for evaluating the ground reaction force at the pile tip is given by the following equations (3a) and (3b).
[0028]
[Equation 3]

Where kv^*: Vertical ground reaction force coefficient (kN / m) at the tip of the new pile^Three)
Apv: Cross section of the tip of the new pile (m²)
α: Es calculation method and correction factor for load conditions
Es: Ground deformation coefficient (kN / m²)
D: Diameter of the tip of the new pile (m)
[0029]
In addition, ground reaction force coefficient kv of equation (3b) and equation (4b) shown below^*, Ksvi^*For the calculation of railroad structure standards (▲ 1 ▼ Civil Engineering Society: Japanese National Railways building design standard explanation, foundation structure anti-earth pressure structure, Gihodo, March 1986. ▲ 2 ▼ supervised by the Ministry of Transport, Railway General Technology Research) Tokoro: We used the method shown in Design Standards for Railroad Structures and Explanations (foundation structure / anti-earth pressure structure), Maruzen, March. 1997). In addition, the ground deformation coefficient Es in the equations (3b) and (4b) is determined from the results of the in-hole horizontal loading test and the indoor soil test.
[0030]
(3) Calculation of spring constant of spring ksv to evaluate ground reaction force on pile circumference
The spring constant ksv of the spring that evaluates the vertical shear ground reaction force of the pile circumference is calculated by the following equations (4a) and (4b).
[0031]
[Expression 4]

Where ksvi^*： Vertical shear ground reaction force coefficient (kN / m)^Three)
Ui: Peripheral area of piles located in each layer (m²)
n: Number of formations
[0032]
(4) Calculation of the spring constant of the spring considering the interaction between piles
When the stress is introduced, the existing piles are displaced vertically upward with the behavior of the building, and the settlement of the new piles is offset. In other words, the load transmitted from the peripheral surface of the existing pile to the surrounding ground is considered to cause the new pile to rise relatively from the temporary simple settlement position by shearing the ground. The displacement prediction of the structure in the conventional underpinning does not show very good agreement because it does not consider the interaction between the piles. In this study, this interaction between piles and piles is considered to be Mindlin's solution (RD Mindlin: Force at a point in the interior of a) when a concentrated load is applied to a semi-infinite elastic ground. semi-infinite solid, Physics, vol 7, pp.195-202, 1936.)
[0033]
(a) Characteristics of Mindlin solution
The basic theory of elasticity used to calculate the stress in the ground includes the Boussinesq solution when a concentrated load is applied vertically to the ground surface, and the Cerruti solution when the load is applied horizontally. In the problem of interaction between piles in underpinning, it is appropriate to use the Mindlin solution when a concentrated load is applied inside the ground considering the action position of the load.
[0034]
In the cylindrical coordinate system (r, θ, z) shown in FIG. 5, the underground stress solution and displacement solution when the vertical concentrated load P is applied to the semi-infinite elastic ground, that is, Mindlin stress solution and displacement solution are as follows. It is given by equations (5a) and (5b).
[0035]
[Equation 5]

