# Design Process for Land Reclamation and Soil Improvement

# Chapter 12

Design Process for Land Reclamation and Soil Improvement

12.1 BEARING CAPACITY OF SEABED SOIL

12.2 SETTLEMENT OF RECLAIMED FILL

12.3 PRIMARY CONSOLIDATION OF COMPRESSIBLE SOIL

12.4 TIME RATE OF CONSOLIDATION

12.5 TIME RATE OF CONSOLIDATION FOR MULTI-LAYER CONDITIONS

12.6 TIME RATE OF CONSOLIDATION WITH RADIAL DRAINAGE

12.7 SMEAR EFFECT DUE TO MANDREL PENETRATION

12.8 WELL RESISTANCE

12.9 SOFTWARE AVAILABLE FOR CONSOLIDATION ANALYSIS

The design process for land reclamation projects require both settlement and bearing capacity analysis. If the fill material is granular soil, the bearing capacity is not an issue but settlement of reclaimed land caused by underlying compressible soil layers would be a major issue. However, the allowable critical height of the embankment should be included as part of the bearing capacity calculation. This chapter will emphasize on the settlement aspect, and the bearing capacity aspect will only be discussed briefly.

## 12.1 BEARING CAPACITY OF SEABED SOIL

If the underlying seabed soil is firm with cohesive or dense granular soil, the bearing capacity of the foundation will not pose a problem. However, if it is soft clay, prevention against shear failure should be considered. Since consolidation may take place after an additional load is placed, the shear strength of the clay may increase from time to time. The critical time may be soon after filling. A simple estimation of the critical height of fill is given by:

where *H _{c}* is the critical height

*c _{u}* is the undrained shear strength

*γ _{fill}* is the unit weight of fill

The critical height related to the formation of the reclamation profile would be largely dependent upon the geometry of the slope, which will be discussed in the section under slope stability. The bearing capacity of the foundation to be built on the reclaimed fill should be calculated separately depending upon the type of foundation. This will not be discussed here.

## 12.2 SETTLEMENT OF RECLAIMED FILL

Concerning the settlement of recently reclaimed land, there are two types of settlement. The first is instantaneous settlement caused by elastic and plastic deformation of soil particles themselves. This settlement is rapid and relatively small in magnitude. Therefore, its effects are usually ignored in land reclamation project design. The second type is significant settlement, which must be considered in the calculations as consolidation settlement. This type of settlement is huge in magnitude and also takes place over a longer time. Therefore, it may cause problems to infrastructure built on the reclaimed land or the earth structure itself. This aspect will be discussed in detail in this chapter.

## 12.3 PRIMARY CONSOLIDATION OF COMPRESSIBLE SOIL

Primary consolidation of compressible soil usually occurs because of the additional load placed on it. This settlement will be discussed under two aspects: (a) magnitude of settlement (b) time rate of settlement.

### 12.3.1 Magnitude of settlement

The magnitude of settlement of the compressible layer is very dependent upon the (i) magnitude of the additional load (Δσ'), (ii) compressibility of the layer (*C _{c} or C_{r}*), (iii) thickness of the layer (

*H*), (iv) initial condition of soil such as the initial void ratio (

*e*), (v) and stress history of the soil, such as preconsolidation pressure (). The greater the magnitude of additional load, compressibility, thickness and initial void ratio, the higher is the magnitude of settlement. The greater the preconsolidation pressure, the lower is the magnitude of settlement.

_{o}**12.3.1.1--** Normally consolidated soil

For clay under normal consolidation conditions (that is, current effective stress is equivalent to the overburden pressure), the magnitude of settlement caused by the additional load is given by:

where *S* is settlement

*C _{c}* is compression index

*e _{o}* is natural void ratio

is initial effective stress and

Δσ' is additional stress

The compression parameters, initial void ratio, and current effective stress can be determined by carrying out the laboratory tests described in Chapter 11.

*Example 12.1*

Reclamation is carried out on the foreshore area where an underlying compressible soft clay of 10 meters thickness exists. The seabed is at –4mCD and the stabilized ground water level is at +2mCD after reclamation. The reclamation is carried out up to +5mCD and this can be considered as instantaneous loading. The geotechnical parameters of soft clay and fill material are given in Figure Example 12.1. Calculate the magnitude of primary consolidation settlement.

