FUNDAMENTALS OF CONSOLIDATION

FUNDAMENTALS OF CONSOLIDATION SAND (Vertical Stress Increase) CLAY CONSOLIDATION: Volume change in saturated soils caused by the expulsion of pore water from loading. Saturated Soils: causes u to increase immediately SAND DEPTH after Figure 7.1a. Das FGE (2005). Sands: Pore pressure increase dissipates rapidly due to high permeability. Clays: Pore Pressure dissipates slowly due to low permeability. Slide 1 of 74

FUNDAMENTALS OF CONSOLIDATION (Vertical Stress Increase) At Time of Initial Loading (t = 0) SAND CLAY SAND DEPTH after Figure 7.1a. Das FGE (2005). Variation in Total, Pore water, and Effective Stresses in Clay Layer Figure 7.1b. Das FGE (2005) Pore water takes initial change in vertical loading (u) since water is incompressible Soil skeleton does not see initial loading Slide 2 of 74

FUNDAMENTALS OF CONSOLIDATION (Vertical Stress Increase) Between time t = 0 to t = SAND DEPTH CLAY SAND Variation in Total, Pore water, and Effective Stresses in Clay Layer Figure 7.1c. Das FGE (2005) Pore water increase due to initial loading dissipates after Figure 7.1a. Das FGE (2005). Soil skeleton takes loading as pore pressure decreases Slide 3 of 74

FUNDAMENTALS OF CONSOLIDATION (Vertical Stress Increase) At time t = SAND CLAY SAND DEPTH after Figure 7.1a. Das FGE (2005). Variation in Total, Pore water, and Effective Stresses in Clay Layer Figure 7.1e. Das FGE (2005) Pore water increase due to initial loading completely dissipated (u = 0) Soil skeleton has taken loading. Effective stress increase now equals vertical stress increase ' Slide 4 of 74

FUNDAMENTALS OF CONSOLIDATION (Vertical Stress Increase) THE SPRING ANALOGY SAND CLAY SAND DEPTH after Figure 7.1a. Das FGE (2005). (a) Initial Loading Water takes load Soil (i.e. spring) has no load (b) Dissipation of Excess Water Pressure Water dissipating Soil starts to t k l d (c) Final Loading Water dissipated Soil has load Slide 5 of 74

ONE DIMENSIONAL (1D) CONSOLIDATION TEST D2435-11 Standard Test Methods for One-Dimensional Properties of Soils Using Incremental Loading Consolidometer Figure 7.2. Das FGE (2005) Slide 6 of 74

1D CONSOLIDATION TEST EQUIPMENT ShearTrac II DSS Equipment (Courtesy of Geocomp Corporation) Figure E-1 USACE EM1110-1-1904. Slide 7 of 74

THREE STAGES 14.330 SOIL MECHANICS 1D CONSOLIDATION TESTING LOAD INCREMENT DATA Stage I: Initial Compression Primarily caused by preloading. Stage II: Primary Excess pore water pressure dissipation and corresponding soil volume change. Stage III: Secondary Occurs after excess pore water pressure dissipation. Due to plastic deformation/ readjustment of soil particles. Figure 7.4. Das FGE (2005). Slide 8 of 74

VOID RATIO-PRESSURE PLOTS Figure 7.5. Das FGE (2005) Initial Void Ratio (e o ): e o V V v s H H v s A A H H v s Slide 9 of 74

VOID RATIO-PRESSURE PLOTS @ End of Load 1 1 1 Change in Void Ratio due to 1 st Loading (e 1 ): New Void Ratio after 1 st Loading: Figure 7.5. Das FGE (2005) H 1 e1 H s e eo 1 e 1 Figure 7.6. Das FGE (2005) Slide 10 of 74

VOID RATIO-PRESSURE PLOTS @ End of Load 2 2 2 Change in Void Ratio due to 2 nd Loading (e 2 ): New Void Ratio after 2 nd Loading: Figure 7.5. Das FGE (2005) H 2 e1 H s H 2 e2 e1 H s Figure 7.6. Das FGE (2005) Slide 11 of 74

