Design and construction for ground improvement - Guidelines, Part 2: Preconsolidation using vertical drains

IS 15284 Part 2: Scope - Key Formulas, Tables & Specifications

Scope:
This part of IS 15284 deals with design and analysis related to radial consolidation around vertical drains and well spacing.

Key Formulas

• Time factor for radial flow (Tr):
  [ T_r = \frac{C_r \cdot t}{R^2} ] where:

  • ( C_r ) = coefficient of consolidation for radial flow
  • ( t ) = time
  • ( 2R ) = well spacing (Fig. 2)

• Degree of consolidation (U):
  [ U_T = 1 - e^{-A} ] (where (A) depends on flow and drainage conditions)

Important Tables

| Table 2: Percentage Consolidation (Uz) vs Time Factor (Tv) for Various Initial Excess Pore Pressure Distributions | |---|---|---|---|---|---| | Tv | Case 1 (Uniform) | Case 2 (Half Sine) | Case 3 (Full Sine) | Case 4 (Triangular) | | 0.004 | 7.35% | 6.49% | 0.98% | 0.85% | | 0.100 | 35.62% | 32.88% | 21.87% | 19.76% | | 1.00 | 93.13% | 92.80% | 91.52% | 91.25% |

| Table 3: Radial Flow Time Factor (T) for Various Degree of Consolidation (U_r) and (R/r_w) Ratios | |---|---|---|---|---|---|---|---|---|---|---|---|---| | (U_r) (%) | 5 | 10 | 15 | 20 | 25 | 30 | 40 | 50 | 60 | 80 | 100 | | 50 | 0.081 | 0.137 | 0.170 | 0.195 | 0.214 | 0.230 | 0.255 | 0.274 | 0.290 | 0.

IS 15284 Part 2 Key Formulas, Tables & Specifications for Radial Flow Consolidation

1. Time Factor for Radial Flow (Clause 6.5.2)

• Cr = coefficient of consolidation for radial flow
• 2R = well spacing (see Fig. 2)
• Time factor ( T_r ) is calculated for given Cr, time ( t ), and radius ( R ).

2. Percentage Consolidation (U) vs Time Factor (Tv) (Table 2)

• Cases refer to initial excess pore pressure distribution (Fig. 1).

3. Radial Flow Equation Solution (Table 3)

• ( R ) = well radius spacing, ( r_w ) = drain radius.

4. Additional Notes

• Cr differs from vertical consolidation coefficient ( C_v ) due to anisotropy.
• Laboratory tests

IS 15284 (Part 2) - Key Definitions & Formulas for Consolidation

Key Definitions:

• Cr: Coefficient of consolidation for radial flow.
• 2R: Well spacing (distance between drains).
• Tr: Time factor for radial flow.
• Ur: Degree of consolidation (radial).
• Tv: Time factor for vertical flow.
• rw: Radius of drain well.

Important Formulas:

1. Time factor for radial flow (Tr):

[ Tr = \frac{C_r \cdot t}{R^2} ]

Where:

• (C_r) = coefficient of consolidation (radial),
• (t) = time,
• (R) = half well spacing.

2. Degree of consolidation (Ut):

[ U_t = 1 - e^{-A} ]

Where (A) depends on consolidation parameters (not fully detailed here).

3. Relationship between radial consolidation (U_r) and vertical time factor (T_v):

Given in Table 3 (values of time factor (T) for different degrees of consolidation (U_r) and radius ratio (R/r_w)).

Tables Summary:

Conceptual Diagram (Drain-Well Pattern):

flowchart TB
    A[Drain Well] -->|Radial Flow| B[

IS 15284 Part 2: Key Information for Design & Installation of Vertical Drains

Necessary Information (Clause 4.1)

• Soil profile and properties (permeability, compressibility)
• Drain spacing and pattern (well spacing = 2R)
• Initial excess pore water pressure distribution (4 cases: half sine, full sine, triangular, linear)
• Drain dimensions (radius rw)
• Consolidation parameters (coefficient of consolidation Cr, time factor Tv)
• Preloading conditions and schedule

Important Formulas

• Time factor for radial flow:

[ T_r = \frac{C_r \cdot t}{R^2} ]

Where:

• (C_r) = coefficient of consolidation for radial flow

• (t) = time

• (R) = half well spacing

• Degree of consolidation (radial flow):

[ U_r = 1 - e^{-A} ]

Where (A) depends on flow parameters (see Table 3).