Additional stress below ground water level = (+ 2 + 4) x (18 – 10) = 48 kN/m^{2}

Additional stress above ground water level = (5 – 2) x (18) = 54 kN/m^{2}

Total additional stress = 102 kN/m^{2}

Current effective stress at the center of the compressible layer, σ_{v}'= [(– 4 – (–14))/2] x (15 – 10) = 25 kN/m^{2}

By applying Equation 12.2,

the ultimate primary consolidation settlement = 2.35 meters

**12.3.1.2--** Overconsolidated soil

Overconsolidated soils settle much less than normally consolidated soil because of its higher yield stress in in-situ conditions. Generally, the yield stress of overconsolidated soil is greater than the existing overburden stress. The magnitude of settlement is much lower when overburden stress plus additional stress is lower than its yield stress. The settlement of overconsolidated soil, when total applied load + Δσ' is lower than its yield stress (), is given by:

where C_{r} is the recompression index

*Example 12.2*

A similar type of reclamation was carried out using the same type of fill material on a similar type of seabed and thickness of compressible soil as in example 12.1. However, the compressible soil was found to be in an overconsolidated condition and its *OCR* (over consolidation ratio) was about 3. The filling was carried out to only +2mCD. Calculate the magnitude of primary consolidation settlement.

Therefore, the current status of effective stress or yield stress

= 3 x 25 = 75*kN* / *m*^{2}

By applying Equation 12.3,

the ultimate primary consolidation settlement = 0.155m

It can be seen that the magnitude of settlement is much smaller compared with Example 12.1.

For overconsolidated soil, when additional stress is applied beyond the yield stress, the settlement becomes greater. However, this magnitude of settlement is still smaller than the additional stress applied to NC condition soil. The magnitude of settlement is given by:

*Example 12.3*

Reclamation was carried out on the same type of soil and seabed conditions as in Example 12.2. However, the sand was filled up to +5mCD. Calculate the magnitude of settlement.

Applying Equation 12.4,

Additional stress above ground water level

= (5 - 2) x (18) = 54 kN/m^{2}

Additional stress below ground water level = (2 + 4) x (18 – 10) = 48 kN/m^{2}

Total additional stress = 102 kN/m2

the ultimate primary consolidation settlement = 0.921 m

It can be seen that the magnitude of settlement occurring in OC clay is smaller than the NC clay even with the same magnitude of additional stress.

**12.3.1.3--** Underconsolidated soil

Sometimes underconsolidated clay can be found naturally. In that case, the current effective stress of clay is lower than its overburden stress. In such conditions, the magnitude of settlement will be much greater. The settlement of underconsolidated clay is given by:

where is the current status of effective stress, which is lower than the existing overburden stress. Discussion on underconsolidated soil such as slurry is found in Bo et al. (1997c).

*Example 12.4*

The reclamation level, condition of seabed and soil conditions are the same as Example 12.1, except that the current status of effective stress (δ_{1}) is less than the existing overburden stress and only 15 kN/m^{3}. Calculate the magnitude of settlement.

By applying Equation 12.5,

the ultimate primary consolidation settlement = 3.09 m

It can be seen that underconsolidated clay settlement is much greater than overconsolidated and normally consolidated clay.

When the compressible layer is not homogenous and has several sublayers with different geotechnical properties, the ultimate settlement is calculated for each sub-layer by applying the relevant equations. The total settlement is the summation of all sub-layer settlement.

Total ultimate settlement Σ*S* = S_{layer1} +S_{layer2} + S_{layer3-------}

*Example 12.5*

This time the compressible layer has about (5) sub-layers, which have five different soil properties, as shown in the figure. Calculate the ultimate primary consolidation settlement.

Additional load is calculated in the same way as Example 12.1.

The ultimate settlement is calculated for each sub-layer by applying Equation 12.4.

Total ultimate settlement is

Σ*S _{ult} = S_{ult1} + S_{ult2} + S_{ult3} + S_{ult4} + S_{ult5}*

Details of the calculation can be found in Table Example 12.5.

