大型多重支撐深開挖數值模擬技術之研究大型多重支撐深開挖數值模擬技術之研究─以台北─以台北 101101 深開挖為例深開挖為例Three-Dimensional Numerical Simulation Techniques in Three-Dimensional Numerical Simulation Techniques in Large Scale Multi-Strutted Deep ExcavationLarge Scale Multi-Strutted Deep Excavation─ A Case History of Taipei 101 Deep Excavation─ A Case History of Taipei 101 Deep Excavation

大型多重支撐深開挖數值模擬技術之研究大型多重支撐深開挖數值模擬技術之研究─以台北─以台北 101101 深開挖為例深開挖為例Three-Dimensional Numerical Simulation Techniques in Three-Dimensional Numerical Simulation Techniques in Large Scale Multi-Strutted Deep ExcavationLarge Scale Multi-Strutted Deep Excavation─ A Case History of Taipei 101 Deep Excavation─ A Case History of Taipei 101 Deep Excavation

論文指導教授：林德貴 博士論文口試學生：周彥妤

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研究動機與目的研究動機與目的研究動機與目的研究動機與目的

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文獻回顧文獻回顧文獻回顧文獻回顧

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研究方法研究方法研究方法研究方法

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(1)台北101大樓興建工程計畫深開挖資料收集

深開挖施工資料:(a) 塔樓區與裙樓區(b) 施工順序(c) 連續壁(D-wall)(d) 撐牆(buttress)(e) 支撐系統(順打及逆打工法)(f) 樁基礎(鑽掘樁 bored pile)

現地調查及岩土試驗資料:(a) 地質鑽探(b) 室內試驗 (DST、TRT、PMT)

(c) 現地試驗 (SPT、PM、LLT、VST)

監測系統量測值資料:(a) 側向位移量(b) 地表沉陷量(c) 孔隙水壓力(d) 施作結構內力

(2) 建立深開挖三維數值模型

結構施工及元素類型:(a) 連續壁(plate element)(b) 撐牆及支撐系統(beam element)(c) 樁基礎 (embeded pile element)(d) 結構材料模式

邊界條件及初始條件:(a) 幾何尺寸(b) 現地地層狀況(c) 初始應力(d) 初始地下水位

土壤模式:(a) Mohr-Coulomb Model (MC-Model)(b) Soft Soil Creep Model (SSC-Model)(c) Soft Soil Model (SS-Model)(d) Hardening Soil Model (HS-Model)(e) Hardening Soil Model with Small-strain Stiffness (HSS-Model)

(3) 進行深開挖三維數值模擬並求得模擬值(a) 側向位移量(b) 地表沉陷量(c) 孔隙水壓力(d) 施作結構內力

量測值與模擬值比對是否吻合? NoNo

修正修正

Yes

繼續

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土壤模型對模擬結果之影響評估

特定結構物對模擬結之影響評估

Hardening Soil Model

(HS-Model)

Soft Soil Creep Model

(SSC-Model)

Mohr-Coulomb Model

(MC-Model)撐牆 基樁

(6) 結果與討論

(5) 分析評估各項模擬值之差異及影響程度

(4)深開挖數值試驗及參數研究

繼續

Soft Soil Model

(SS-Model)

Hardening Soil Model with Small-strain

Stiffness(HSS-Model)

43.5 m

49 m

裙樓區( 逆打 - 由上而下 )

塔樓區( 順打 - 由下而上 )

裙樓區( 逆打 - 由上而下 )

塔樓區( 順打 - 由下而上 )

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撐牆 -A2(40 m)

撐牆 -A1(-55 m)

撐牆 -A1(-55 m)

縱向鋼支柱 : H4001321 1st 橫向鋼支撐 :H35012192nd~6th 橫向鋼支撐 :H4001321

連續壁 -A(40 、 55 m)

樁基礎 : -21.7~ -75.9 m( 平均長度 48.8 m)

