JP4555977B2 - Ground improvement method - Google Patents
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- JP4555977B2 JP4555977B2 JP2005109173A JP2005109173A JP4555977B2 JP 4555977 B2 JP4555977 B2 JP 4555977B2 JP 2005109173 A JP2005109173 A JP 2005109173A JP 2005109173 A JP2005109173 A JP 2005109173A JP 4555977 B2 JP4555977 B2 JP 4555977B2
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本発明は、主として砂質地盤の液状化防止を目的とした薬液注入による地盤改良工法に関する。 The present invention relates to a ground improvement method by chemical injection mainly for the purpose of preventing liquefaction of sandy ground.
従来、地震発生時における砂質地盤の液状化防止の工法としては、地中に一定間隔毎に縦向きの透水性砂杭を形成し、地震によって遊離した砂土壌間隙水を、前記砂杭を通じて排出させることによって地盤の液状化を防止するサンドコンパクションパイル工法や、回転軸の外周に撹拌翼を備えるとともに該撹拌翼からセメントミルクなどの固化材を吐出できるようにした地盤撹拌器を使用し、該地盤撹拌器を縦向きに地盤中に回転させながら挿入し、地盤を撹拌させながら固化材を注入することにより地盤中に固化材を混合させ、これによって縦向きの円柱状をした地盤固化柱を形成する機械撹拌方式による地盤改良工法(深層混合工法とも称される工法)がある。 Conventionally, as a method of preventing liquefaction of sandy ground in the event of an earthquake, a vertically permeable sand pile is formed in the ground at regular intervals, and sand soil pore water released by an earthquake is passed through the sand pile. Using a sand compaction pile method that prevents liquefaction of the ground by discharging, a ground agitator equipped with a stirring blade on the outer periphery of the rotating shaft and capable of discharging a solidified material such as cement milk from the stirring blade, The ground agitator is inserted into the ground while being rotated vertically, and the solidified material is mixed into the ground by injecting the solidified material while stirring the ground. There is a ground improvement method (a method called a deep mixing method) using a mechanical agitation method to form a layer.
これらの工法は、既存の建造物下の地盤に対して施工する場合には、既存建物を撤去しなければならない場合が多く、また撤去しなくともその建物共用停止期間が長くなり、社会的影響が大きいという問題がある。更に使用機材や固化剤に多くの費用を要し、経済的理由による問題も大きい。 When these methods are applied to the ground under existing structures, existing buildings often have to be removed. There is a problem that is large. In addition, the equipment used and the solidifying agent require a large amount of money, and there are significant problems for economic reasons.
これらの問題を解決できるものとして、近年、土壌間隙に固化用の薬液を浸透させて、地盤の強度を高める溶液型薬液注入工法(浸透固化処理工法とも称されている)が開発されている。この方法は、地盤中にシリカ系の溶液型薬液を注入して固化する工法であり、地盤中に挿入したストレーナを通じて薬液を注入することによって地盤を固化させる工法である。 In order to solve these problems, in recent years, a solution-type chemical solution injection method (also referred to as an osmotic solidification treatment method) has been developed in which a solid chemical solution is infiltrated into a soil gap to increase the strength of the ground. This method is a method of injecting and solidifying a silica-based solution-type chemical into the ground, and a method of solidifying the ground by injecting the chemical through a strainer inserted into the ground.
この薬液注入工法は、ドリリングマシンを使用することによって、垂直のみならず、傾斜方向、水平方向、更にはそれらを織り交ぜた方向の穿孔が可能であるため、基礎杭や地中配管が複雑に入り組んでいる石油貯蔵設備下のような地盤に対しても既存施設の共用を停止させないで施工できるという利点がある(例えば非特許文献1)。 In this chemical injection method, drilling machines can be used to drill not only vertically but also in the inclined direction, the horizontal direction, and the direction in which they are interwoven. There is an advantage that construction can be carried out without stopping the sharing of existing facilities even for ground such as under complicated oil storage facilities (for example, Non-Patent Document 1).
また、この薬液注入工法において、地盤をより均一に固化させるための工法(例えば特許文献1)や、使用する薬液量をより少なくして必要な地盤改良を行うための工法(例えば特許文献2)が開発されている。 In addition, in this chemical solution injection method, a method for solidifying the ground more uniformly (for example, Patent Document 1) and a method for performing necessary ground improvement by reducing the amount of chemical solution to be used (for example, Patent Document 2). Has been developed.
