PE Exam Review - Geotechnical

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PE Exam Review - Geotechnical Resources and Visual Aids Item Page I. Glossary... 11 II. Parameters... 9 III. Equations....11 IV. Tables, Charts & Diagrams... 14 1. Module 1 - Soil Classification.

1 PE Exam Review - Geotechnical Resources and Visual Aids Item Page I. Glossary II. Parameters... 9 III. Equations IV. Tables, Charts & Diagrams Module 1 - Soil Classification Module 2 Phase Relationships Module 3 Effective Stress and Stress Distribution Module 4 - Consolidation Module 5 Strength & Bearing Capacity Module 6 Earth Retaining Structures Module 7 - Piles... 26

2 Visual Aids Geotechnical 2 Glossary A-line - In the Unified Soil Classification System, the A-line on the plasticity chart is used to delineate inorganic clays from silts and organic clays. Clay soils fall above the A-line on the plasticity chart. The A-line has the equation: I p = 0.73(w l 20). Active earth pressure coefficient The active earth pressure coefficient is the ratio of the horizontal to vertical effective stresses when the retaining wall moves away from the retained soil mass. Active lateral earth pressure (or active earth pressure) - The earth pressure that acts on a retaining structure when the structure moves away from the retained soil. allowable capacity - The load that a pile will support. Allowable capacity is computed by dividing the ultimate capacity by the safety factor. (AASHTO) System: American Association of State Highway and Transportation Officials Soil Classification System - The AASHTO soil classification system was developed to classify soils for roadway construction based on the soil s gradation characteristics, liquid limit, and plasticity index. Angle of Internal Friction The angle of internal friction (φ), or the friction angle is a measure of the strength of the soil. It is used to compute earth pressure coefficients, bearing capacity, and other parameters involving frictional resistance or strength. Aquifer - An underground source of water capable of supplying a well or other use. Average Degree of Consolidation, U - The ratio of the settlement at any time (ρ t ) to the total consolidation settlement (ρ). average vertical effective stress - Effective stress is the load carried by the soil skeleton. Average stress along a vertical pile is the average vertical effective stress. Coefficient of Consolidation, c v - A parameter used to estimate the rate of dissipation of excess pore pressure during consolidation. This parameter takes into account the permeability and compressibility of the soil. Coefficient of Permeability, k (or Hydraulic Conductivity) - A measured soil parameter that is related to the rate that water can flow through the soil mass. The coefficient of permeability is used in various flow equations to determine the rate of seepage. Compression index, C c - The slope of the compression curve on a void ratio versus logarithmic vertical effective stress in the normally consolidated range (i.e. the

3 Visual Aids Geotechnical 3 vertical stress is greater than the maximum past pressure). See the Consolidation Parameters diagram. Confined Aquifer - A pervious zone of soil confined between two or more impervious strata. Degree of Saturation, S - The ratio of the volume of water to the volume of voids. A soil is considered saturated when the degree of saturation, S, is equal to 1.0. Drainage Height, H d - The length of the longest drainage path for a particle of water to travel during consolidation. If the soil above and below the compressible layer are more permeable than the compressible layer, there is double-drainage and the drainage height is equal to one-half times the layer thickness. Otherwise, there is single-drainage and the drainage height is equal to the thickness of the layer. Dry Unit Weight (γ d ) (or Dry Density) - The ratio of dry solids to the total volume of soil, including voids. Eccentricity Eccentricity describes the location of the resultant force relative to the center of the base of the retaining wall. It is desirable to have the resultant within the middle third of the base of the wall. effective stress analysis (beta method) - An analysis that is conducted using skin friction to ascertain the allowable capacity of a pile. Elevation Head, h e - The elevation of a point relative to a fixed datum. end bearing capacity - The value that reflects the amount of load that the tip of the pile or set of piles will support. When added to the side friction produces the ultimate capacity. Excess Pore Pressure, u e / Initial Excess Pore Pressure, u i - When an increase in stress is applied to a soil, that stress increase results in an increase in pore water pressure, referred to as excess pore pressure (u e ). As consolidation occurs, the pore water pressure dissipates and over time, the applied stress is transferred to the soil skeleton. The increase in pore pressure immediately after the stress increase is applied, is referred to as the initial excess pore pressure (u i ), and is equal to the increase in applied stress ( σ v ). Note that the excess pore pressure is in addition to the pore water pressure that existed in the soil prior to the increase in applied stress. F Percent passing through the No. 200 sieve. This term is used in the equation to compute the group index in the AASHTO soil classification system. Factor of safety against bearing capacity failure One of the three safety checks in a stability analysis of a retaining wall is the factor of safety against bearing capacity