Where σ_z: Vertical stress
P: Concentrated load
ν: Poisson's ratio
z, D, R1, R2: See Fig. 5
u: Vertical displacement
G: Shear elastic modulus
[0036]
(b) Examination of applicability of Mindlin solution to interaction problems
There are many studies on the interaction between piles and piles in the field of group pile foundations. In the method based on elasticity theory, Yamazato and Yao (9th Geotechnical Engineering Conference, pp.481-484, 1974.6.) This study discusses the resistance and subsidence mechanism of a pile group foundation subjected to vertical load. Due to the displacement influence coefficient using Mindlin's solution, the pile pile foundation has a reduced load sharing ratio and frictional resistance around the pile at the center (because the ground sinks with the pile), resulting in reduced pile efficiency. Explain what to do. Yamamoto, Tominaga, Yamashiro (Evaluation Method of Underground Displacement in Pile Interaction Problems, Structural Engineering, Vol 32B, pp.29-38, 1986.3.) It shows that the influence of the difference in rigidity between the ground and the pile body occurs only in the vicinity of the applied point. An event common to these is to use a Mindlin solution as a displacement influence coefficient for obtaining a displacement at an arbitrary point, and to evaluate an interaction by this, and an evaluation of an interaction using a spring is not observed.
[0037]
On the other hand, the Mindlin solution is due to concentrated loads in semi-infinite elastic ground, so care must be taken in its application.
[0038]
First, regarding the problems related to the deformation characteristics of the ground, it is necessary to examine this effect because the Mindlin solution includes Poisson's ratio. Hirayama (consolidation analysis of pile foundation, soil and foundation, pp.15-17, 1997.2.) Reveals that the influence of Poisson's ratio on the stress solution is not so great. Here, the influence of the ground characteristics on the displacement solution is considered.
[0039]
FIG. 6 shows the displacement distribution in the ground using the Poisson's ratio as a parameter. In the figure, δv is the vertical displacement found in the Mindlin solution, Pi is the load acting vertically on the center of the pile, Es is the ground deformation coefficient, z is the depth in the ground, and L is the depth of the pile. The length, r is the horizontal distance from the center of the pile, and D is the diameter of the pile. From this figure, it can be seen that the influence of the Poisson's ratio in the displacement solution is not so small even in the region where r / D> 10. Therefore, when the ground around the underpinning is complex, the spring constant k-int of the interaction spring using the method shown in FIG.^n-1Was considered to be able to be calculated. That is, the underground stress σz at the boundary due to the peripheral frictional stress fn of the existing pile of n layer, which is the lower layer of n-1 layer^n-1And the spring constant kint of the interaction spring of the n-1 layer from the sum of the elastic solutions by the peripheral frictional stress fn-1 of the n-1 layer^n-1It is an idea that can be evaluated.
[0040]
[Formula 6]

Where kint^n-1: Spring constant of interaction spring of n-1 layer
kint^n-1(σ_zn-1): Spring constant of the interaction spring due to the influence of the stress in the ground of n-1 layer
kint^n-1(f_n-1) ： The spring constant of the interaction spring due to the influence of the frictional stress around the n-1 pile
[0041]
Next, regarding the concentrated load, this can be dealt with by replacing the concentrated load with a distributed load equivalent to the concentrated load. However, since the calculation becomes complicated, it is considered that the influence of the interaction may be directly evaluated from the concentrated load when there is a certain distance from the loading point.
[0042]
(c) Calculation of spring constant of spring for evaluating interaction
Based on the above, the spring constant kint of the spring for evaluating the interaction between the existing pile and the new pile is obtained by the following method.
[0043]
A vertically upward force acts on the peripheral surface of the new pile due to the force transmitted from the peripheral surface of the existing pile to the ground. Now, as shown in FIG. 8, assuming a minute area dA of the pile peripheral surface, τ_rz ^{r = a}It is thought that the force becomes. In the section of the minute length dz in the axial direction of the pile, the force of the following formula (7) is acting.
[0044]
[Expression 7]

[0045]
On the other hand, the ground around the pile surface is δ upward in the vertical direction due to the upward force due to the force transmitted from the peripheral surface of the existing pile to the ground._ziDisplace only. Assuming that there is no relative displacement between the pile and the ground at the periphery of the pile, the vertical upward displacement δ_ziIs the amount of settlement of the new pile that is offset. If this phenomenon is regarded as the resistance of settlement of the new pile, it is convenient to evaluate this with a spring, and the spring constant of this spring is the vertical upward force acting on the peripheral surface of the new pile and the vertical upward force of the new pile. It can be expressed as a ratio to the amount of displacement.
[0046]
The spring constant kint of the spring for evaluating the interaction between the existing pile and the new pile was calculated from the following equations (8a) and (8b) with reference to FIG.
[0047]
[Equation 8]