Examples 12.1 to 12.5 use a simple method of calculating the magnitude of settlement. However, the magnitude of settlement is traditionally calculated for several sub-divided layers, and the total magnitude of settlement is the summation of all sub-layer settlement.

Estimating the magnitude of settlement without subdividing usually gives an overestimated magnitude of settlement. The accurate magnitude of settlement can be obtained only if sufficient sub-division is made. This

Table Example 12.5 1 Calculations for multi-layer settlement. | |||||||||||

Seabed (mad) | -4 | ||||||||||

Fill level (mCD) | 10 | ||||||||||

GW level (mCD) | 2 | ||||||||||

Density of fill (KN/m^{3}) | 18 | ||||||||||

Density of water (KN/m^{3}) | 10 | ||||||||||

Additional load (KN/m^{2}) | 192 | ||||||||||

Note: The settlement formula is given as S = C_{r}/(l+e)*H*log(P_{c}/P_{0})+C_{c}/(l+e)*H*log(P_{f}/ P_{c}) | |||||||||||

El of mid of sub-layer (mCD) | Boundary El (mCD) | Density Clay | e | OCR | C_{c} | C_{r} | H (m) | P_{r} | settlement (m) | ||

-5 | -6 | 15 | 2 | 5 | 2 | 10 | 1 | 0.1 | 2 | 197 | 0.883 |

-7.5 | -9 | 15.5 | 1.8 | 18.25 | 2 | 36.5 | 0.8 | 0.08 | 3 | 210.25 | 0.678 |

-10 | -11 | 16 | 1.5 | 32.5 | 4 | 130 | 0.4 | 0.04 | 2 | 224.5 | 0.095 |

-12 | -13 | 15.5 | 1.6 | 44 | 3 | 132 | 0.6 | 0.06 | 2 | 236 | 0.138 |

-13.5 | -14 | 16 | 1.7 | 52.5 | 3 | 157.5 | 0.7 | 0.07 | 1 | 244.5 | 0.062 |

Total settlement | 1.856 |

is demonstrated in Figure 12.1 in which the reference settlement is 2.75 meters for NC clay, and 1.31meters for OC clay.

This figure shows the variation of settlement with different numbers of sub-divisions for normally consolidated clay and overconsolidated clay, as explained in Examples 12.1 and 12.3. It was found that the magnitude of settlement stabilized only after certain numbers of sub-layers are made. The variation is much greater for OC clay than NC clay.

## 12.4 TIME RATE OF CONSOLIDATION

The time rate of consolidation largely depends on the permeability of the clay and the thickness. For the consolidation process, the time rate of consolidation is rather related to the coefficient of consolidation (c_{v}). This

parameter varies depending upon the stress level, and it is more or less constant in the normally consolidated range. The coefficient of consolidation can be obtained from oedometer tests, as described in Chapter 11.

Casagrande (1938) and Taylor (1948) provide the relationship between the degree of settlement or the degree of consolidation as follows:

where *U _{v}* is the degree of consolidation,

*T*is the time factor.

_{v}Sivaram and Swames (1977) has suggested that there is a closely matching relationship between the degree of consolidation and the time factor for the whole range, as follows:

The time factor can then be obtained if the coefficient of consolidation and drainage length are known, by using the following equation:

where *t* is time. *H _{dr}* is the drainage path and for single drainage it is equivalent to the thickness of the layer and for double drainage, it is half of the thickness of the layer.

Therefore, using Equations 12.8 and 12.9, the degree of consolidation and time rate of consolidation can be calculated.

*Example 12.6*

Reclamation was carried out as shown in Example 12.1 and the geotechnical parameters of soft clay is also the same as Example 12.1, and *C _{V}* is 1m

^{2}/yr.

Calculate (i) the time required for 90% consolidation if the drainage is double, (ii) time required for 90% consolidation if the drainage is single, (iii) time required for consolidation of 50% if the drainage is double, (iv) settlement at five years from the date of filling if the drainage is double, (v) produce a time vs settlement curve for double and single drainage.