4 Visual Aids Geotechnical 4 failure. The factor of safety is the ratio of the ultimate bearing capacity (or load) to the actual load. The minimum factor of safety against bearing capacity failure may vary based on building codes and professional standards. Typically, however, the minimum value is 3.0. Factor of safety against overturning One of the three safety checks in a stability analysis of a retaining wall is the factor of safety against overturning. The formula is the ratio of the resisting moment to the overturning moment. The minimum factor of safety against overturning may vary based on building codes and professional standards. Typically, however, the minimum value is 2.0. Factor of safety against sliding One of the three safety checks in a stability analysis of a retaining wall is the factor of safety against sliding. The factor of safety is the ratio of the horizontal resisting forces divided by the horizontal driving forces. Resisting forces are the passive forces and the shear force along the base of the wall. Driving forces include forces due to active pressure and surcharge loads. The minimum factor of safety against sliding may vary based on building codes and professional standards. Typically, however, the minimum value is 1.5. See Visual Aids for the equation. Flow Net - A graphical representation of steady-state flow of water through soil indicating the path of seepage (flow path) and lines of piezometric head (equipotential lines). The flow net is the graphical representation of Laplace s differential equation which governs total head. Group Index (I g ) - The American Association of State Highway and Transportation Officials (AASHTO) soil classification system includes a Group Index to rate a soil within its overall group classification with respect to performance as a roadway construction material. The group index is included in parenthesis after the soil group classification and is reported to the nearest whole number. The group index is reported as zero if it is calculated to be negative. Hydraulic Gradient, I - The change in total head due to flow divided by the distance over which this change occurs, ( h T /L). Initial Void Ratio, e o - The void ratio existing prior to an applied stress increase. Liquid Limit (w l or LL) - The moisture (water) content below which the soil behaves as a plastic material. Above the liquid limit, the soil behaves as a viscous fluid. Maximum Past Pressure, σ vm - The maximum vertical effective stress that has ever acted on a soil at any given depth. The maximum past pressure is equal to the existing vertical effective stress for a normally consolidated soil, and is greater than the existing vertical effective stress for an overconsolidated soil. The maximum past pressure is also referred to as the preconsolidation pressure.

5 Visual Aids Geotechnical 5 Moisture/Water Content (w) - The ratio of weight of water to weight of dry solids. Normally consolidated - If the existing vertical effective stress is the largest that has ever existed, the soil is referred to as Normally Consolidated. See also the General Equations for overconsolidated and Normally Consolidated soil. Overconsolidated - Overconsolidated refers to a soil that has an existing vertical effective stress that is less than the stress that has acted on the soil in the past. Also referred to as preconsolidated. Overconsolidation Ratio, OCR - The ratio of the maximum past pressure to the existing vertical effective stress. The OCR is equal to 1.0 for a normally consolidated soil and is greater than 1.0 for an overconsolidated soil. Overturning Moment The overturning moment is the summation of moments due to forces causing the overturning of the wall; generally includes forces due to active pressure and surcharge loads. Passive forces are not included. Passive earth pressure (or passive earth pressure) The earth pressure that acts on a retaining structure when the structure moves toward the resisting soil mass. Passive earth pressure coefficient The passive earth pressure coefficient is the ratio of the horizontal to vertical effective stresses when the retaining wall moves toward the retained soil mass. Piezometer - Instrument installed in the ground to measure either total head or pore pressure, depending on the type of piezometer. Open-standpipe piezometers measure total head and closed-end piezometers measure pore pressure. Piezometric Surface - A locus of points defining the total head. In an openstandpipe piezometer, it is the level to which water rises. Plastic limit (w p or PL) - The moisture (water) content below which the soil behaves as a brittle solid. This is the lower range of plastic behavior. Plasticity Chart - A chart of plasticity index versus liquid limit used in the Unified Classification System to classify fine-grained soils and fine fractions of coarsegrained soils. Plasticity Index (I p or PI) - The Plasticity Index is the difference between the liquid limit and plastic limit. It represents the range in water contents through which the soil behaves as a plastic solid.