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傾斜管： SI3 沉陷監測點： S14 壓力計： EP1

109.1 m

Wall

114.1 m

Wall

GC-GM

Wall

SM

Wall CL2

Wall SS

Wall

CL1c

Wall

CL1b

Wall

CL1a

Wall

SF

Wa

ll

Column

Wall

Pile

Wall

Mat

Wall

Buttress Wall

Wall

Diaphragm Wall

Wall

109.1 m

Wall

114.1 m

Wall

GC-GM

Wall

SM

Wall CL2

Wall SS

Wall

CL1c

Wall

CL1b

Wall

CL1a

Wall

SF

Wa

ll

Column

Wall

Pile

Wall

Mat

Wall

Buttress Wall

Wall

Diaphragm Wall

Wall

CL1a

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Soil Layer

Depth (m)SPT-N

Thick-t (m)

Model(Material Type)

unsat

(sat)(kN/m3)

cref

(Kn/m2) (°)

(°)

E(kPa)

     

SF0-2.2

N=1~12(7)t=2.2

Mohr-Coulomb(Drained)

17.15(18.13)

10.00 35.00 0.00 7500 0.30      

SM37-42

N=9~76t=5

Mohr-Coulomb(Drained)

19.35(20.03)

20.00 37.00 0.00 75000 0.30      

GC-GM

45-48N=30~>100

t=3

Mohr-Coulomb(Drained)

20.75(22.08)

30.00 39.00 0.0027000

00.30      

SS48-62

N=50~>100t=14

Mohr-Coulomb(Drained)

20.57(20.64)

79.40 45.00 0.0068000

00.25      

Soil Layer

Depth (m)SPT-N

Thick-t (m)

Model(Material Type)

unsatt

(sat)(kN/m3)

c(kPa)

(°)

(°)

* * *ur

K0nc

CL242~45

N=6~27(18)t=3

Soft Soil Creep(Undrained)

18.62(18.91)

25.00 35.00 0.00 0.060.07

50.0015 0.2 0.4224

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Soil Layer

Depth (m)SPT-N

Thick-t (m)

unsatt

(sat)(kN/m3)

c(kPa)

(°)

(°)

* * * ur K0nc

CL1a2.2~13.4N=2~5(3)

t=11.2

18.33(18.53)

22.50 31.00 0.00 0.0176 0.0922 0.003 0.2 0.3982

CL1b13.4~24.5N=4~13(7)

t=10.9

18.72(19.32)

24.00 33.40 0.00 0.0182 0.0779 0.003 0.2 0.4408

CL1c24.5~37

N=10~37(16)t=12.5

18.48(18.74)

23.00 32.10 0.00 0.0169 0.0865 0.003 0.2 0.3982

Soil Layer

Depth (m)SPT-N

Thick-t (m)

unsatt

(sat)(kN/m3)

c(kPa)

(°)

(°)

* *ur

K0nc

CL1a2.2~13.4N=2~5(3)

t=11.2

18.33(18.53)

22.50 31.00 0 0.0176 0.0922 0.2 0.3982

CL1b13.4~24.5N=4~13(7)

t=10.9

18.72(19.32)

24.00 33.40 0 0.0182 0.0779 0.2 0.4408

CL1c24.5~37

N=10~37(16)t=12.5

18.48(18.74)

23.00 32.10 0 0.0169 0.0865 0.2 0.3982

SSC-Model (Soft Soil Creep Model)

SS-Model (Soft Soil Model)

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Soil Layer

Depth (m)SPT-N

Thick-t (m)

unsatt

(sat)(kN/m3)

c(kPa)

(°)

(°)

Eref 50(KN/m2)

Erefode(KN/m2)

Erefur (KN/m2)

Grefo (KN/m2)

urpref

(KN/m2)0.7

CL1a2.2~13.4N=2~5(3)

t=11.2

18.33(18.53)