特許文献2に示されている使用薬液量を減少させる方法は、図8に示すように地盤改良予定地盤1中に所定間隔毎に設定した多数の薬液注入点aからそれぞれストレーナ2を使用して薬液を注入することにより、各注入点を中心にしてその周囲に球状に薬液を浸透させて球状固化体3,3......多数を形成するものであり、その際の薬液注入量を調整して球状固化体3,3相互間を互いに接触させることによって、安定した固化地盤を形成させるものである。図9(a)〜(d)は注入量の違いによる改良率を示しており、(a)は改良率が100%である場合、(b)は改良率が70%である場合、(c)は改良率が50%である場合、(d)は改良率が30%である場合をそれぞれ示している。地盤中の地下水を除いた場合の土壌間空隙量に対する50%以上の薬液を注入した場合に(c)に示すように球状固化体3,3が接触し、相互に移動不能となって安定した地盤が形成されるものである。
上述した従来の薬液注入工法における薬液使用量の低減化方法では、各球状固化体間に未改良部分を残すことによって薬液使用量を低減させてコストダウンを図るものであるが、この場合、薬液量が少ないと地盤中に残る未改良部分が連続した状態となり、このため、図10に示すように、地震発生時に改良範囲の外側で生じた液状化によって発生した過剰土壌間隙水圧が改良範囲4内に作用し、球状固化体間の未改良部分を液状化させるという問題がある。 In the method for reducing the amount of chemical used in the conventional chemical injection method described above, the amount of chemical used is reduced by leaving an unimproved portion between the spherical solidified bodies. When the amount is small, the unimproved portion remaining in the ground is in a continuous state. For this reason, as shown in FIG. 10, the excess soil pore water pressure generated by liquefaction occurring outside the improved range at the time of the earthquake is improved. There is a problem that the unmodified portion between the spherical solidified bodies is liquefied.
本発明は、このような問題に鑑み、土壌間空隙より少ない薬液使用量であっても、液状化がより効果的に防止できる薬液注入による地盤改良工法の提供を目的としてなされたものである。 In view of such problems, the present invention has been made for the purpose of providing a ground improvement method by injecting a chemical solution that can more effectively prevent liquefaction even when the amount of the chemical solution used is less than the space between soils.
上述の如き従来の問題を解決し、所期の目的を達成するための請求項1に記載の発明の特徴は、改良しようとする砂質地盤中に上下方向及び水平方向に間隔を隔てて多数の薬液注入位置を設定し、その各薬液注入位置に地盤固化用の溶液型薬液を注入して該地盤中の土壌間空隙内に浸透させることにより各薬液注入位置の周囲の地盤に薬液が浸透した薬液浸透域を形成し、その互いに隣り合う薬液注入位置の外側に形成される薬液浸透域の外周部分を互いに連続させることにより前記各囲薬液浸透域が連続した固化体が形成されるようにしてなる薬液注入による地盤改良工法において、
前記各薬液注入位置において所定量の前記地盤固化用の薬液を注入した後、その薬液注入位置から、先に形成された注入された地盤中の薬液を外側に押し出すための水を注入して該地盤中に浸透させることにより前記各薬液浸透域内に水浸透域を形成し、該水浸透域を形成することによって拡張された各薬液浸透域の外周部分を連続させて互いに連続した固化体となすことにある。
In order to solve the above-mentioned conventional problems and achieve the intended object, the features of the invention described in claim 1 are many in the sandy ground to be improved at intervals in the vertical and horizontal directions. The chemical solution injects into the ground around each chemical injection position by injecting the solution type chemical solution for solidification into each chemical injection position and penetrating it into the space between soils in the ground. And forming a solidified body in which the surrounding permeation liquid permeation areas are continuous by forming the permeation areas of the medicinal liquid permeation areas that are formed outside the adjacent chemical liquid injection positions. In the ground improvement method by chemical injection,
After injecting a predetermined amount of the chemical solution for solidification at each chemical solution injection position, water for injecting the chemical solution in the injected ground formed previously is injected from the chemical solution injection position to to each chemical penetration region by infiltrating into the ground to form a water-permeable zone solidified body and which is sequencing outer peripheral portion of each liquid chemical penetration range has been extended by forming the water penetration zone continuous with each other There is to do.
