1

構造物の安全性安全な基礎構造物建設の流れ：

•計画： 適切な場所の選定（場所選定に自由度がある場合（目的、周辺）構造物からの要求項目（性能）

•設計： 地盤構成の詳細、（サンプリング、原位置試験、室内試験）基礎設計（安定解析）：

（性能に応じた）パフォーマンスの予測：=> 性能設計(Performance Base Design)

基礎形式、施工法、補助工法の決定

•施工： 計測, 安全性の確認、設計変更観測施工(Observational Method)、情報化施工（？？）

•維持管理： 長期計測（沈下、基礎構造物の劣化）、対策（補修、補強)構造物の建設の最適化、この一連の流れの整合性が重要（1箇所だけが完璧でもダメ）

2

地盤工学における構造物の設計

ex) 地盤上の構造物基礎土に荷重作用地盤内の応力の変化 沈下: s

:載荷重q

p’:増加τ:：増加

bearing stress q

settl

emen

t s

first

yie

ld

loca

l she

ar fa

ilure

gene

ral s

hear

failu

re

bearing stress q

settl

emen

t s

bearing stress q

settl

emen

t s

first

yie

ld

loca

l she

ar fa

ilure

gene

ral s

hear

failu

reAB

C弾性域

破壊域非破壊域に拘束

qult

•支持力問題 qd＜ qult/Ｆs ← せん断力の増加（qult：極限支持力，Fs：安全率＞１）

地盤耐力の評価方法：安定解析

•沈下問題 ｓ ＜ sa（sa：許容沈下量←構造物の重要度）

沈下計算：弾性計算（土質１）、圧密計算（土質２）

3

局所荷重下の平均応力とせん断力の増加

'pmvv ∆=ετγ ∆=

G1

1εv

τγ

1

q q

∆p ∆τ

弾性地盤

increase of p’volume compression

increase of τshear strain

settlement

4

地盤中の降伏（破壊）域の拡大

全般せん断破壊(general failure)

局所せん断破壊(local shear failure)初期降伏

荷重強度: qA 荷重強度: qB 極限荷重強度: qult

τ=τf

•土質

•深さ条件：

5

qb

6

許容沈下量 sa、沈下のタイプ許容沈下量設定の理由:-景観:内、外壁のクッラク; 目視できる傾き.

-用途、機能:クレーン等の機械の操作;ポンプ,コンプレッサー等の配管;精密機器（レーダー、電子顕微鏡).

-構造物自体の損傷:構造材の破壊.

•最大沈下量: smax(Maximum settlement)

•不等沈下量： δ=ρmax-ρmin, (Differential settlement)

•傾斜角：(Angular distortion) ll

s δ=

∆

s

sminsmax

smax

smin

δ

(a)均等沈下

(b)傾斜

(c)不等沈下

l

l

7

The sa depends on many factors:type, size, location, and intended use of the structure;pattern, rate, cause and source of settlement.

Depending on height and width0.004l0.01l0.01l0.003l0.0002l0.003l 0.01-0.02l

Stability against overturning

Tilting of smokestacks, towersRolling of trucks, etc.Stacking of goodsMachine operation-cotton loomMachine operation-turbogeneratorCrane railsDrainage of floors

Titling

150-300mm300-600mm

25-50mm50-100mm75-300mm

DrainageAccessProbability of nonuniform settlement:

Masonry walled structureFramed structuresSmokestacks, silos, mats

Total settlement

Maximum Settlement

Limiting FactorType of MovementAllowable settlement from Sowers (1962)

examples

8

Allowable settlement from Sowers (1962) cont’dLambe & Whitman, “Soil Mechanics SI Version”, John Wiley & Sons. (1979)

0.0005-0.001l0.001-0.002l

0.001l0.0025-0.004l0.003l0.002l 0.005l

High continuous brick wallsOne-story brick mill building, wall crackingPlaster cracking (gypsum)Reinforced-concrete building frameReinforced-concrete building curtain wallSteel frame, continuousSimple steel frame

Differential movement

Maximum Settlement

Limiting FactorType of Movement

note. l= distance between adjacent columns that settle different amounts, or between any two points that settle differently. Higher values are for regular settlements and more tolerant structures. Lower values are for irregular settlements and critical structures.