VOID RATIO-PRESSURE PLOTS Final e log plots consist of results of numerous load & unload increments Two Definitions of Clays based on Stress History: Normally Consolidated (NC): The present overburden pressure (a.k.a. effective in-situ stress) is the most the soil has ever seen. Overconsolidated Clay (OC): The present overburden pressure is less than the soil has experienced in the past. The maximum effective past pressure is called the preconsolidation pressure ( c) or Maximum Past Pressure ( vm ) Figure 7.7. Das FGE (2005). Slide 12 of 74

DETERMINATION OF MAXIMUM PAST PRESSURE ( c or vm ) Graphical Method (Casagrande, 1936) Figure 7.8. Das FGE (2005). 1. Visually identify point of minimum radius of curvature on e-log curve (i.e. Point a). 2. Draw horizontal line from Point a (i.e. Line ab). 3. Draw Line ac tangent to Point a. 4. Draw Line ad bisecting Angle bac. 5. Project the straight line portion of gh on e-log curve to intersect Line ad. This intersection (Point f) is the maximum past pressure (a.k.a. preconsolidation pressure). Slide 13 of 74

OVERCONSOLIDAITON RATIO (OCR) ( c or vm ) Where: OCR c c (a.k.a. vm ) = Preconsolidation Pressure (a.k.a Maximum Past Pressure). Figure 7.8. Das FGE (2005). = Present Effective Vertical Stress General Guidelines: NC Soils: 1 OCR 2 OC Soils : OCR > 2 Possible Causes of OC Soils: Preloading (thick sediments, glacial ice); fluctuations of GWT, underdraining, light ice/snow loads, desiccation above GWT, secondary compression. Slide 14 of 74

EFFECTS OF SAMPLE DISTURBANCE NC and OC soils of low to medium sensitivity will experience disturbance due to remolding. This changes the consolidation characteristics of the 1D consolidation tests. NC Clays - Figure 7.9. Das FGE (2005) OC Clays - Figure 7.10. Das FGE (2005) Virgin Compression Curve Curve Insitu (i.e. w/o disturbance) qu( undisturbed ) Sensitivity (S St t ) q u( remolded ) Where q u = Unconfined Compressive Strength Slide 15 of 74

EFFECTS OF SAMPLE DISTURBANCE Reconstruction of Virgin Curves (EM 1110-1-1904) Figure 3-12. EM 1110-1-1904 Settlement Analysis. Slide 16 of 74

EFFECTS OF SAMPLE DISTURBANCE Reconstruction of Virgin Curves (EM 1110-1-1904) Table 3-6. EM 1110-1-1904 Settlement Analysis. Slide 17 of 74

EFFECTS OF SAMPLE DISTURBANCE Reconstruction of Virgin Curves (EM 1110-1-1904) Table 3-6. EM 1110-1-1904 Settlement Analysis. Slide 18 of 74

SETTLEMENT FROM 1D PRIMARY CONSOLIDATION At End of Primary = Figure 7.11. Das FGE (2005) V V V HA ( H S ) A S o 1 Where: V = Volume, V o = Initial Volume, V 1 = Final Volume, S p = Primary Settlement p p A Slide 19 of 74

SETTLEMENT FROM 1D PRIMARY CONSOLIDATION At End of Primary = V S p A Vvo Vv1 V Where: V vo = Initial Void Volume, V v1 = Final Void Volume V v ev s v Figure 7.11. Das FGE (2005). Where: e = Change in Void Ratio V s Vo 1 e o AH 1 e Where: e 0 = Initial Void Ratio o Slide 20 of 74

SETTLEMENT FROM 1D PRIMARY CONSOLIDAITON At End of Primary = Figure 7.11. Das FGE (2005). V Therefore: S S p S p H A ev p or H e 1 e o s e 1 e o AH 1 e v Where: v = Vertical Strain o e Slide 21 of 74