Key Tables

| Table 2: % Consolidation (Uz) vs Tv for Various Initial Pore Pressure Distributions (Cases 1-4) |
|---|---|---|---|---|
| Tv | Case 1 | Case 2 | Case 3 | Case 4 |
| 0.10 | 35.62% | 32.88% | 21.87% | 19.76% |
| 0.50 | 76.40% | 76.28% | 70.88% | 69.94% |
| 1.00 | 93.13% | 92.80% | 91.52% | 91.25% |

| Table 3: Time Factor (T) for Radial Flow vs Degree of Consolidation (U_r) and (R/r_w) |
|---|---|---|---|
| (U_r)% | (R/r_w=5) | (R/r_w=50) | (R/r_w=100) |
| 50 | 0.081 | 0.274 | 0.334 |
| 90 | 0.270 | 0.911 | 1.110

IS 15284 Part 2: Vertical Drains - Types & Installation Methods

Types of Vertical Drains (Clause 5.1 & Table 1)

Installation Methods

• Driven/Vibratory Mandrel: Displacement type; physically pushes sand into soil.
• Jetting with Water: Non-displacement; sand is flushed into the soil by water jets.
• Continuous Flight Auger: Non-displacement; auger drills and sand is placed simultaneously.

Key Notes:

• Spacing: Typically 2 to 8 times the drain diameter.
• Length: Up to 30-35 m depending on method.
• Smear Zone: Area of disturbed soil around the drain affecting consolidation.

flowchart TD
    A[Vertical Drains] --> B[Driven/Vibratory Mandrel]
    A --> C[Continuous Flight Auger]
    A --> D[Jetted]
    B --> E[Displacement Type]
    C --> F[Non-Displacement Type]
    D --> F

For detailed design, consider soil sensitivity, drain diameter, spacing, and installation impact as per IS 15284 Part 2.

IS 15284 Part 2: Design of Vertical Drains for Preloading

Key Design Steps (Clause 6.1 & 6.2)

• Drain Depth (d): Extend through major compressible soil layers causing consolidation.
• Drain Spacing (s): Typically arranged in equilateral triangular or square grids for uniform consolidation.
• Loading Rate & Stages: Controlled to avoid plastic flow; consider soil stratification and adjacent ground topography.

Typical Drain Spacing Formula (for radial consolidation):

[ s = \sqrt{\frac{4A}{\pi}} ]

Where:

• ( A ) = area influenced by each drain (depends on grid pattern)
• For triangular grid: ( A = \frac{\sqrt{3}}{2} s^2 )

Design Parameters to Determine (Clause 4.1):

• Soil permeability, compressibility, and stratification
• Preload magnitude and duration
• Drain diameter and length

Typical Drain Arrangement:

graph TD
  A[Vertical Drains] --> B[Equilateral Triangular Grid]
  A --> C[Square Grid]
  B --> D[Uniform consolidation]
  C --> D

Summary Table: Drain Depth & Spacing

Note: Final design requires site-specific soil data and consolidation analysis to ensure effective preloading without ground damage.

IS 15284 Part 2: Special Requirements for Installation and Drainage of Vertical Drains

Key Specifications & Tables

1. Installation Methods for Sand Drains (Clause 5.1, Table 1)

2. Drainage Layer (Clause 7.2)

• Provide a sand blanket ≥ 400 mm thick at ground level.
• Embed at least 150 mm length of prefabricated vertical drain into this sand blanket.
• Purpose: Connect vertical drains to a permeable layer for pore water discharge.

3. Design Inputs (Clause 4.1)

• Soil profile and properties.
• Drain dimensions and spacing.
• Loading pattern and intensity (from structural analysis).