(i) For double drainage:

*H* Drainage is double, therefore *H _{dr}*= = 5

*m*

Applying Equation 12.8 to find *T _{v}* when

*U*= 0.9

_{v}*T _{v}*= 0.848

Applying Equation 12.9 to find the time required

Therefore, the time required for 90% consolidation with double drainage is 21.2 years.

(ii)For single drainage:

H_{d} = H = 10m

Applying Equation 12.9 to find the time required:

Therefore, the time required for 90% consolidation with single drainage is much longer, up to four times that required for double drainage.

(iii) For time required for 50% consolidation, find *T _{v}* first using Equation 12.8.

*T _{v}*- 0.216

Find the time required, with double drainage conditions by applying Equation 12.9:

*t* = 5.40 years

Therefore, the time required for 50% consolidation with double drainage is not half, but much shorter.

(iv) To find out the settlement at five years from the date of instantaneous filling, we must first find out the time factor *T _{v}* by applying Equation 12.9.

Find the degree of consolidation, using Equation 12.8.

In order to simplify the example, the ultimate primary consolidation settlement is taken from Example 12.1 as 2.35 meters. Therefore, the degree of consolidation is defined as:

*.:S _{5yers}=* 0.4856x2.35 = 1.141 meters

Settlement at five years, with double drainage conditions, is found to be 1.141 meters. As an example (12.1), settlement at various times is calculated using Equation 12.8 and 12.10 for both single and double drainages. The resulting settlements at time “t” is shown in Table Examples 12.6a and 12.6b. Settlement vs time curves is shown in Figure Example 12.6.

For single drainage,

*C _{v}*(m

^{2}/year) = 1

*H _{dr}, * = 10

For double drainage,

Equivalent *C _{v}*(m

^{2}/year) = 1

*H _{dr}*5

## 12.5 TIME RATE OF CONSOLIDATION FOR MULTI-LAYER CONDITIONS

The above examples are simple calculations for time rate of settlement or consolidation of homogeneous soft soil where C_{v} is assumed to be constant throughout the soil profile. In nature, this will be a rare case. Various soil layers with various C_{v} values can be encountered. However, Equation 12.9 only allows for single values of C_{v}. As such, an equivalent C_{v} method is used to calculate the time rate of consolidation for multi-layers. In the equivalent C_{v} method, one C_{v} values can be the average of several C_{v} values from various soil layers, or any selected C_{v} value can be assumed as an equivalent C_{v}. From these, the equivalent drainage length is calculated by applying the following equation:

Table Example 12.6a Time rate of settlement calculation. The ultimate settlement is 2.35 from Example 12.1. | |||||

Time (year) | T_{v} | 4T_{v}/3.14 | A | U_{v} | Settlement (m) |

A=1+(4T_{v}/3.14)^{2.8} | |||||

0 | 0 | ||||

1 | 0.01 | 0.013271 | 1.000006 | 0.11520145 | 0.270723404 |

2 | 0.02 | 0.026543 | 1.000039 | 0.16291849 | 0.382858442 |

4 | 0.04 | 0.053086 | 1.000269 | 0.23039203 | 0.541421268 |

10 | 0.1 | 0.132714 | 1.003501 | 0.36407151 | 0.855568057 |

20 | 0.2 | 0.265428 | 1.024381 | 0.51298039 | 1.20550391 |

50 | 0.5 | 0.66357 | 1.317163 | 0.77540373 | 1.822198754 |

100 | 1 | 1.32714 | 3.208853 | .93503182 | 2.197301274 |

200 | 2 | 2.65428 | 16.38335 | 0.98763232 | 2.32093595 |

400 | 4 | 5.30856 | 108.1359 | .9963405 | 2.341400178 |

Table Example 12.6b Time rate of settlement calculation. The ultimate settlement is 2.35 from Example 12.1. | |||||