請求項2に記載の発明特徴は、前記請求項1の構成に加え、前記各薬液浸透域内への水の注入により、互いに隣り合う薬液浸透域間に薬液未注入部分が残らない状態まで各薬液浸透域の外周部分を拡張させることにある。
Invention features of
請求項3に記載の発明特徴は、前記請求項1又は2の構成に加え、改良しようとする地盤にドリリングマシンにより注入作業孔を穿孔し、該注入作業孔にストレーナを挿入し、該ストレーナに形成した同一の注液ノズルを使用して薬液及び薬液浸透域拡張用の水を順に注入することにある。
The invention feature of
請求項4に記載の発明特徴は、前記請求項1,2又は3の構成に加え、ストレーナの注液ノズル位置を挟む上下の2箇所に、注水によって膨張するパッカーを設置しておき、注入作業孔内にストレーナを所定の深さまで挿入した後、前記パッカーを膨張させて前記注液ノズルの上下において該ストレーナと地盤に開けた注入作業孔の内面との隙間を水密状態に埋めた状態で前記薬液及び薬液浸透域拡張用の水の注入を行うことにある。 In addition to the structure of the first, second, or third aspect, the invention feature of the fourth aspect is characterized in that packers that are expanded by water injection are installed at two locations above and below the position of the liquid injection nozzle of the strainer. After inserting the strainer into the hole to a predetermined depth, the packer is expanded to fill the gap between the strainer and the inner surface of the injection hole formed in the ground above and below the liquid injection nozzle in a watertight state. The purpose is to inject the chemical solution and water for expanding the chemical solution permeation area.
請求項5に記載の発明特徴は、前記請求項1〜3又は4の構成に加え、地盤固化用の薬液として、シリカ系水溶液型薬液を使用することにある。 The invention feature of claim 5 is that, in addition to the structure of claims 1 to 3 or 4 described above, a silica-based aqueous solution type chemical solution is used as the chemical solution for solidifying the ground.
本発明に係る薬液注入による地盤改良工法においては、請求項1のように改良しようとする地盤中に上下方向及び水平方向に間隔を隔てて多数の薬液注入位置を設定し、その各薬液注入位置に地盤固化用の薬液を注入することにより該地盤中の土壌間空隙内に薬液を浸透させ、互いに隣り合う薬液注入位置に形成される薬液浸透域の外周部分が地盤中で連続されて連続した固化体が形成させるに際し、前記各薬液注入位置において、所定量の薬液を注入した後、各薬液注入位置から前記薬液浸透域内の地盤中に該薬液浸透域を押し広げる薬液浸透域拡張用液体を注入して各薬液浸透域を拡張させ、該各薬液浸透域の外周部分を連続させて互いに連続した固化体となすようにすることにより、地盤固化用の薬液浸透域は、内部に別の液体が充填された球形の殻状に拡張されて隣接するものと一体がされるため、高価な薬液の使用量が減少する。特に、薬液浸透域の拡張用として水を使用しているため、使用材料が廉価であり、コストがより低減される。 In the ground improvement method by chemical solution injection according to the present invention, a number of chemical solution injection positions are set in the ground to be improved as in claim 1 at intervals in the vertical and horizontal directions, and each of these chemical solution injection positions is set. By injecting the chemical solution for solidification into the soil, the chemical solution penetrates into the inter-soil gap in the ground, and the outer peripheral part of the chemical solution infiltration area formed at the adjacent chemical solution injection position is continuous in the ground. When forming the solidified body, after injecting a predetermined amount of the chemical solution at each of the chemical solution injection positions, a liquid for extending the chemical solution infiltration area that spreads the chemical solution infiltration area into the ground in the chemical solution infiltration area from each of the chemical solution injection positions. By injecting and expanding each chemical solution permeation area, the peripheral part of each chemical solution permeation area is made continuous to form a continuous solidified body. Filled Because the is the shell-like integral with adjacent ones being expanded spherical amount of expensive chemical solution decreases. In particular, since water is used for expansion of the chemical solution permeation area, the material used is inexpensive and the cost is further reduced.