SETTLEMENT FROM 1D PRIMARY CONSOLIDATION e o Virgin Line Where: NC Clay VOID RATIO C s or C r C c C c = Slope of Field Virgin Curve = Compression Index C s (or C r ) = Slope of Rebound Curve = Swell Index vm = Maximum Past Pressure ~0.4e o v (Log Scale) vm = o o = Initial Vertical Effective Stress Slide 22 of 74

e o VOID RATIO ~0.4e o C s or C r v (Log Scale) 14.330 SOIL MECHANICS SETTLEMENT FROM 1D PRIMARY CONSOLIDATION e f vm = o Virgin Line C c f S p CcH e NC Clay Settlement (S p ) using Void Ratio o log o 1 0 Where: S p = Settlement H = Height of Soil Layer vm = Final Vertical Effective Stress = o - Current Vertical Effective Stress = Change in Vertical Effective Stress f = Final Vertical Effective Stress e f = Final Void Ratio Slide 23 of 74

SETTLEMENT FROM 1D PRIMARY CONSOLIDATION e o VOID RATIO C s or C r Same Slope as C r Virgin Lines C c Where: OC Clay C c = Slope of Field Virgin Curve = Compression Index C s (or C r ) = Slope of Rebound Curve = Swell Index ~0.4e o v (Log Scale) o vm or c vm = Maximum Past Pressure o = Initial Vertical Effective Stress Slide 24 of 74

e o 14.330 SOIL MECHANICS SETTLEMENT FROM 1D PRIMARY CONSOLIDATION Same Slope as C r OC Clay Settlement (S p ) using Void Ratio VOID RATIO C s or C r S p C c CrH e log o vm C ch 1 e 1 0 0 Where: o log o e f ~0.4e o v (Log Scale) o vm or c f S p = Settlement H = Height of Soil Layer = Change in Vertical Effective Stress o = Initial Vertical Effective Stress f = Final Vertical Effective Stress e f = Final Void Ratio Slide 25 of 74

SETTLEMENT FROM 1D PRIMARY CONSOLIDATION Compression Index (C c ) Estimates from Other Laboratory Tests Soil C c Equation Reference Undisturbed Clays Disturbed Clays Organic Soils, Peat Clays Varved Clays C c C c 0.009( LL 10) C c 0.007( LL 10) Cc 0. 0115W n C c 1.15( e 0.35) C c ( 1 e ) 0.1 0.006( W Uniform Silts C c 0. 20 o o Cc 0. 012W n 0.01( LL 13) n 25) Terzaghi & Peck (1967) EM 1110-1-1904 Slide 26 of 74

SETTLEMENT FROM 1D PRIMARY CONSOLIDATION Compression Index (C c ) Estimates from Other Laboratory Tests Soil C c Equation Reference 1.21 e Clays 0.141 o Cc Gs Rendon-Herrero (1983) Gs C LL 0.2343 100 Clays c G s Nagaraj & Murty (1985) 2.38 Where: G s = Specific Gravity of Solids LL = Liquid Limit (in %) W n = Natural Water Content e o = Initial Void Ratio Slide 27 of 74

SETTLEMENT FROM 1D PRIMARY CONSOLIDATION Compression Index (C c ) Estimates from Other Laboratory Tests Soil C c Equation Reference 1.21 e Clays 0.141 o Cc Gs Rendon-Herrero (1983) Gs C LL 0.2343 100 Clays c G s Nagaraj & Murty (1985) 2.38 Slide 28 of 74

1.12 1.1 14.330 SOIL MECHANICS EXAMPLE: SETTLEMENT FROM VIRGIN CONSOLIDATION CURVES GIVEN: 1.08 OC CH layer VOID RATIO (e) 1.06 1.04 1.02 1 o = 855 psf vm = 1460 psf = 1005 psf e o = 1.1 0.98 0.96 500 600 700 800 900 1000 2000 3000 4000 5000 6000 Vertical Effective Stress ' v (psf) Height of CH Layer = 10 ft Figure 1. Example of Virgin Curves. Slide 29 of 74