6 Visual Aids Geotechnical 6 Pore water pressure - Refers to the pressure of the water in the voids of soil. Where there is no seepage, the pore water pressure is simply equal to the depth below the water table times the unit weight of water. The pore water pressure acts with equal intensity in all directions. See also vertical effective stress and total vertical stress. Preconsolidated - Preconsolidated refers to a soil that has an existing vertical effective stress that is less than the stress that has acted on the soil in the past. Also referred to as overconsolidated. Pressure Head, h P - Pressure divided by the total unit weight of water. It is also the level to which water rises in an open-standpipe piezometer above the point where the pressure head is measured. The pressure head is equal to the pore pressure divided by the unit weight of water. Rankine s Theory Rankine s Theory assumes that there are no shear stresses on vertical planes. In other words, it is based on principal stresses. Therefore, Rankine s active and passive coefficients can not be used when there is friction between the wall and the soil. Also, the backfill must be horizontal. Recompression Index, C r - The slope of the compression curve on a void ratio versus logarithmic vertical effective stress in the overconsolidated range (i.e. the vertical stress is less than the maximum past pressure). See the Consolidation Parameters diagram. reduction coefficient - The value obtained by a graph utilizing unconfined compressive strength and a range of scores to assess how much the side friction factor must be reduced to produce an allowable capacity (see Alpha Method Graph). Resisting Moment The resisting moment is the summation of moments due to all forces resisting the overturning of the wall; includes the weight of the wall and passive resistance. Active forces are used to compute the overturning moment. safety factor - The amount that the ultimate capacity of a pile is divided by to insure that a load can be handled safely. Saturated - A soil is saturated when the voids of the soil are completely filled with water. The total unit weight of a saturated is referred to as the saturated unit weight. Shear resistance along the base The shear resistance along the base of a retaining wall is the force available from friction between bottom of the wall and the soil that resists sliding. It is the product of the vertical component of the resultant and the tangent of the friction angle between the bottom of the wall and the soil. side friction - The sideways force a pile exerts against the soil. A chart using

7 Visual Aids Geotechnical 7 pressure per square foot is used to determine this force. This force when measured is used to conduct a total stress analysis (alpha method). skin friction - The amount of friction that is produced by the exterior surface of a pile embedded in soil at a certain depth. This friction keeps the pile in place and the measurement of this friction is used to produce the side friction factor when conducting an effective stress analysis (beta method). (see Beta Method Graph) Specific gravity, G s - The ratio of the unit weight of the soil grains to the unit weight of water. Specific Gravity of Solids (G s ) - The ratio between the unit weight of the soil grains and the unit weight of water. Summation of Vertical Forces The summation of vertical forces is found by adding together the products of the areas and unit weights of each section of the wall and the soil resting on the wall. Time Factor, T - A dimensionless parameter used to estimate the time required for a specified degree of consolidation. Total Head, h T - The sum of pressure head plus elevation head. Total head is used to compute the hydraulic gradient and determine the direction of flow. Groundwater flows from higher total head to lower total head. total stress analysis (alpha method) - An analysis that is conducted using side friction to ascertain the allowable capacity of a pile. Total Unit Weight (γ t ) - Unit weight of moist soil. Total vertical stress - The total vertical stress at the bottom of a layer of soil is equal to the total weight of a column of unit area extending from the top to the bottom of the layer. The total vertical stress includes the weight of the soil plus the weight of water in the soil voids (pore water).

8 Visual Aids Geotechnical 8 Total vertical stress, σ v - The total vertical stress at any depth is equal to the total weight of the column of soil above that depth divided by the area of the soil column. The total vertical stress includes the weight of the soil plus the weight of the water in the soil voids. ultimate capacity - The load a pile or set of piles will support. This is computed by adding the side friction to the end bearing capacity. unconfined compressive strength - Twice the shear strength. This value is used to produce the reduction coefficient in a total stress analysis. undrained shear strength - Shear strength is the property that enables a material to remain in equilibrium when water is absent. Unified Soil Classification System - The Unified Soil Classification System is a system originally developed to classify soils for airfield construction based on particle size and Atterberg Limits. This system is widely used in the United States and has been adopted by the American Society for Testing and Materials (ASTM). Vertical effective stress - The effective stress is equal to the total vertical stress minus the pore water pressure. Void ratio, e - The ratio of the volume of voids to the volume of solids. e = V v /V s Water content / moisture content, w - The ratio of the weight of water to the weight of dry solids. w = W w /W s Water table - The top level of an aquifer, defined as the locus of points where the water pressure is equal to the atmospheric pressure, or in other words, where pore water pressure is equal to zero.

9 Visual Aids Geotechnical 9 Parameters φ: angle of internal friction δ: friction angle between pile and soil (skin friction) θ: inclination of resultant of vertical and horizontal forces ρ: settlement σ: total stress γ: unit weight σ : effective stress σ D : effective stress at depth D a: active A: area B : effective footing width C c : compression index c v : coefficient of consolidation d: dry; distance e: void ratio; eccentricity; elevation; excess eff: effective G s : specific gravity H: depth; thickness h: head; depth H d : drainage height i: hydraulic gradient k: coefficient of permeability K: lateral earth pressure coefficient m: maximum N γ : bearing capacity factor N q : bearing capacity factor p: passive P: pressure Q: flow; seepage S γi : correction factor for inclined load S γs : correction factor for footing