Where τ_rzi: Stress solution (kN / m by Mindlin's first solution)²)
δ_zi: Mindlin's first solution (m)
I_p: Coefficient representing the effect of pile shape (1.0 here)
n: Number of existing piles affecting the new pile
l: Length of new piles in the ground (m)
a: Radius of new pile (m)
[0048]
(5) Calculation of spring constant of spring to evaluate ground reaction force under replacement plate
The spring constant ks of the ground spring under the replacement version is calculated by the following formulas (9a) and (9b). The ground reaction force coefficient was estimated using the method indicated in the railway structure standards.
[0049]
[Equation 9]

Where A_v0: Unit area at the bottom of replacement plate (m²)
ks^*: Ground reaction force coefficient in the vertical direction at the bottom of the replacement plate (kN / m^Three)
ks0^*: Ground reaction force coefficient (kN / m) estimated from the deformation coefficient obtained from soil tests^Three(Determined by the following formula (10).)
[0050]
[Expression 10]

α: Es calculation method and correction factor for load conditions
Es: Ground deformation coefficient (kN / m²)
Bs: Converted loading width of foundation (m)
[0051]
(6) Calculation of spring constant of spring to evaluate the behavior of existing structure
In general, when the object of underpinning is a relatively large building or the like, there are many cases where a part of the object is replaced by multipoint support. For this reason, it is desirable to calculate the amount of displacement at an arbitrary point by applying a load or displacement to a structural model obtained by evaluating a building with a three-dimensional frame structure or the like. However, since the rigidity of the building is affected not only by the rigidity of the underground beam and foundation slab but also by the rigidity of the upper beams, walls, columns, etc., it is difficult to properly model the structure. In addition, it is difficult to properly evaluate the rigidity of aging buildings.
[0052]
Therefore, the displacement of the building was calculated by the following formulas (11a) and (11b).
[0053]
[Expression 11]

Where δi is the vertical displacement of the pile head of the existing pile (m)
Pi: Stress introduction load (kN)
K_v ^u： Spring constant (kN / m) of vertical composite spring for evaluating the behavior of existing piles
[0054]
As shown in FIG. 9, the vertical displacement δi of the pile head of each existing pile was calculated by equation (11a), and this was taken as the displacement at that point of the building. The predicted value of the building displacement by this method does not consider the rigidity of the building. Therefore, when unequal displacement occurs at each point of the building, it can be inferred that the predicted value is calculated to be slightly larger than the actually measured value.
[0055]
Also, the vertical spring constant K when calculating the displacement of the existing pile shown in equation (11b)_v ^uIs different from the spring constant of the compound spring shown in equation (1a) in that kvt in the first term on the right side and kint in the third term on the right side.^uIt is two places. Next, consider this.
[0056]
(a) Calculation of the spring constant of the spring to evaluate the main behavior of the ground near the pile tip
Kimura and Koizumi taking the design of shield tunnel lining as an example (For the design method of shield tunnel considering the interaction between ground and lining, Journal of Japan Society of Civil Engineers, No.624 / III-47, pp.123-134, According to the research of 1999.6.), When the lining deforms to the outside of the tunnel and the ground shows passive behavior, and when the lining deforms to the air side inside the tunnel and the ground shows primary behavior, The deformation characteristics are different. When modeling these behaviors with elastic springs, it is determined from model experiments that the spring constant of the spring that evaluates the primary behavior is about half that of the passive behavior. FIG. 10 is a diagram schematically showing the concept, and state a) is a state in which only the weight of the soil is acting on the soil column. The state b) is a state in which the soil pillar is contracted more than the state a) due to a building load or the like, and this is the state before the replacement. State c) is a state in which a new load is applied to state b) and the soil column is further compressed, and represents the passive behavior of the ground at the tip of the new pile when stress is introduced. State d) is a state in which the load is reduced to some extent from state b) and the soil column extends, and represents the main behavior of the ground at the tip of the existing pile at the time of stress introduction.
[0057]
From this, the spring constant kvt of the spring that evaluates the main behavior of the ground at the tip of the existing pile was calculated by the following equation.
[0058]
[Expression 12]