VOID RATIO (e) 1.12 1.1 1.08 1.06 1.04 1.02 1 0.98 14.330 SOIL MECHANICS EXAMPLE: SETTLEMENT FROM VIRGIN e o CONSOLIDATION CURVES 1.1 C s ' 1.076 e f C c 1.045 S p H e 1 e o e 1.11.045 0.055 e o 1.1 S p (10 ft) 0.055 11.1 S p 0.262 ft S p 3.14in 3 1 4 in 0.96 500 600 700 800 900 ' o 1000 ' vm ' f 2000 3000 4000 5000 6000 Vertical Effective Stress ' v (psf) Figure 1. Example of Virgin Curves. Slide 30 of 74

SC = 105 pcf sat = 110 pcf 0 14.330 SOIL MECHANICS EXAMPLE: SETTLEMENT FROM 1D TEST STRAIN RESULTS Q = P = 144 kips 0 0 TOTAL STRESS () 0 2000 0 0 PORE PRESSURE (u) 0 2000 0 EFFECTIVE STRESS (') 0 2000 0 0 B = 6 ft SQ Depth from Existing Ground Surface (ft) 5 10 15 20 CL sat = 105 pcf SM sat = 115 pcf 5 10 15 20 5 10 15 20 5 10 15 20 5 10 15 20 5 10 15 20 5 10 15 20 5 10 15 20 DepthfromExistingGroundSurface (ft) MH sat = 115 pcf 25 25 25 0 2000 25 25 0 2000 25 25 0 2000 25 Slide 31 of 74

EXAMPLE: SETTLEMENT FROM 1D TEST STRAIN RESULTS 15 20 CL Layer Sample from 12 ft VERTICAL STRAIN (%) 25 30 35 40 45 50 200 400 600 800 2000 4000 6000 100 1000 Vertical Effective Stress ' v (psf) Slide 32 of 74

SC = 105 pcf sat = 110 pcf 0 14.330 SOIL MECHANICS EXAMPLE: SETTLEMENT FROM 1D TEST STRAIN RESULTS Q = P = 144 kips 0 0 TOTAL STRESS () 0 2000 0 0 0 PORE PRESSURE (u) 0 2000 0 EFFECTIVE STRESS (') 0 2000 0 0 ' o 0 B = 6 ft SQ 315 0 315 ' f Depth from Existing Ground Surface (ft) 5 10 15 20 CL Layer 1 A B C CL sat = 105 pcf CL Layer 2 D E SM sat = 115 pcf F 5 10 15 20 5 10 15 20 525 635 980 1325 1670 2015 2360 5 10 15 20 5 10 15 20 0 60 250 435 625 810 1000 5 10 15 20 5 10 15 20 525 575 730 890 1045 1205 1360 1455 1250 1185 1240 1345 2525 5 10 15 20 DepthfromExistingGroundSurface (ft) MH sat = 115 pcf 25 G 25 25 0 2000 2820 25 25 1250 0 2000 25 25 1570 0 2000 25 Slide 33 of 74

EXAMPLE: SETTLEMENT FROM 1D TEST STRAIN RESULTS 15 S p1 S S CL Layer 1 S p1 p1 p1 H 1 v1 (6 ft)(0.065) 0.39 ft 4.7in VERTICAL STRAIN (%) 20 25 30 35 40 45 v1 = 6.5% = 0.065 CL Layer Sample from 12 ft 50 200 400 600 800 ' 2000 f1 ' o1 100 1000 Vertical Effective Stress ' v (psf) Slide 34 of 74