9

Tiltnorth south Tiling increase the possibility

not only overturning of towerbut also overstressing of the structural member

decreaseof stress Fig.14.7

increaseof stress

overstressing

year

Leaning Tower of Pisa Lambe & Whitman, “Soil Mechanics SI Version”, John Wiley & Sons. (1979)

10

Limiting angular distortion

Bjerrum:1963

Lambe & Whitman, “Soil Mechanics SI Version”, John Wiley & Sons. (1979)

11

安全率（Safety factor）The selection of safety factors for design cannot be made properly

without assessing the degree of reliability of all other parameters thatenter into design, such as design loads, strength and deformation characteristics of the soil mass, etc. In view of this, each case is to be considered separately by the designer.

Vesic( 1975) has suggested the total (global) factor of safety (Fs)on the basis of classification of structures, knowledge of foundation conditions, and the consequence failure.

種々の安全率（global factor of safety)：

•強度安全率：Fs•支持力安全率：Fb•高さ安全率：Fh•モーメント安全率：Fm•重量に対する安全率：Fγ

12

Minimum safety factor for design of shallow foundationVesic (1975)

Complete Limited

3.02.0Maximum design

load unlikely to occur

Apartment and officebuilding

C

3.52.5

Maximum design load may occur occasionally; Consequence of failure serious

Highway bridgeLight industrial and public building

B

4.03.0

Maximum design load likely to occur often;

Consequence of failure disastrous

Railway bridgeWarehouses blast furnacesHydraulic retaining wallsSilosA

Soil ExplorationCharacteristics of the Category

Typical structuresCategory

Remarks on the table: next page Total factor of safety: Fs

13

Remarks on the table

1. For temporary structure, these factors can be reduced to 75% of the above values. However, in no case should safety factors lower than 2.0 be used.

2. For exceptionally tall buildings, such as chimneys and towers, or generally whenever progressive bearing capacity failure may be feared, these factors should be increased by 20-50%.

3. The probability of flooding of foundation soil and/or removal of existing overburden by scour or excavation should be given adequate consideration.

4. It is advisable to check both the short term (end-of construction) and long term stability, unless one of the two conditions is clearly less favorable.

5. It is understood that all foundations will be analyzed also with respect to maximum tolerable total and differential settlement. If settlement governs the design, higher safety factor must be used.

14

安定係数(partial factor)荷重係数(load factor) と 抵抗係数(resistance factors)

(fd) 1.25(0.85)(fl) 1.5 (fu) 1.25(0.85)

Load Factor

(fc) 0.65(fc) 0.5(ff)0.8

Dead loadsLive loads, wind or earthquakeWater pressureCohesion (c)

(stability; earth pressure)Cohesion(c) (foundations)Friction (tanφ)

Loads

Shear strength

Resistance Factor

ItemCategoryValue of minimum partial factors (Meyerhof,1984)

note: Load factors given in parentheses apply to dead loads and water pressures when their effects are beneficial, as for dead loads resisting instability by sliding, overturning or uplift.

15

Total factor of safety vs. partial factorsBasic philosophy using total factor of safety:

Foundation should be capable of resisting a load Fs times greater than the design load. Fs covers both uncertainties in load and resistance.Load and resistance factor design (LRFD) method applies separate or partial factors to load and resistance. Limit state design concept

（限界状態設計法)The load factors are provided mainly for the variability and pattern of

loading, which differ for dead loads, live loads, environmental loads, and water pressures.

The resistance factors consider the variability and uncertainty of the assessment of soil resistance, which differ for the cohesion and friction components. The factored shear strength at ultimate state (τff) may be expressed as for Coulomb criterion.

The factors fc and fφ are the resistance factors for the cohesive and friction components, respectively. The total factor of safety obtained will depend on the relative contribution of the cohesive and friction components.

φστ φ tanfcfcff +=

16

Elements of a basic course of soil mechanics by Burland(1989)

：圧密

PRACTICE:（実務)Empiricism based on well-winnowed experience.LIQIDITY INDEX(液性指数）INSITU TEST（原位置試験)BEARING CAPACITY（支持力)EARTH PRESSURE(土圧)GEOTECHNICAL PROCESSESETC.