Time (year) | T_{v} | 4T_{v}/3.14 | A | U_{v} | Settlement (m) |

A=1+(4T_{v}/3.14)^{2.8} | |||||

0 | 0 | ||||

1 | 0.04 | 0.053086 | 1.000269 | 0.23039203 | 0.541421268 |

2 | 0.08 | 0.106171 | 1.001874 | 0.32573003 | 0.765465576 |

4 | 0.16 | 0.212342 | 1.013053 | 0.45973781 | 1.080383853 |

10 | 0.4 | 0.530856 | 1.169799 | 0.70842921 | 1.66480865 |

20 | 0.8 | 1.061712 | 2.182548 | 0.89604297 | 2.105700984 |

50 | 2 | 2.65428 | 16.38335 | 0.98763232 | 2.32093595 |

100 | 4 | 5.30856 | 108.1359 | 0.9963405 | 2.341400178 |

200 | 8 | 10.61712 | 747.1375 | 0.99693002 | 2.342785545 |

400 | 16 | 21.23424 | 5197.403 | 0.99630566 | 2.341318298 |

The equivalent drainage path can be calculated for all various layers and the total equivalent drainage length is given by:

From these time rates of consolidation, the settlement or degree of consolidation can be calculated using the C_{vassum} and the *H _{dr equivalent}* applying Equations 12.8, 12.9 and 12.10. This method is only used for calculating the time rate of consolidation for multi-layer soil. However, it has been reported to give poor results. Therefore it is not widely used in practice. Nevertheless, it is described here for completeness.

*Example 12.7*

Reclamation is carried out on the foreshore area where the underlying soil is not homogenous and has various soil parameters, as shown in Example 12.5. (i) Calculate the time required for 90% consolidation for double drainage conditions. (ii) Calculate the time rate of settlement for double drainage conditions.

(i) As shown in Figure Example 12.5, C_{V} values vary throughout the profile of soil.

Let us assume C_{v} values of 1 m^{2}/yr as equivalent to C_{v(equi).}

The equivalent drainage lengths of various layers are found by applying

Equation 12.11.

Therefore, *H _{dri}_{equi}*= 6.0515 meters

As calculated in Example 12.6, the time factor for 90% consolidation is 0.845.

Therefore, the time required for 90% consolidation is

(ii) As explained in Example 12.5, in order to obtain the settlement vs time curve for the whole consolidation process, it is necessary to calculate the settlement for varying time intervals. By applying Equations 12.8 and 12.9 and with the help of a spreadsheet, the following results can be obtained, as shown in Table Example 12.7. The time rate of settlement is shown in Figure Example 12.7.

Table Example 12.7 Assume different values of C_{v} to one assumed C_{v} value. Assumed C_{v}(m^{2}/year) = 1. | ||||||||||

Org H | Org C_{v} | Eq H | ||||||||

H1^{l} | 2 | 0.6 | 2.581989 | |||||||

H2^{l} | 3 | 0.5 | 4.242641 | |||||||

H3^{l} | 2 | 1 | 2 | |||||||

H4^{l} | 2 | 0.7 | 2.390457 | |||||||

H5^{l} | 1 | 2 | 0.707107 | |||||||

10 | 11.92219 | |||||||||

Time (year) | T_{v} | 4T_{v}/3.14 | A | U_{v} | Settlement (m) | |||||

1 | 0.028142 | 0.035849 | 1.0009 | 0.018934 | 0.35140667 | |||||

2 | 0.056283 | 0.071698 | 1.000624 | 0.267735 | 0.496916534 | |||||

4 | 0.112566 | 0.143396 | 1.004348 | 0.378383 | 0.702278992 | |||||

10 | 0.281415 | 0.358491 | 1.056564 | 0.592873 | 1.100372268 | |||||

20 | 0.562831 | 0.716982 | 1.393933 | 0.797874 | 1.480855446 | |||||

50 | 1.407076 | 1.792454 | 6.124534 | 0.967917 | 1.796453138 | |||||

100 | 2.814153 | 3.584908 | 36.68933 | 0.993542 | 1.844014578 | |||||

200 | 5.628305 | 7.169816 | 249.5549 | 0.9969222 | 1.850287552 | |||||

400 | 11.25661 | 14.33963 | 1732.037 | 0.996706 | 1.849887128 |

## 12.6 TIME RATE OF CONSOLIDATION WITH RADIAL DRAINAGE

When the thickness of the clay layer is greater, consolidation takes much longer. In order to accelerate the consolidation process either a sand drain or PVD is installed. The drainage path then becomes shorter. There are two patterns of installation, such as square and triangular spacing. Some are installed with rectangular spacing. The equivalent drainage path (d_{e}) can be calculated from the spacing.