EXAMPLE: SETTLEMENT FROM 1D TEST STRAIN RESULTS CL Layer 2 S p2 H 2 v2 S p2 (6 ft)(0.024) S p2 0.14 ft S p2 1.7in Total Settlement S Ptotal S p1 S p2 VERTICAL STRAIN (%) 15 20 25 30 35 40 v2 = 2.4% = 0.024 CL Layer Sample from 12 ft S Ptotal 6.4in 45 50 S Ptotal 6 1 2 in 100 1000 ' o2 200 400 600 800 'f2 2000 Vertical Effective Stress ' v (psf) Slide 35 of 74

SETTLEMENT FROM SECONDARY CONSOLIDATION C e logt2 logt 1 Where: C = Secondary Compression Index e = Change in Void Ratio t = Time Results of 1D Test @ One Load Increment Figure 7.15. Das FGE (2005). Slide 36 of 74

SETTLEMENT FROM SECONDARY CONSOLIDATION S s C H log C C 1 e p t t 2 1 Where: H = Height of Soil Layer e p = Void Ratio @ End of Primary t = Time Results of 1D Test @ One Load Increment Figure 7.15. Das FGE (2005). Slide 37 of 74

TIME RATE OF CONSOLIDATION Theory of 1D (Terzaghi, 1925) Assumptions: Clay Layer Undergoing Figure 7.17a. Das FGE (2005). 1. The clay-water system is homogenous. 2. Saturation is complete (S = 100%). 3. Compressibility of water is negligible. 4. Compressibility of soil grains is negligible (but soil particles rearrange). 5. Flow of water is in one direction only. 6. Darcy s Law is Valid. Slide 38 of 74

TIME RATE OF CONSOLIDATION Clay Layer Undergoing Figure 7.17a. Das FGE (2005). Flow of Water @ Point A Figure 7.17b. Das FGE (2005). Slide 39 of 74

TIME RATE OF CONSOLIDATION (Rate of Water Outflow) (Rate of Water Inflow) = Flow of Water @ Point A Figure 7.17b. Das FGE (2005). (Rate of Volume Changes) Mathematical Equation: v z vz z Where: dzdxdy v or v z z dxdydz z dxdy V dt V dt V = Volume of Soil Element v z = Velocity of flow in z direction Slide 40 of 74

Slide 41 of 74 14.330 SOIL MECHANICS Flow of Water @ Point A Figure 7.17b. Das FGE (2005). Where: V s = Volume of Solids v v = Volume of Voids t V e t e V t V t ev V t V t V t V dxdydz 1 z u k z u k z h k ki v t V dxdydz z v s s s s s v 2 2 w w z z Using Darcy s Law (v = ki) Where u = excess pore pressure. From algebra: Rate of change in V = Rate of Change in V v TIME RATE OF CONSOLIDATION

Slide 42 of 74 14.330 SOIL MECHANICS Flow of Water @ Point A Figure 7.17b. Das FGE (2005). t e e 1 1 z u k t e e 1 dxdydz t V e 1 dxdydz e 1 V V 0 t V t V e t e V t V t ev V t V t V o 2 2 w o o o s s s s s s s v From Previous Slide Assuming soil solids are incompressible and e o = Initial Void Ratio. Substituting: Combining equations: TIME RATE OF CONSOLIDATION

14.330 SOIL MECHANICS TIME RATE OF CONSOLIDATION Flow of Water @ Point A Figure 7.17b. Das FGE (2005). From Previous Slide k w k u 2 z w e a 2 z v m 2 v u 2 av 1 e 1 1 e o u t av 1 e o o a e t The change in void ratio is caused by the increase in effective stress. Assuming linear relationship between the two: v u a v = Coefficient of Compressibility. Can be considered constant over narrow pressure increases. Combining equations: m m v = Coefficient of Volume Compressibility. v u t Slide 43 of 74

Slide 44 of 74 14.330 SOIL MECHANICS v w v v o v v v o v w m k c z u c t u e a m t u m t u e a z u k 2 2 2 2 1 1 From Previous Slide Rearranging Equations: a v = Coefficient of Compressibility. m v = Coefficient of Volume Compressibility. Where c v = Coefficient of. TIME RATE OF CONSOLIDATION Flow of Water @ Point A Figure 7.17b. Das FGE (2005).