10 Visual Aids Geotechnical 10 S: saturation s: solids; shear resistance S qi : correction factor for inclined load S qs : correction factor for footing T: time factor t: total; time u: pore water pressure v: voids; vertical V: volume w: water; water content W: weight w l : liquid limit w p : plastic limit

11 Visual Aids Geotechnical 11 Equations Active force: P a 1 2 = γ th K 2 a Active lateral earth pressure coefficient: Arm (for moment) = ½ d K a 1 sin φ = 1+ sin φ Bearing capacity for sand with c = 0: q ult = 0.5B' γeff Nγ Sγ ssγi + σ D N S q qs S qi Consolidation time: TH t = c v 2 d Correction factor for inclined load: S γ i = 1 θ φ 2 θ Correction factor for inclined load: Sqi = 1 = Darcy s equation: Q = kia Degree of consolidation: ρ U = t ρ 2 Dry unit weight: γ d γ t = 1+ w Eccentricity: W e = 2 base Effective footing width: B = B 2e Factor of safety (for bearing capacity): Factor of safety (for overturning): Factor of safety (for sliding): Force (for moment): F = Aγ x F.S. = F.S. = Mr F.S. = M s P a Group index: I = (F 35)[ (w 40)] 0.01(F 15)(I 10) g 200 l 0 Q ΣF ult v 200 p

12 Visual Aids Geotechnical 12 Horizontal distance between vertical resultant and pivot point: M r M x = ΣF v o Hydraulic gradient: i h = H Overturning moment: M o = P a H 3 Plasticity index: I p = w l w p Pore water pressure (with seepage): u = h p γ w Pore water pressure (without seepage): u = γ w h Pressure head: h p = h t h e Resisting moments: M r = Σ (F i arm i ) Saturated unit weight: γ sat = ( w Gs + e) γ 1+ e Seepage: N Q = k N f d h Settlement for normally consolidated clay ( σ ' = σ' ): v m v f Cc ρ = 1+ e 0 σ' H log σ' v v f 0 Shear resistance: s = ΣF tan φ v s Total unit weight: γ t ( Gs + S e) γ = 1+ e w Total vertical stress: σ v = γh Ultimate end-bearing capacity: Q t = σ ' N A v q tip Unit skin friction: f s = Kσ ' tan δ v Vertical effective stress: σ, v = σ v u Void ratio: V e = V v s Volume of solids: Ws Vs = G γ s w

13 Visual Aids Geotechnical 13 Water content: W w = W w s Se = wg s u e σv ' = 1 u u i i

14 Visual Aids Geotechnical 14 Tables, Charts & Diagrams Module 1 Soil Classification AASHTO Soil Classification System Chart Consolidation Ratio as a Function of Depth and Time Factor

15 Visual Aids Geotechnical 15 Unified Soil Classification System Chart Unified Soil Classification System Identification Procedure

16 Visual Aids Geotechnical 16 Plasticity Chart

17 Visual Aids Geotechnical 17 Module 2 Phase Relationships Phase Diagrams Consolidated Soil Indexing Formulas

18 Visual Aids Geotechnical 18 Phase Relationships Diagram V V = V A + V W Phase Diagrams

19 Visual Aids Geotechnical 19 Module 3 Effective Stress and Distribution Situation Diagram for Module 3

20 Visual Aids Geotechnical 20

21 Visual Aids Geotechnical 21 Module 4 Consolidation Phase Relationships Diagram Consolidation Parameters Percent Consolidation U vs. Time Factor T

22 Visual Aids Geotechnical 22 Consolidation Ratio as a Function of Depth and Time Factor Consolidation Model and Graph

23 Visual Aids Geotechnical 23 Module 5 Strength and Bearing Capacity Bearing Capacity Factors Chart Sample Continuous Footing Diagram used in calculating Ultimate Bearing Capacity (See Demo Problem 5a)

24 Visual Aids Geotechnical 24 Bearing Capacity Factor Graph

25 Visual Aids Geotechnical 25 Module 6 Earth Retaining Structures Sample Diagrams of Earth Retaining Walls (See Demo and Practice Problems for Module 6) Relationship between Angle of Internal Friction and Bearing Capacity Factors Active and Passive Condition

26 Visual Aids Geotechnical 26 Module 7 Piles Piles Diagram

Brooks/Cole Thomson LearningiM. Fundamentals of Geotechnical Engineering. Braja M. Das. California State University, Sacramento

Fundamentals of Geotechnical Engineering Braja M. Das California State University, Sacramento Brooks/Cole Thomson LearningiM Australia Canada Mexico Singapore Spain United Kingdom United States CHAPTER