Where kvt: spring constant of the spring that evaluates the ground reaction force when the ground shows the dominant behavior in the compression region
kv: a spring constant of a spring for evaluating the ground reaction force when the ground exhibits passive behavior.
[0059]
(7) Calculation of spring constant of spring to evaluate interaction between replacement plate and existing pile
In the case of underpinning in this construction procedure in which stress is introduced with the ground pile under the replacement plate left, the interaction between the existing pile and the existing pile and between the existing pile and the bottom of the replacement plate Occurs during. Considering the distance from the load application position, the latter seems to be dominant. Therefore, we decided to evaluate the interaction between the existing pile and the replacement version.
[0060]
Spring constant kint of the spring that evaluates this interaction^uIs calculated by the following formulas (13a) and (13b). Note that the concept of calculating the spring constant is the same as Equation (8). However, considering the state in which the load acts, the underground stress propagation is evaluated by the Boussinesq solution. The acting load at this time was a replacement load acting on the jack shaft core.
[0061]
[Formula 13]

Where τ_rzi: Stress solution by Boussinesq (kN / m²)
δ_zi: Displacement solution by Boussinesq (m)
Ip: Coefficient representing the effect of pile shape (1.0 here)
n: Number of jack pedestals that affect existing piles
[0062]
In the cylindrical coordinate system (r, θ, z) shown in FIG. 11, the underground stress solution and displacement solution when the vertical concentrated load is applied to the ground surface, that is, the Boussinesq stress solution and displacement solution are expressed by the following equations ( 14a) (14b).
[0063]
[Expression 14]

Where σz: vertical stress
P: Concentrated load
z, R, r: see Fig. 11
ν: Poisson's ratio
G: Shear elastic modulus
[0064]
【Example】
Next, in this example, the validity of the displacement prediction method using the composite spring model was verified from the measurement results of the displacement of each point of the building obtained by actual underpinning work.
[0065]
(1) Overview of underpinning work
The target construction was underpinning of three buildings in the No. 1 Hiromachi tunnel construction area for the second stage construction of the Rinkai Fukutoshin Line. Daiichi Hiromachi Tunnel, located between Oimachi Station and Osaki Station, is a single-track railway tunnel with an outer diameter of 7100mm constructed by the shield method. On this route, there are two buildings, 12 buildings of JR Hiromachi company building (Buildings 6 and 3) and 8 buildings of RC building, Shinagawa Ward Disaster Prevention Center, 3 buildings in total. Underpinning was carried out because some of the foundation piles obstructed tunnel excavation.
[0066]
The replacement is the under beam method, and as shown in Table 1, 152.8MN of the total building weight of 618MN is replaced. In addition, as described above, in all three buildings, prestressing is introduced for the purpose of shortening the construction period (preloading is performed with the ground under the replacement plate remaining).
[0067]
[Table 1]

[0068]
As for the soil quality, the buried layer is distributed from the surface to about 1.8m, and the Musashino gravel layer with N value of about 30 is distributed below it with a thickness of about 3.4m. Furthermore, the Tokyo clay layer with an N value of about 10 (partially intervening with the Tokyo sand layer) is distributed about 16 m below it, and the Tokyo gravel layer with an N value of 50 or more, which is a supporting layer for surrounding structures, is distributed below it. This Tokyo gravel layer is rich in water. Permeability coefficient is k = 10^-1~Ten^-2It is in the range of cm / sec and has a pressure head of about 20m. For this reason, in order not to hinder the construction of replacement piles and the removal of existing piles, the ground is improved in advance by the double-pipe multiphase injection method over the entire replacement range.
[0069]
Moreover, as shown in Table 2, the removal piles are a total of 53 pieces having a diameter of φ800 to φ2000, and only the disaster prevention center is an expanded bottom pile. There are a total of 37 replacement piles with a diameter of φ2000 to φ2200. 12 to 15 show the status of the replacement.
[0070]
[Table 2]