TIME RATE OF CONSOLIDATION Basic Differential Equation of 1D Theory u t z z 0, u 2H dr t 0, u 0, u 2 u cv 2 z Can be solved with the following boundary conditions: u 0 The solution yields 0 Clay Layer Undergoing Figure 7.17a. Das FGE (2005). u m m0 u M sin Mz H 2 o M dr e 2 T v Slide 45 of 74

TIME RATE OF CONSOLIDATION u m m0 From Previous Slide u M o Mz sin H dr e 2 2 M T v u o Where: M 2m 1 2 Initial excess pore water pressure T v c H t v 2 dr TIME FACTOR Clay Layer Undergoing Figure 7.17a. Das FGE (2005). Slide 46 of 74

TIME RATE OF CONSOLIDATION Because consolidation progress by dissipation of excess pore pressure, the degree of consolidation (U z ) at a distance z at any time t is: U z uo uz 1 u o u u z o Clay Layer Undergoing Figure 7.17a. Das FGE (2005). Figure 7.18. Das FGE (2006). Slide 47 of 74

TIME RATE OF CONSOLIDATION Figure 7.18. Das FGE (2006). Slide 48 of 74

14.330 SOIL MECHANICS TIME RATE OF CONSOLIDATION Clay Layer Undergoing Figure 7.17a. Das FGE (2005). Average degree of consolidation (U) for the entire depth of the clay layer at any time t is: Where: U Average degree of S S t p U Settlement of layer at time t Settlement of Layer from Primary U S S t p Substituting U for u m 2 M 1 e 2 m0 M 1 2H 1 dr u 2H 0 o dr u 2 T v U can be approximated by the following relationships: z dz U % For U 0% to 60%, Tv 4 100 For U 60%, T 1.781 0.933log(100 U %) v 2 Slide 49 of 74

TIME RATE OF CONSOLIDATION Variation of T v with U Table 7.1 Das PGE (2006). Slide 50 of 74

TIME RATE OF CONSOLIDATION Difference between Average Degree of and Midplane Degree of Figure 7.28. Das FGE (2006). Slide 51 of 74

COEFFICIENT OF CONSOLIDATION (c v ) Generally decreases as Liquid Limit (LL) increases. Determined from 1D Test Lab per Load Increment. Logarithm of Time Method (Casagrande and Fadum, 1940) Figure 7.19 Das FGE (2006). Square Root of Time Method (Taylor, 1942) Figure 7.20 Das FGE (2006). Slide 52 of 74

COEFFICIENT OF CONSOLIDATION (c v ) Logarithm of Time Method 1. Extend the straight line portion of primary and secondary consolidations to interest at Point A. Point A represents d 100 (Deformation at 100% primary consolidation). 2. The initial curved portion of the deformation plot versus log t is approximated to be a parabola on a natural scale. Select times t 1 and t 2 on the curved portion such that t 2 = 4t 1. Let the difference of the specimen deformation between (t 2 t 1 ) be equal to x. Figure 7.19. Das FGE (2006). 3. Draw a line horizontal to DE such that the vertical distance BD is equal to x. The deformation corresponding to the line DE is d 0 (Deformation at 0% primary consolidation). Slide 53 of 74

COEFFICIENT OF CONSOLIDATION (c v ) Logarithm of Time Method 4. The ordinate of Point F on the consolidation curve represents the deformation at 50% primary consolidation (d 50 ). 5. For 50% average degree of consolidation (U = 50%), T v = 0.197 (see Table 7.1, Das FGE 2006). T 50 0.197 or c H t v 50 2 dr Figure 7.19. Das FGE (2006). c v 0.197H t 50 2 dr Where: H dr = Average longest drain path during consolidation. Slide 54 of 74