22.50 31.00 0 40830 36750 122500 51040 0.2 196 0.0014

CL1b13.4~24.5N=4~13(7)

t=10.9

18.72(19.32)

24.00 33.40 0 70560 63504 211680 88200 0.2 392 0.0014

CL1c24.5~37

N=10~37(16)t=12.5

18.48(18.74)

23.00 32.10 0 76767 69090 230300 95958 0.2 392 0.0014

Soil Layer

Depth (m)SPT-N

Thick-t (m)

unsatt

(sat)(kN/m3)

c(kPa)

(°)

(°)

Eref 50(KN/m2)

Erefode(KN/m2)

Erefur (KN/m2)

Grefo (KN/m2)

urpref

(KN/m2)

CL1a2.2~13.4N=2~5(3)

t=11.2

18.33(18.53)

22.50 31.00 0 40830 36750 122500 51040 0.2 196

CL1b13.4~24.5N=4~13(7)

t=10.9

18.72(19.32)

24.00 33.40 0 70560 63504 211680 88200 0.2 392

CL1c24.5~37

N=10~37(16)t=12.5

18.48(18.74)

23.00 32.10 0 76767 69090 230300 95958 0.2 392

HSS-Model (Hardening Soil Model with Small-Strain)

HSS-Model (Hardening Soil Model)

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MC-Model (Mohr-Coulomb Model)

Soil Layer

Depth (m)SPT-N

Thick-t (m)

unsatt

(sat)(kN/m3)

c(kPa)

(°)

(°)

E(kPa)

CL1a2.2~13.4N=2~5(3)

t=11.2

18.33(18.53)

22.50 31.00 0.00 14088

CL1b13.4~24.5N=4~13(7)

t=10.9

18.72(19.32)

24.00 33.40 0.00 17422

CL1c24.5~37

N=10~37(16)t=12.5

18.48(18.74)

23.00 32.10 0.00 19600

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類型 編號 厚度(mm)

fc'(kg/cm2)

Depth(m)

Unit Weight (kN/m3)

連續壁 A 1200 280 40, 55 23.50 0.15

撐牆 A11200 280

5523.51 0.15

A2 40

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基礎結構 厚度 (m) 單位重 (kN/m3) 柏松比 楊氏模數 E (kPa)

筏基 (PC 底板 ) 0.3 23.52 0.15 3.02107

基礎結構 Tmax (kN/m) 單位重 (kN/m3) Fmax ((kN)) 楊氏模數 E (kPa)

樁基礎 35.48 24.09 7.26105 1.444107

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　 1st Support 2nd~6th Support Column

類型 H 350×350×12×19 H 400×400×13×21 H 400×400×13×21

A (m2) 0.017387 0.021869 0.021869

γ(kN/m3) 76.94 76.94

E (MPa) 2×105 2×105

I3 (m4) 0.002241 0.002241

I2 (m4) 0.006662 0.006662

H 350×350×12×19=

H-beam with 350 mm ( 翼緣寬度 )12 mm ( 腹板厚度 )19 mm ( 邊緣厚度 )

H 400×400×13×21=

H-beam with 400 mm( 翼緣寬度 )13 mm ( 腹板厚度 )21 mm ( 邊緣厚度 )

模擬步驟 施工模擬項目施工時間(day)

潛變累計時間

(day)

Phase 1 施作連續壁 1 1

Phase 2 施作外撐牆 1 2

Phase 3(1) 打設模擬區內一半數量之基樁(2) 安裝模擬區內一半數量之縱向支撐

1 3

Phase 11

(1) 打設模擬區內剩餘一半數量之基樁(2) 安裝模擬區內剩餘一半數量之縱向支撐

1 4

模擬步驟 施工模擬項目施工時間(day)

潛變累計時間

(day)Phase 4

(1st 施工階段 )(1) 開挖至地下 -4.4 m(2) 於地下 -3.4 m 安裝第 1 層橫向支撐 11 15

Phase 5(2nd 施工階

段 )

