Chapter 15 Soil-Bearing Capacity for Shallow Foundations 연세대학교 지반공학연구실

개요 ○ 구조물 기초 설계시 고려사항 상부구조에 의해 기초에 전달되는 하중 기초를 지지할 흙의 거동 및 응력과 관련된 변형조건 흙의 토질공학적 조건

개요 - Foundation <기초> 1. Shallow FDN [ Df≤B , Df≤(3 ~ 4)B ] • spread footing (확대기초) • mat foundations (전면기초) 2. Deep FDN • Pile FDN • Caisson FDN • Drilled shaft FDN

개요 - Two main characteristics for shallow foundations 1. Should be safe against overall shear failure safe load bearing capacity 2. Should not undergo excessive settlement Allow. Settlement Figure 15.1 Common types of foundations; (a) spread footing; (b) mat foundation; (c) pile foundation; (d) drilled shaft foundation

15.1 Ultimate Soil-Bearing Capacity for Shallow Foundations - 전단파괴의 3가지 형태 (Fig 15.3) 1. General shear failure (Ⅰ) • Dense sand, stiff clay • qu(단위 면적당 하중)에 도달시 흙에서 갑작스런 파괴가 일어나고 파괴면은 지표면까지 확장

15.1 Ultimate Soil-Bearing Capacity for Shallow Foundations 2. Local shear failure (Ⅱ) • Medium sand or clay • 기초하중증가로 침하도 증가, 파괴면은 기초의 바깥방향으로 점차확산 • qu 의 최대치가 나타나지 않음

15.1 Ultimate Soil-Bearing Capacity for Shallow Foundations 3. Punching shear failure <관입전단파괴> • Fairly loose soil • 파괴면이 지표면까지 확장되지 않음 • qu를 넘어서도 하중-침하곡선은 경사가 급하고 직선에 가깝다

15.1 Ultimate Soil-Bearing Capacity for Shallow Foundations qult : max load per unit area which the soil can sustain without plastic failure

15.2 Terzaghi’s Ultimate Bearing Capacity Equation • 얕은기초의 극한지지력 산정이론 제안 • Df≤B shallow foundation • Continuous, strip footing 에 극한하중 작용시 전반 전단 파괴면 (General shear failure)

15.2 Terzaghi’s Ultimate Bearing Capacity Equation • Zone Ⅰ : Triangular elastic zone Ⅱ : Radial shear zone bounded by logarithmic spiral Ⅲ : Triangular Rankine passive zone Df Ⅲ Ⅱ Ⅰ G E J D F A B 

15.2 Terzaghi’s Ultimate Bearing Capacity Equation • 파괴면 GH, FI를 따라 생기는 전단저항은 무시 • Square FDN • Circular FDN Local shear failure • (strip FDN) • (square FDN) • (circular FDN) 여기서 : 수정지지력계수 <table 15.2 참조> Df Ⅲ Ⅱ Ⅰ G E J D F A B 

15.2 Terzaghi’s Ultimate Bearing Capacity Equation • Equilibrium (15.1) where • (15.2)

15.2 Terzaghi’s Ultimate Bearing Capacity Equation (15.3) : earth PR. coefficients, < Fig 15.6 참조 >

15.2 Terzaghi’s Ultimate Bearing Capacity Equation (15.2) (15.3) eq(15.3) eq(15.2) where (15.5) (15.6) (15.7) <table 15.1 참조>

15.3 General Bearing Capacity Equation - Terzaghi’s bearing capacity equation • Not consider rectangular FDN, 0< <1 • Not consider shear resistance • Load inclination •

15.3 General Bearing Capacity Equation 지지력계수 ( 적용시 ) Reissner(1924) Prandtl(1921) Caquot and kerisel Meyerhof Hansen

15.3 General Bearing Capacity Equation Meyerhof(1963) where <table 15.5참조>

15.4 Effect of Groundwater Table D1 Case 1 Df D2 d Case 2 • Case Ⅰ : 지하수위가 0≤D1≤Df 인 상태에 있을 때 • Case Ⅱ : 지하수위가 0≤d≤B 인 상태에 있을 때 • Case Ⅲ : 지하수위가 d≥B 위치에 있을 때 지하수위는 극한지지력에 영향을 주지 않음

15.5 Factor of Safety 1) 지지력에 대한 F·S , 전허용지지력 Net stress increase on soil, , 순허용지지력 , ( F·S는 적어도 3.0이상 )

15.5 Factor of Safety 2) 전단파괴에 대한 F·S (F·S. shear) 계산하는 과정 ① Developed cohesion. Cd & ② Cd와 를 이용하여 를 계산

15.5 Factor of Safety ③  Example 15.1 15.2 15.3 15.4 15.5

15.6 Ultimate Load for Shallow Foundations under Eccentric Load One-way Eccentricity where L B P : Vertical Load e : eccentricity of vertical load B·L : Dimensions of footing q : intensity of soil pressure B + = P M

15.6 Ultimate Load for Shallow Foundations under Eccentric Load for if tensile stress P B e P=R M P M Y X L B e R=P

15.6 Ultimate Load for Shallow Foundations under Eccentric Load Meyerhof(1953) : effective area method ① ② Determine the effective dimensions B′ = B-2e effective width L′ = L effective length 혹은 길이(L)방향으로 편심이 있을 때 B′=B , L′=L-2e L′과 B′중 작은값이 기초의 유효폭이 된다 B′<L′

15.6 Ultimate Load for Shallow Foundations under Eccentric Load ③ 는 B′,L′ 사용하여 table 15.5 에서 결정 는 B를 사용하여 table 15.5 에서 결정 ④ 유효면적 ⑤ 지지력 파괴에 대한 안전율

15.6 Ultimate Load for Shallow Foundations under Eccentric Load Two-Way Eccentricity  Example 15.6

15.7 Bearing Capacity of Sand Based on Settlement • N치 : KSF – 2318 Split – spoon sampler를 지반에 관입시켜 그 저 항치를 기록하고 동시에 토질분류 및 실내시험을 위한 대표적인 시료를 채취하는 방법으로 규정 N값은 중량 64.5㎏ 의 Hammer를 76㎝의 높이 에서 자유낙하시켜 관입시험용 sampler를 지반에 30㎝ 관입시키는데 필요한 타격수

15.7 Bearing Capacity of Sand Based on Settlement According to Meyerhof’s theory, for 25 mm (1 in.) of estimated maximum settlement,  (for  (for >1.22 m) where corrected standard penetration number

15.7 Bearing Capacity of Sand Based on Settlement  (for 1.22m) (for > 1.22 m) where depth factor = tolerable elastic settlement, in mm

15.8 Plate Load Test - Plate load test • Plates : 25㎜ thick 150∼762㎜ in diameter • Hole : a minimum diameter 4B (B:diameter of the test plate) to a depth of Df • Loading : about of the estimated ultimate load elapsed one hour between / each load application step • Test : until failure or at least 25㎜ settlement S q

15.8 Plate Load Test • Clay independent of the plate size • Sandy soils • For load intensity , q0

15.9 Ultimate Bearing Capacity on Layered Soil

15.10 Summary and General Comments • Bearing capacity of foundations depends on few factors 1. Subsoil stratification 2. Shear strength parameters of the subsoil 3. Location of the groundwater table 4. Environmental factors 5. Building size and weight 6. Depth of excavation 7. Type of structure