[0071]
(2) Comparison between measured values and predicted values and discussion
(a) Behavior of building and replacement version
FIGS. 16 and 17 show the displacement behavior of the building and the replacement version at the time of stress introduction in the two JR company houses (Building No. 6, Building No. 3). In the figure, black circles represent measured values, white triangles represent predicted values obtained by the conventional method, and white diamonds represent predicted values obtained by the composite spring model according to the present invention. The conventional method used here is based on the spring constant of the spring that evaluates the behavior of the pile, based on the Japan Society of Civil Engineers: National Railway Building Design Guidelines, Pile Earth Structure, pp.182-183, 1986.3. Calculated. The upper half shows the amount of uplift at each point of the building, and the lower half shows the amount of subsidence at each point of the replacement version.
[0072]
From these figures, it can be seen that the predicted value by the composite spring model shows better agreement with the actually measured value as compared with the predicted value by the conventional method. The predicted value of the building displacement at point E-6 shown in Fig. 16 (d) and B-3 point shown in Fig. 17 (b) is slightly different from the actual measured value. It is thought to be due to. In other words, the effects of rigidity of underground beams, foundation slabs and columns, walls, upper beams, etc. of buildings outside the scope of the prediction calculation, or peripheral friction of the foundation piles in that part are compared with other points. Since it is large, it seems that the displacement of the point was suppressed. This is related to the leveling of the building, etc. When it is necessary to jack up a place adjacent to such a non-replacement part, a jack having sufficient margin for the design load is arranged. It shows that it is necessary.
[0073]
FIG. 18 shows the behavior of the Shinagawa Ward Disaster Prevention Center building and the replacement version. From this figure, it can be seen that the predicted value by the composite spring model explains the measured value better than the predicted value by the conventional method. However, the displacement of the building (displacement shown in the upper half in the figure) does not show a very good agreement, which seems to be due to the fact that the existing pile at the Disaster Prevention Center is an expanded bottom pile. Because the bottom of the pile has a tapered shape where the tip of the pile spreads downward, it is considered that when a vertically upward load is applied to the pile, this tapered portion behaves in the direction pressed against the ground, It is considered that the actual displacement amount has been reduced.
[0074]
If the coefficient Ip for evaluating the shape of the pile in the above equation (13b) is calculated back so that the predicted value and the actual measurement value coincide with each other, Ip = 6 to 7 in the case of this expanded bottom pile. The shape factor Ip should be determined in consideration of factors such as the type of pile, the shape of the expanded bottom, and the deformation characteristics of the surrounding ground, and this result cannot be applied to other constructions as it is. However, the predicted value by the composite spring model has the same displacement distribution shape as the actual measurement value, and the value shows a better match compared to the conventional method. Even in the vicinity of the non-replacement part, it seems that it can be applied to the health check of buildings.
[0075]
(b) Quantitative evaluation of compatibility of composite spring model
It was found that the predicted value by the composite spring model is much more compatible with the measured value than the conventional method. Moreover, it was shown that the displacement of the building may be affected by the rigidity of the building body in the vicinity of the non-replacement part. Here, we attempt to quantitatively evaluate the suitability of the composite spring model using the position from the non-replacement part as an index. The method for evaluating conformity is described below.
[0076]
The actual measured value and the predicted value of the displacement of each point of the building are m_i, A_iIn addition, when the total number of measurement points having the same distance from the non-replacement unit is N, an average difference between the actual measurement value and the predicted value over the entire replacement unit is expressed by Expression (15). S in formula (15)²Is called dispersion for convenience, and this dispersion S²The smaller the value of, the higher the suitability.
[0077]
[Expression 15]