(1) 開挖至地下 -8.4 m(2) 於地下 -7.0 m 安裝第 2 層橫向支撐 21 36

Phase 6(3rd 施工階

段 )

(1) 開挖至地下 -11.3m(2) 於地下 -10.3 m 安裝第 3 層橫向支撐

19 55

Phase 7(4th 施工階

段 )

(1) 開挖至地下 -14.3 m(2) 於地下 -13.3 m 安裝第 4 層橫向支撐

20 75

Phase 8(5th 施工階

段 )

(1) 開挖至地下 -16.7 m(2) 於地下 -15.5 m 安裝第 5 層橫向支撐

17 92

Phase9(6th 施工階

段 )

(1) 開挖至地下 -18.7m(2) 於地下 -17.7 m 安裝第 6 層橫向支撐

18 110

Phase10(7th 施工階

段 )

(1) 開挖至地下 -21.7m(2) 於地下 -21.7 m 往上施作 3 m 厚之筏式混凝土底板

83 193

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結果與討論結果與討論結果與討論結果與討論

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將原始數值模型予以簡化

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土壤模式最大剪切力

(kN/m)Positive Negative

SSC-Model 1514.41 -1937.00SS-Model 644.47 -1511.43

HHS-Model 595.43 -1225.54HS-Model 363.96 -1288.74

MC- Model 611.89 -741.56Measurement none none

土壤模式最大軸向力

(kN/m)Positive Negative

SSC-Model 986.25 -156.63SS-Model 928.74 -334.85

HHS-Model 720.63 -88.95HS-Model 801.71 -178.14

MC- Model 1000.21 -476.07Measurement none none

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土壤模式

不同施工階段之開挖深度 (第 1至第 7施工階段 )

-4.4 m(1st階段施工 )

-8.4 m(2nd階段施工 )

-11.3 m(3rd

階段施工 )

-14.3 m(4th

階段施工 )

-16.7 m(5th

階段施工 )

-18.9 m(6th階段施工 )

-21.7 m

(7th

階段施工)

塔樓區不同開挖深度之側向位移 (mm)

SSC-Model 10.79 5.494.44

23.64

45.00

65.20 64.57

SS-Model 20.48 26.4028.25

53.27

81.10

108.63101.1

3

Measurement (SI3) 24.93 35.6946.79

52.81

56.92

49.68 55.28

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土壤模式

不同施工階段之開挖深度 (第 1至第 7施工階段 )

-4.4 m(1st階段施工 )

-8.4 m(2nd階段施工 )

-11.3 m(3rd

階段施工)

-14.3 m(4th

階段施工)

-16.7 m(5t

h

階段施工)

-18.9 m(6th階段施工 )

-21.7 m(7th

階段施工)

塔樓區不同開挖深度之側向位移 (mm)

HSS-Model 3.67 8.27

16.05

26.22

41.18

58.5257.47

HS-Model 3.59 7.70

13.42

22.28

35.01

49.7848.13

Measurement (SI3)

24.93 35.69

46.79

52.81

56.92

49.6855.28

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結論與建議結論與建議結論與建議結論與建議

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深開挖複雜三維數值模型之演算問題 解決方法結構元素多重 設定結構物交疊點之元素細長網格寬厚比過長 適當合併薄層土層元素數目過多 合併相同且相鄰之結構物

數值解無法收斂將大量結構物分別在多次計算階段中，依次點選加入更改其收斂計算法

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土壤模式

側向位移模擬結果 地表沉陷模擬結果

前期施工階段

後期施工階段

前期施工階段

後期施工階段

Soft Soil Creep 偏低 吻合 過高 過高

Soft Soil 吻合 過高 過高 過高

Hardening Small-Strain 偏低 吻合 偏低 偏低

Hardening Soil 偏低 吻合 偏低 偏低

Mohr-Coulomb 逐漸偏高 過高 接近 接近

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