COEFFICIENT OF CONSOLIDATION (c v ) Square Root of Time Method 1. Draw a line AB trough the early portion of the curve. 2. Draw a line AC such that OC = 1.15OB. The time value for Point D (i.e. the intersection of line AC and the data) is the square root of time for t 90 (i.e. the time to 90% primary consolidation). Figure 7.20. Das FGE (2006). 3. For 90% consolidation, T v = 0.848 (see Table 7.1, Das FGE 2006). T 90 c c t 0.848 H v or 0.848H t 90 v 90 2 dr 2 dr Slide 55 of 74

COEFFICIENT OF CONSOLIDATION (c v ) Example 5ft SP FILL ( = 115 pcf) SC ( = 115 pcf) 3ft 4ft REQUIRED: Determine the following: a. The change in pore pressure in the CL layer immediately after the application of the 3 ft of SP Fill. CL ( = 115 pcf) 6ft b. The degree of consolidation in the middle of the clay layer when the excess pore pressure (u e ) is 170 psf. SM ( = 115 pcf) c. How high would the water in a piezometer located in the middle of the layer rise above the GWT when u e = 170 psf? GIVEN: Soil Profile (NTS). 2 way drainage. d. If c v = 0.000004 ft²/sec, how long would it take to get to 25% average degree of consolidation? To U = 50%? To U = 99%? Slide 56 of 74

PRECOMPRESSION GENERAL CONSIDERATIONS PRECOMPRESSION: Loading an area prior to placement of the planned structural loading to limit post-construction settlement. Also known as Surcharging. Settlement caused by structural loading (S p ): S p CcH e 1 0 o log o Settlement caused by structural loading and surcharging (S p or S p+f ): S p S p f CcH e 1 0 o log o f Where: f = Change in vertical stress due to Fill added. Slide 57 of 74

PRECOMPRESSION GENERAL CONSIDERATIONS Where: p) = Change in vertical stress due to structural load. f) = Change in vertical stress due to Fill added. Figure 7.26. Das FGE (2006). Where: S p = Settlement due to structural load. S p+f = Settlement due to structural load and Fill. Slide 58 of 74

Slide 59 of 74 14.330 SOIL MECHANICS ) ( ) ( ) ( ) ( ) ( ) ( ) ( 1 1 log 1 log log log p f o p o p o f p o o p o p p U U S S U Mathematical Equations Definition of average Degree of U Substitution Re-arranging (Eqn 7.56 Das FGE 2006) Place in graphical form for design use (Figure 7.27 Das FGE 2006) PRECOMPRESSION PLANNING

PRECOMPRESSION Where: PLANNING f) = Change in vertical stress due to Fill added. p) = Change in vertical stress due to Structural Loading. o = Initial vertical effective stress. 14.330 SOIL MECHANICS Figure 7.27. Das FGE (2006). Slide 60 of 74

PRECOMPRESSION STEPS: 1. Calculate primary consolidation settlement from planned loading (S p ). 2. Calculate primary consolidation settlement from planned loading plus surcharge (S p+f ). 3. Calculate average degree of consolidation U. Note U = S p /S p+f. Can also use Figure 7.27 or Eqn 7.56 (Das FGE 2006). 1. Find T v from calculated U. To find time to when surcharge loading should be removed (i.e. t 2 ): PLANNING t 2 T v H c v 2 dr 14.330 SOIL MECHANICS Figure 7.27. Das FGE (2006). Slide 61 of 74

TIME RATE OF CONSOLIDATION Difference between Average Degree of and Midplane Degree of Removal of Surcharge may still cause net settlement (swelling near drainage layers, settlement @ middle) Conservative Approach: Assume U is the midplane degree of consolidation. Figure 7.28. Das FGE (2006). Slide 62 of 74

TIME RATE OF CONSOLIDATION Midplane Degree of Figure 7.29. Das FGE (2006). Slide 63 of 74