また、請求項2のように、薬液浸透域拡張用液体の注入により、互いに隣り合う薬液浸透域間に薬液未注入部分が残らない状態まで薬液浸透域を拡張させることにより、地盤改良を施した範囲内には、全体が薬液によって固化され地盤内に、拡張用液浸透域が独立して一定間隔を開けた状態で散在することとなり、地震時に地盤改良範囲外の遊離水によって加圧されたとしても、改良部分にこれが流れ込むことがなくなり、液状化がより完全に防止される。
In addition, as described in
更に、請求項3のように、改良しようとする地盤にドリリングマシンにより注入作業孔を穿孔し、該注入作業孔にストレーナを挿入し、該ストレーナに形成した同一の注液ノズルを使用して薬液及び薬液浸透域拡張用液体を順に注入することにより、効率よく薬液及び薬液浸透域拡張用液体の注入がなされる。
Furthermore, as in
更に、請求項4のようにストレーナの注液ノズル位置を挟む上下の2箇所に、注水によって膨張するパッカーを設置しておき、注入作業孔内にストレーナを所定の深さまで挿入した後、前記パッカーを膨張させて前記注液ノズルの上下において該ストレーナと地盤に開けた注入作業孔の内面との隙間を水密状態に埋めた状態で前記薬液及び薬液浸透域拡張用液体の注入を行うことにより、地盤に対する注入面を両パッカー間の間隔を広く取ることによって大きくでき、また、ストレーナの全周から地盤への注入が可能になり、注入効率が高い。 Furthermore, after the packer which expand | swells by water injection is installed in the upper and lower two places which pinch | interpose the liquid injection nozzle position of a strainer like Claim 4, after inserting a strainer into the injection | pouring operation hole to predetermined depth, the said packer By injecting the chemical solution and the liquid for expanding the chemical solution penetration region in a state where the gap between the strainer and the inner surface of the injection work hole opened in the ground is filled in a watertight state above and below the liquid injection nozzle, The injection surface with respect to the ground can be increased by widening the space between both packers, and the entire circumference of the strainer can be injected into the ground, resulting in high injection efficiency .
更に、請求項5のように、地盤固化用の薬液として、シリカ系水溶液型薬液を使用することにより、安定度の高い固化地盤を形成できる。 Further, as described in claim 5, by using a silica-based aqueous solution as the chemical for solidifying the ground, a highly stable solidified ground can be formed.
次に本発明の実施の形態を図1〜図7に示した実施例に基づいて説明する。図1はストレーナを使用した液体注入の状態を示しており、図において10は地盤改良予定地盤であり、11はドリリングマシンによって地表より先行した注入作業孔、12は該注入作業孔に挿入したストレーナ、13はストレーナ12へ注入液を圧送する加圧送液装置である。ストレーナ12内には中心部分に注入液流路14が形成され、その上端より加圧送液装置13より注入しようとする液体が供給されるようになっている。
Next, embodiments of the present invention will be described based on the examples shown in FIGS. FIG. 1 shows a state of liquid injection using a strainer. In FIG. 1, 10 is a ground to be improved, 11 is an injection work hole preceding the ground surface by a drilling machine, and 12 is a strainer inserted into the injection work hole. , 13 is a pressurized liquid feeding device that pumps the injected liquid to the
ストレーナ12には注入液流路に14に連通した注液ノズル15が外周の所定位置に開口され、その注液ノズル15を挟む上下の位置にパッカー16,16が備えられている。このパッカー16,16は内部に水などの液体を注入することにより膨張し、ストレーナ12の外周と注入作業孔11の内周面との間の隙間を液密状態に閉鎖するものであり、ノズル位置を所定の注入位置高さになるようにストレーナ12を挿入した後、パッカー16,16に注水して膨張させ、ノズル上下のストレーナ外周隙間を閉鎖させ、この状態で加圧送液装置13から注入液を注入する。これによって注入された液体は、パッカー16,16間の注入作業孔全内周面から注入液が地盤10中に、注入位置aを中心にして放射状に浸透し、球状の液浸透域Mが造成される。
The
同様にして図2に示すように、改良予定地盤10の表面より前後左右に一定間隔を隔て、多数の注入作業孔11,11...を格子状配置乃至は千鳥上配置に多数穿孔し、注入作業孔11,11...毎に液体の注入作業を行う。 Similarly, as shown in FIG. 2, a large number of injection work holes 11, 11... A liquid injection operation is performed for each of the injection operation holes 11, 11.