Summary Diagram of Drain Installation & Drainage

flowchart TB
    A[Ground Surface] --> B[Sand Blanket (≥400 mm thick)]
    B --> C[Prefabricated Vertical Drain (≥150 mm embedded)]
    C --> D[Vertical Drain in Soil]
    D --> E[Pore Water Flow Out]

Use these guidelines for effective vertical drain design and installation to ensure rapid consolidation and drainage.

Control and Monitoring of Preloading in Field (IS 15284 Part 2)

Key Specifications:

• Factor of Safety (FoS) against slip or bearing failure at each preload stage: ≥ 1.25 (Clause 6.4)
• Preloading is typically staged to achieve ≥ 90% consolidation per stage (Clause 6.3, 6.7).
• Pause period between stages is controlled based on settlement and pore pressure dissipation monitoring (Clause 8).

Monitoring Instruments:

• Settlement gauges (e.g., settlement plates, extensometers)
• Pore water pressure transducers (piezometers)

Important Parameters:

• Degree of consolidation (U) is evaluated at each preload stage.
• Radial and vertical drainage effects considered.
• Improvement in shear strength is assessed before next preload increment.

Estimation of Radial Consolidation Coefficient (Cr):

• Preferably measured from horizontal consolidation tests.
• If unavailable, estimate from ratio of horizontal to vertical permeability:
  [ C_r = C_v \times \frac{k_r}{k_v} ] where (k_r) and (k_v) are horizontal and vertical permeabilities.

Consolidation Monitoring:

• Ensure settlement stabilizes and pore pressure dissipates before next preload.
• Use pore pressure and settlement data to decide preload duration.

Summary Table for Preload Control

flowchart TD
    A[Start Preloading] --> B[Apply Load Stage]
    B --> C[Monitor Settlement & Pore Pressure]
    C --> D{Is Settlement & Pore Pressure Stable?}
    D -- No --> C
    D -- Yes --> E[Calculate Degree of Consolidation]
    E --> F{FoS ≥ 1.25 and U ≥ 90%?}
    F -- No --> B[Increase Load Stage]
    F -- Yes --> G[Proceed to Next Stage or Final Load]

Key Formulas and Tables for Consolidation and Time Factors (IS 15284 Part 2: 2004)

1. Degree of Consolidation for 3D Flow

[ U = 1 - (1 - U_z)(1 - U_r) ]

• (U): Overall degree of consolidation
• (U_z): Degree of vertical consolidation (function of (T_v))
• (U_r): Degree of radial consolidation (function of (T_r))

2. Time Factor for Vertical Flow

[ T_v = \frac{C_v t}{H^2} ]

• (C_v): Coefficient of vertical consolidation
• (t): Time elapsed
• (H): Drainage path length (half or full thickness depending on drainage)

Use Table 2 for (U_z) values vs. (T_v) for different initial excess pore pressure distributions (Cases 1 to 4).

3. Time Factor for Radial Flow

[ T_r = \frac{C_r t}{R^2} ]

• (C_r): Coefficient of radial consolidation
• (R): Half well spacing (drain spacing)
• (t): Time elapsed

Use Table 3 to find (T_r) for given degree of consolidation (U_r) and ratio (R/r_w) (well radius).

4. Important Notes:

• (C_r) is generally different from (C_v) due to soil anisotropy.
• Laboratory tests on horizontal samples or permeability ratio estimates are used to determine (C_r).
• Well spacing (= 2R).
• Drain-well pattern schematic shown in Fig. 2 of the code.

Table Snippet: Degree of Consolidation (U_z) vs (T_v) (Case 1 example)

Table Snippet: Rad

IS 15284 Part 2: Evaluation of Shear Strength Improvement

Key Points from Clauses 6.4 & 6.8:

• Shear strength improvement is proportional to the degree of consolidation achieved at each preload stage.
• Safety against failure is checked at each stage considering the improved shear strength.
• A factor of safety (FoS) = 1.25 is recommended for each preload stage.
• Consolidation degree is determined from radial and vertical drainage measurements.