SURCHARGING EXAMPLE 5ft SP FILL ( = 115 pcf) 3ft SC ( = 115 pcf) CL ( = 115 pcf) SM ( = 115 pcf) GIVEN: Soil Profile (NTS). 2 way drainage. 4ft 6ft REQUIRED: Determine the following: a. If c v = 0.000004 ft²/sec, how long would it take to get to 99% average degree of consolidation? b. If a surcharge of 4 ft of fill was placed in addition to the 3 ft of fill planned, when would you be able to remove the surcharge? Use the same value for c v given in a. Slide 64 of 74

GROUND MODIFICATION FOR CONSOLIDATION SAND DRAINS r w = Sand Drain Radius d e = Effective Diameter Plan View Triangular Spacing Figure 10.38. Das PGE (2006) Section View Figure 10.38. Das PGE (2006). Reduction Drainage Path = Reduction in Drainage Time Slide 65 of 74

GROUND MODIFICATION FOR CONSOLIDATION STEPS 1 SAND DRAINS 2 3 4 5 1. Place auger at drain location. 2. Screw auger to selected depth. 3. Rotate auger at selected depth to remove soil. 4. Inject sand while auger is extracted. 5. Complete sand drain to working platform level. Sand Drain Installation: Auger Method (Kirmani, 2004) Figure 10.39. Das PGE (2006). Slide 66 of 74

GROUND MODIFICATION FOR CONSOLIDATION PREFABRICATED VERTICAL DRAINS (PVD S) (A.K.A. WICK DRAINS) Conceptual Concept Courtesy of www.americanwick.com Courtesy of www.americandrainagesystems.com Figure 7.31. Das FGE (2006). Slide 67 of 74

GROUND MODIFICATION FOR CONSOLIDATION PREFABRICATED VERTICAL DRAINS (PVD S) (A.K.A. WICK DRAINS) Courtesy of www.americandrainagesystems.com Courtesy of www.nilex.com Courtesy of www.nilex.com Slide 68 of 74

m c U vr r 8T 1 exp m 2 n n n ln( ) 2 1 de n 2r T r c w vr 2 e d k h t e (1 e o r 3n ) 14.330 SOIL MECHANICS GROUND MODIFICATION FOR CONSOLIDATION RADIAL CONSOLIDATION U r = Average Degree of Radial 2 4n w 1 2 Barron (1948) d e = Effective Diameter r w = Sand Drain Radius c vr = Coefficient of Radial T r = Time Factor for Radial k h = Coefficient of Horizontal Permeability T r = Time Factor for Radial e o = Initial Void Ratio Plan View Sand Drain Triangular Spacing Figure 7.30. Das FGE (2006). Slide 69 of 74

TIME RATE OF RADIAL CONSOLIDATION Variation of T r with U - Table 7.3 Das PGE (2006). Slide 70 of 74

TIME RATE OF RADIAL CONSOLIDATION Variation of T r with U - Table 7.3 Das PGE (2006). Slide 71 of 74

GROUND MODIFICATION FOR CONSOLIDATION AVERAGE DEGREE OF CONSOLIDATION DUE TO VERTICAL & RADIAL DRAINAGE Sand U (1 U )(1 U v, r r v Where: 1 ) Drain Drainage Clay U v,r = Average Degree of due to Vertical & Radial Drainage U v = Average Degree of due to Vertical Drainage Sand U r = Average Degree of due to Radial Drainage Vertical and Radial Drainage Courtesy of www.nhi.fhwa.dot.gov Slide 72 of 74

Settlement Rod (Steel) 14.330 SOIL MECHANICS CONSOLIDATION MONITORING SETTLEMENT PLATES Rod Protection (Typically PVC Pipe) Fill Layer Settlement Plate Base (Plywood or Steel) Insitu Soil Layer to be Monitored General Concept Standard Plan Detail (Courtesy of Iowa DOT) Slide 73 of 74

SURCHARGING INSTRUMENTATION EXAMPLE Settlement Platforms Permanent Fill Surcharge Drainage Blanket Inclinometers Soft Clay Vertical Drain Firm Soil Piezometers Courtesy of www.nhi.fhwa.dot.gov Not to Scale Slide 74 of 74