また図3に示すように、各注入作業孔11において上下に所定間隔を置いて注入位置aを設定し、改良予定地盤10の全深さにわたって順次一定間隔毎に液体の注入作業を行い、図4に示した模式図のように、液浸透域M,M......が上下左右に略等間隔に造成され、それらの周囲が隣り合うものと連続させるようにする。 Further, as shown in FIG. 3, the injection position a is set at a predetermined interval in each injection work hole 11, and liquid injection work is sequentially performed at regular intervals over the entire depth of the ground to be improved 10. As shown in the schematic diagram shown in FIG. 4, the liquid permeation areas M, M... Are formed at substantially equal intervals in the upper, lower, left, and right directions so that their periphery is continuous with adjacent ones.
各注入位置aでは先ず始めに予め設定した所定量の地盤固化用の溶液型薬液(以下単に薬液と記す)を注入する。これによって図5(a)に示すように、地盤中に、注入位置aを中心にして球形に薬液が浸透した薬液浸透域M1が形成される。ついで同じストレーナ12を使用して、水を使用した薬液浸透域拡張用の液(以下単に拡張用液と記す)を注入する。これによって図5(b)に示すように、拡張用液浸透域Wが注入位置aを中心にして形成され、この拡張用液によって薬液が地盤中を半径方向外側に移動されて薬液浸透域M1が半径方向に拡張された球形殻状の薬液浸透域M2が形成される。
At each injection position a, first, a predetermined amount of a solution-type chemical solution for ground solidification (hereinafter simply referred to as a chemical solution) is injected. As a result, as shown in FIG. 5A, a chemical solution permeation region M1 in which the chemical solution penetrates in a spherical shape with the injection position a as the center is formed in the ground. Next, the
このようにして、拡張用液浸透域Wを中心部に有する球形殻状の薬液浸透域M2を注入位置a,a......毎に形成し、隣り合う薬液浸透域M2が互いに連続されるように順次、薬液及び拡張用液の注入を行う。このようにして予定改良地盤全域に亘って薬液注入を行うことにより、各注入位置aを中心にした各薬液浸透域M2,M2......が一体化して固化した改良地盤が形成される。 In this way, a spherical shell-shaped medicinal solution permeation area M2 having an expansion liquid permeation area W at the center is formed for each injection position a, a..., And adjacent medicinal liquid penetration areas M2 are continuous with each other. Then, the chemical solution and the expansion solution are sequentially injected. In this way, by injecting the chemical solution over the entire area of the planned improved ground, an improved ground is formed in which the chemical solution infiltration regions M2, M2,... The
各注入位置aにおける薬液及び拡張用液の注入量を調整することによって、図6に示すように隣り合う薬液浸透域M2,M2......によって囲まれる未浸透域S,S......を残し、その各未浸透域が互いに連通する形状、又は未浸透域が残らないように地盤改良予定地盤全域に薬液及び拡張用液が浸透した形状のいずれかを、改良地盤の必要度に応じて選択する。 By adjusting the injection amount of the chemical liquid and the expansion liquid at each injection position a, as shown in FIG. 6, the non-permeation areas S, S... Surrounded by the adjacent chemical liquid infiltration areas M2, M2,. ..., the shape where each non-penetrated area communicates with each other, or the shape where the medicinal solution and expansion liquid penetrated the entire ground to be improved so that no non-penetrated area remains. Select according to need.
前述した未浸透域S,S......間を互いに連通させた状態で隣り合う薬液浸透域M2,M2......間を連続させる場合には、薬液と拡張用液の合計量が土壌間空隙量の50%であればよく、この場合に必要な薬液量と拡張用液との量割合を、例えば2:1程度とすると、前述した従来例に薬液使用量の2/3に減量させることができる。 In the case where the adjacent chemical solution permeation areas M2, M2... Are continuously connected with the non-permeation areas S, S. The total amount may be 50% of the amount of voids between soils. In this case, when the amount ratio between the amount of the chemical solution and the expansion solution is, for example, about 2: 1, the amount of the chemical solution used is 2 in the conventional example described above. / 3 can be reduced.