In addition, all the measuring points of Shinagawa City Disaster Prevention Center are excluded here because the distance from the non-replacement part is the same. In addition, the position of the non-replacement unit is indexed based on the dimensionless expression according to Equation (16) (see FIG. 19).
[0078]
[Expression 16]

Where Lx, Ly: width and depth of the whole building (m)
Lx^u, Ly^uA: Width and depth of the replacement part (m)
Lxⁱ: Distance from non-replacement part to measurement point (m)
[0079]
FIG. 20 shows a result of comparison between the predicted value obtained by the conventional method and the predicted value obtained by the composite spring model. From this figure, it can be seen that the predicted value by the composite spring model is more compatible with the actually measured value quantitatively than the predicted value by the conventional prediction method. In addition, the dispersion is large when the dimensionless position from the non-replacement unit is within 0.2. That is, it can be seen that the prediction accuracy is reduced.
[0080]
In predicting the behavior of underpinning work, the accuracy required depends on the type of existing structure to be replaced and its importance. For example, in the case of JR company building No. 6, the primary control value of 4.20mm relative displacement between piles and 10.00mm absolute displacement of piles is combined with an average error of 4.18mm as predicted by the conventional method. It can be seen from FIG. 16 that the predicted value by the spring model has an average error of 0.48 mm. Assuming a case in which the predicted values of adjacent piles are values on the danger side, in this construction, it is necessary to have a prediction accuracy of at least about 2.00 mm.
[0081]
(3) Examination of the applicability of the composite spring model to an underpinning construction example where the surrounding area is a complex alternating layer ground
From the above results, it was found that the composite spring model has applicability in a layered ground of about two or three layers. Next, the displacement behavior was predicted for underpinning under more complex ground conditions, and it was decided whether or not the composite spring model could be applied to alternate layers. The interaction spring in the composite spring model is calculated based on the Mindlin solution. As already mentioned, the Mindlin solution is intended for semi-infinite elastic ground, so it cannot be applied directly to alternate ground. Therefore, in this study case, we decided to evaluate from the sum of elastic solutions due to distributed load as shown in Eq. (6).
[0082]
(a) Overview of underpinning work
The target verification example is Nanya Building's underpinning work in Ningyocho No. 11 Ningyo-cho, constructed in 1985. Nanya Building is an 8-story SRC structure and is supported by a total of 10 cast-in-place piles (φ1500 = 8, φ1000 = 2). The total weight of the building is 31MN, of which 26.3MN is replaced (see Fig. 21).
[0083]
The soil is a soft layer about 4.5m from the pile head, and the alternating layer of fine sand and sand mixed silt with N value of about 0-1 is distributed. Below that, a clay layer with an N value of 8 is about 8.0 m, a fine sand layer with an N value of 30 is about 3.0 m, and a clay layer with an N value of 10 is about 5.0 m.
[0084]
(b) Comparison between the measured value and the predicted value and its consideration
FIG. 22 shows measured values and predicted values of displacement behavior of the building and the replacement version at the time of stress introduction in Nanya Building. From this figure, it can be seen that the predicted value by the composite spring model is in good agreement with the actually measured value as compared with the predicted value by the conventional method.
[0085]
Fig. 23 shows the distributed S in the case of Nanya Building and JR Building No. 6²Is a comparison. The horizontal axis in the figure represents the distance from the end of the replacement plate, but Nanyaville's underpinning has no non-replacement portion, so it has no engineering significance. In addition, JR Building 6 is excluded from the area affected by the non-replacement department.
[0086]
From this figure, it can be seen that the predicted value of the displacement behavior of the Nanya Building has a larger range of dispersion compared to that of the JR Building No. 6, and the estimation accuracy is reduced. However, the square root S of dispersion is 0.60 mm on average, and considering the scale of replacement and the span of the pile, the prediction accuracy in practical use is considered to be sufficiently high. The composite spring model presented in this study is It can be seen that it can also be applied to underpinning work in alternate layers.
[0087]
【The invention's effect】
As described above in detail, according to the present invention, in underpinning work, when predicting the displacement behavior of an existing structure or a structure such as a replacement structure when stress is introduced (at the time of replacement), the predicted value and the actual measurement value It is possible to propose a prediction method in which the two are accurately matched, and it is possible to appropriately evaluate the soundness of the building at the beginning of replacement, the replacement load, and the soundness of the final building and replacement structure. Become.
[Brief description of the drawings]
FIG. 1 is a construction procedure diagram of underpinning in the present embodiment.
FIG. 2 is a conventional underpinning construction procedure diagram.
FIG. 3 is a conceptual diagram of a composite spring model according to the present invention.
FIG. 4 is an explanatory diagram of a calculation method of a spring constant of a rotary spring of a pile group.
FIG. 5 is a diagram showing a coordinate system of a Mindlin solution.
FIG. 6 is a relationship diagram between a displacement solution by Mindlin and ground characteristics.
FIG. 7 is an explanatory diagram of a method for calculating an interaction spring in an alternating layer ground.
FIG. 8 is an explanatory diagram of a method for calculating a spring constant of an interaction spring based on a Mindlin solution.
FIG. 9 is an explanatory diagram of a method for calculating a building displacement.
FIG. 10 is an explanatory diagram of a spring for evaluating the ground reaction force when the ground shows a main earth pressure behavior in the compression region.
FIG. 11 is a diagram illustrating a coordinate system of a Boussinesq solution.
FIG. 12 is an example (part 1) of underpinning of JR company housing No. 6 in the example.
FIG. 13 is an example (part 2) of underpinning of JR company housing No. 3 in the example.
FIG. 14 is an example (part 3) of underpinning of the Shinagawa Ward Disaster Prevention Center in the example.
FIG. 15 is a sectional view of the replacement status.
FIG. 16 is a comparison diagram between actual measurement values and predicted values in an underpinning example (part 1).
FIG. 17 is a comparison diagram between actual measurement values and predicted values in an underpinning example (part 2).
FIG. 18 is a comparison diagram between an actual measurement value and a predicted value in an underpinning example (part 3).
FIG. 19 is an index diagram in which the position from the non-replacement unit used for quantitative evaluation of the analysis model is made dimensionless.
FIG. 20 is a quantitative evaluation diagram of an analysis model.
FIG. 21 is a diagram showing the replacement status of Nanya Building.
FIG. 22 is a comparison diagram between actually measured values and predicted values in Nanya Building.
[Figure 23] Variance S of predicted building displacement between Nanya Building and JR Building 6²FIG.