Shear Strength Improvement Formula (Conceptual):

[ \tau_{u,new} = \tau_{u,initial} + \Delta \tau_u ]

Where:

• (\tau_{u,new}) = Improved undrained shear strength after consolidation
• (\tau_{u,initial}) = Initial undrained shear strength
• (\Delta \tau_u = k \times \text{Degree of Consolidation} \times \tau_{u,initial})

(k) is an empirical coefficient (often close to 1, assuming proportionality).

Evaluation Procedure:

Summary:

• Shear strength gain is directly proportional to consolidation.
• Use improved (\tau_u) for stability checks at each preload stage.
• Maintain FoS ≥ 1.25 for safe design progression.

flowchart TD
    A[Start Preload Stage] --> B[Measure Degree of Consolidation (U)]
    B --> C[Calculate Improved Shear Strength \tau_u]
    C --> D[Check Factor of Safety (FoS)]
    D -->|FoS ≥ 1.25| E[Proceed to Next Stage]
    D -->|FoS < 1.25| F[Modify Preload or Design]
``

IS 15284 Part 2: Safety and Stability Considerations Summary

Key Points:

• Factor of Safety (FoS): Minimum FoS = 1.25 at each preload stage (Clause 6.4).
• Shear strength improves proportionally with consolidation percentage (Clause 6.8).
• Stability checks include slip and bearing capacity failure.

Important Formulas:

• Degree of Consolidation (Ur) for radial flow:

[ U_r = 1 - e^{-F_n} ]

where (F_n) is a function of time factor (T_r), drain radius, and soil properties.

• Time factor for radial flow (Clause 6.5.2):

[ T_r = \frac{C_r \cdot t}{R^2} ]

where:

• (C_r) = coefficient of consolidation for radial flow
• (t) = time
• (2R) = well spacing

Tables Summary:

Design & Stability Check Workflow:

1. Calculate degree of consolidation (U_r) using Table 3 or formula.
2. Estimate shear strength gain proportional to (U_r).
3. Check factor of safety ( \geq 1.25 ) against slip or bearing failure.
4. Determine preload magnitude for next stage.

Visual: Drain-Well Pattern (Fig. 2)

flowchart TB
    A[Drain-Well Installation] --> B[Plan View: Wells spaced 2R apart]
    A --> C[Section View: Radial and vertical drainage]
    B --> D[No flow across outer boundary]

This ensures safe staged loading with improved soil strength and controlled consolidation.

IS 15284 (Part 2) - Instrumentation & Field Monitoring Guidelines

Key Points from Clause 7.4 & 8:

• Cr (Coefficient of Consolidation in horizontal direction) differs from Cv (vertical) due to soil anisotropy.
• Cr is best obtained from lab consolidation tests on horizontal samples or estimated via the ratio of horizontal to vertical permeability.
• For varved clay, in-situ permeability tests are recommended.

Instrumentation for Preloading Control (Clause 8):

• Settlement measurement: Use settlement gauges or plates to monitor ground settlement at each loading stage.
• Pore water pressure measurement: Install piezometers to track dissipation during consolidation.
• Loading stages: Pause periods should be controlled based on real-time settlement and pore pressure data to ensure consolidation is nearly complete before further loading.

Typical Instrumentation Setup:

Important Formula:

• Estimate Cr from permeability ratio:

[ C_r = C_v \times \frac{k_h}{k_v} ]

Where:

• ( C_r ) = horizontal consolidation coefficient
• ( C_v ) = vertical consolidation coefficient
• ( k_h ), ( k_v ) = horizontal and vertical permeability respectively

Summary Diagram: Instrumentation Scheme for Preloading Monitoring

graph TD
    A[Preloading Stage] --> B[Settlement Gauges]
    A --> C[Piezometers]
    B --> D[Settlement Data]
    C --> E[Pore Pressure Data]
    D & E --> F[Consolidation Status]
    F --> G[Control Loading Pause]

Note: Refer to IS 15284 (Part 2) Table 1 for sand drain installation methods relevant to instrumentation planning.