また、未浸透域が残らないように薬液浸透域M2,M2......が連続する形状に固化させた場合の改良地盤は、拡張用液浸透域Wのみが、薬液浸透域M2,M2......によって単独の状態に分離された状態で改良地盤中に分散されて存在することとなり、全域に薬液を浸透させる従来技術に比べ、注入されている拡張用液量分の薬液を節減させることができ、しかも分散されている拡張用液浸透域は、周囲と完全に隔離されているため、地震発生時において流れ出ることが無く、また改良地盤周囲の過剰土壌間隙水圧が改良地盤に作用しても、液状化が生じることがない。 In addition, the improved ground in the case where the chemical solution penetration areas M2, M2,... Are solidified so that no non-penetration area remains is the only solution liquid penetration area W for expansion. Compared to the conventional technology that penetrates the chemical solution throughout the entire area, it is dispersed in the improved ground in a state separated into a single state by M2 ....... The expansion liquid infiltration area that can save chemicals and is dispersed is completely isolated from the surroundings, so it does not flow out in the event of an earthquake, and the excess soil pore water pressure around the improved ground is improved. Even if it acts on the ground, liquefaction does not occur.
尚、上述した薬液には、シリカ系溶液型薬液が使用でき、所謂「水ガラス」製造用の原料である Na2O/nSiO2 又は K2O/nSiO2とその硬化剤である無機塩類、有機塩類、金属酸化物、金属水酸化物、無機酸、有機酸、酸性塩、塩基性塩等とを組み合わせて調製したもの並びにシリカ微粒子とその硬化剤、例えば旭電化工業株式会社製のパーマロック NS (商標) とを組み合わせて調製したものとに大別される。両者は薬液の構成素材や固化原理が若干異なるが、本発明の原理は何れの場合にも適用可能である。 In addition, a silica-based solution type chemical solution can be used for the above-described chemical solution, and Na2O / nSiO2 or K2O / nSiO2 that is a raw material for manufacturing a so-called “water glass” and an inorganic salt, an organic salt, or a metal oxide that is a curing agent thereof. , Metal hydroxides, inorganic acids, organic acids, acidic salts, basic salts and the like, as well as silica fine particles and curing agents such as Permalock NS (trademark) manufactured by Asahi Denka Kogyo Co., Ltd. Broadly divided into those prepared in combination. Both are slightly different in the constituent materials of the chemical solution and the solidification principle, but the principle of the present invention can be applied to either case.
また、拡張用液には水が使用されているが、この水は、例えば薬液と混合されにくいように粘性度を調整した水であってもよい。Moreover, although water is used for the expansion liquid, this water may be water whose viscosity is adjusted so that it is difficult to mix with the chemical liquid, for example.
10 地盤改良予定地盤
11 注入作業孔
12 ストレーナ
13 加圧送液装置
14 注入液流路
15 注液ノズル
16 パッカー
a 注入位置
M 液浸透域
M1 M2 薬液浸透域
W 拡張用液浸透域
10 Ground Improvement Planned Ground 11
Claims (5)
前記各薬液注入位置において所定量の前記地盤固化用の薬液を注入した後、その薬液注入位置から、先に形成された注入された地盤中の薬液を外側に押し出すための水を注入して該地盤中に浸透させることにより前記各薬液浸透域内に水浸透域を形成し、該水浸透域を形成することによって拡張された各薬液浸透域の外周部分を連続させて互いに連続した固化体となすことを特徴としてなる薬液注入による地盤改良工法。 A large number of chemical solution injection positions are set in the sandy ground to be improved at intervals in the vertical direction and the horizontal direction, and a solution type chemical solution for solidification is injected into each of the chemical solution injection positions. By infiltrating into the gap, a chemical solution infiltration area where the chemical solution penetrates into the ground around each chemical injection position is formed, and the outer peripheral parts of the chemical solution penetration area formed outside the adjacent chemical injection positions are continuous with each other In the ground improvement method by injecting the chemical solution in which the solidified body in which each of the peripheral solution infiltrating areas is continuously formed is formed,
After injecting a predetermined amount of the chemical solution for solidification at each chemical solution injection position, water for injecting the chemical solution in the injected ground formed previously is injected from the chemical solution injection position to to each chemical penetration region by infiltrating into the ground to form a water-permeable zone solidified body and which is sequencing outer peripheral portion of each liquid chemical penetration range has been extended by forming the water penetration zone continuous with each other Ground improvement method by chemical injection, which is characterized by
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