Claims (4)

In order to predict the displacement behavior of the existing structure or replacement structure in underpinning in which part or all of the existing structure including the pile foundation is replaced by a replacement structure including a pile foundation newly provided in the basement Prediction method,
In modeling by the existing structures and受替structure to frame structure, sets the model having a composite spring in consideration of the spring to assess the interaction between existing設杭a new pile that intervention of the surrounding ground The method for predicting the displacement behavior of a structure in underpinning, characterized by analyzing the displacement behavior at the time of replacement. The composite spring model includes an interaction between a spring for evaluating the elastic deformation of the pile, a spring for evaluating the ground reaction force at the tip of the pile, a spring for evaluating the ground reaction force on the circumferential surface of the pile, and the existing pile and the new pile. The springs that act on the axis of the pile are connected in series, and the springs that act on the circumferential surface of the pile are connected in parallel, and the behavior between the pile body and the pile and the ground The method for predicting the displacement behavior of a structure in underpinning according to claim 1, wherein: The prediction method of the displacement behavior of the structure in the underpinning according to claim 2, wherein a composite spring in the rotation direction of the pile is set according to the basic structure of the replacement structure. In calculating the spring constant of a spring that evaluates the interaction between an existing pile and a new pile, Mindlin's solution that gives stress and displacement at an arbitrary point when concentrated load acts on a semi-infinite elastic ground is used. The prediction method of the displacement behavior of the structure in the underpinning in any one.

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