Engineering description

Applied Mechanics

Ground Profile

Soil Behaviour

Geological processes Ground water

Classification

Mineralogy

Particulate

Effective stress

Stress path

Compressibility

Seepage

Strain

Stress

Consolidation

Elasticity

Plasticity

Elastic solution

Failure

Limit equilibrium

Limit Analysis

C.S. models

Stress characteristics

：透水

：地下水 ：地質作用鉱物学：

土質分類：

：工学的記述

：極限解析極限平衡法：

：特性曲線法

17

基礎の安定問題の分類

３つの観点

1) 浅い(Shallow) or 深い(Deep)

2) 2 D or 3 D

3) 受働(Passive) or 主働(Active)載荷問題、除荷問題

8 cases

What are the other conditions very important for stability?

/ drained（排水） or undrained（非排水)/ long term（長期問題） or short term（短期問題)/??

18

1) 浅基礎、深基礎

地盤内応力

εa

応力ひずみ関係のモデル化（弾完全塑性モデル)

ひずみ軟化体積膨張

σ

εa

弾塑性挙動

ひずみ硬化

体積圧縮

すべり面（ひずみの局所化）

樽型の変形明確なすべり面なし（ひずみの一様化)

εv

εv

σ

different stress strainbetw.

shallow and deep depth

19

2) 2 D and 3D conditions

σθσr

r

2D 3D平面ひずみ問題

plane strain problemex) 円筒空洞押し拡げ

cylindrical cavity

ex) spherical cavity球状空洞

地盤中の応力・ひずみ大きく異なる

釣合い式

σθσr

r

押し拡げ

0=−+rdr

d rr θσσσ 02 =−+rdr

d rr θσσσ

2

1rr

∝σ 31rr

∝σ2

1rr

∝ε 31rr

∝ε

20

3) 受働(Passive) and 主動(active)

Pδ- δ+

easy to monitor behavior

difficulty in monitoring

P

δ- δ+

gradual&

large displacementto ultimate condition

受働土圧

K0abrupt &small displacementto ultimate condition

主働土圧

tensioncut off

Mohr Coulomb rapture surface

plasticflow

active

passive

q’=σv-σh

p’=1/3(σ’v+2σ’h)

K0 line

∆p’：increase（載荷問題)

∆p’：decrease（除荷問題)

21

2 x 2x 2 = 8 cases 浅い帯基礎の支持力

shallow + 2D + passive

shallow + 2D + active

shallow + 3D + passive(axisymmetric)

長い鉛直切土の安定

浅い円形基礎の支持力

22

2 x 2x 2 = 8 cases, cont’d. 杭基礎

deep+ 2D + passive

deep + 3D + passive

deep+ 3D + active

shallow +3D + active

deep + 2D + active深く長い掘削溝

円筒押し拡げ

球状押し拡げ

23

小テスト（4/20）

(スライド11-13を訳せ）

24

土質力学に関する基礎知識の確認（試験：4/27）

土質分類、

基本物理量、

有効応力、

透水、

締め固め、

圧密、

せん断、

に関する用語説明、用語訳（英語から日本語)、簡単な計算問題

構造物の安全性地盤工学における構造物の設計局所荷重下の平均応力とせん断力の増加地盤中の降伏（破壊）域の拡大Key steps of foundation design許容沈下量 sa、沈下のタイプThe sa depends on many factors: type, size, location, and intended use of the structure; pattern, rate, cause and source oAllowable settlement from Sowers (1962) cont’dLambe & Whitman, “Soil Mechanics SI Version”, John Wiley & Sons. (1979)TiltLimiting angular distortion安全率（Safety factor）Minimum safety factor for design of shallow foundation VesicRemarks on the table安定係数(partial factor) 荷重係数(load factor) と 抵抗係数(resistance factors)Total factor of safety vs. partial factorsElements of a basic course of soil mechanics by Burland(1989)基礎の安定問題の分類1) 浅基礎、深基礎2) 2 D and 3D conditions3) 受働(Passive) and 主動(active)2 x 2x 2 = 8 cases2 x 2x 2 = 8 cases, cont’d.小テスト（4/20）土質力学に関する基礎知識の確認（試験：4/27）