When vertical drain systems are introduced, the permeability along the vertical direction becomes less important and the permeability along the horizontal direction becomes more important. Most natural soil deposits are anisotropic and form a thin horizontal layer. Therefore, the permeability along the horizontal plane is usually greater than the vertical plane unless the soil is homogenous and isotropic. The coefficient of consolidation as a

result of horizontal flow *(C _{h}),* which is related to permeability with compressibility parameters given by the following equation, becomes much more important.

where *K _{h},* is the permeability along the horizontal plane,

*m _{v}* is the volume compressibility.

The time rate of consolidation is given by:

where *T _{h},* is the time factor for horizontal drainage.

The degree of consolidation due to horizontal flow is given by:

Although the vertical drainage is insignificant in soil consolidation with smaller spacing of horizontal drainage, Carrillo (1942) combined the average degree of consolidation as follows:

Therefore, the degree of consolidation and the time rate of consolidation can be calculated by applying Equation 12.17.

*Example 12.8*

The soil model is the same as Example 12.1, with double drainage conditions. However, the consolidation process is to be accelerated with prefabricated vertical drains at 2 meters spacing: (i) in a square pattern and (ii) in a triangular pattern. If *C _{h}=2* m

^{2}/yr and

*C*= 1m

_{v}^{2}/yr, calculate the degree of consolidation at six months for

*(a)*square spacing, and

*(b)*triangular spacing. Also calculate the time rate of settlement for

*(a)*square spacing

*(b)*triangular spacing.

For the double drainage with PVD, first calculate the degree of consolidation with vertical drainage for six months using Equations 12.8 and 12.9.

Secondly, calculate the degree of consolidation at six months with PVD, using Equation 12.16.

Assume vertical drain width *(a)* = 100 mm

Thickness *(b) =* 4 mm

.:d_{w}=[2(100 + 4)] π = 66.208 mm

For square spacing

*d =* 1.128 x 2 = 2.256

*n =* 34.074

For triangular spacing

*d =* 1.05 x 2 = 2.1

*n =* 31.718

*T _{h}* for square spacing using Equation 12.15

*T*_{h for} triangular spacing

_{for square} spacing using Equation 12.17

For square spacing

*F _{(n)}* = 2.783

For triangular spacing

*F _{(n)}* = 2.7195

For square spacing

Combined degree of consolidation can be calculated using Equation 12.18:

(1-*U _{vh}*)=(1-0.16)(1-0.4317)

*U _{vh}*=0.522=52.2%

For triangular spacing

The time rate of settlement for both square and triangular spacing can be calculated with the help of a spreadsheet program, as shown in Table Example 12.8. Figure Example 12.8 shows the time rate of settlement with 2 meter square spacing and triangular spacing compared with no vertical drain conditions. For comparison purposes, the ultimate settlement is taken as 2.35 meters.

Table Example 12.8a Square spacing. | |||||||

Given B = 100 mm, T = 4 mm. So dw = 2*(B+T)/3.14 = 66.24204 mm = 0.06624 mm, H = 10 m. Ultimate settlement is 2.35 m. S = 2m square spacing. | |||||||

dw(m) | de(m) | n=de/dw | Ln (n) | n2 | a | Cv(m2/yr) | |

0.06624 | 2.26 | 34.11836 | 3.529836 | 1164.062 | 2.783085 | 1 | |

Note: Ch=2 m2/yr | |||||||

Time(year) | Tv | Uv | Ch(m2/yr) | Tr | Uh | Uvr | Settlement(m) |

0.2 | 0.008 | 0.100951 | 2 | 0.078315 | 0.201576 | 0.282178 | 0.663118 |

0.4 | 0.016 | 0.142766 | 2 | 0.156629 | 0.36252 | 0.45353 | 1.065796 |

0.6 | 0.024 | 0.17485 | 2 | 0.234944 | 0.491021 | 0.580016 | 1.363038 |

0.8 | 0.032 | 0.201897 | 2 | 0.313259 | 0.593619 | 0.675666 | 1.587816 |

1 | 0.04 | 0.225723 | 2 | 0.391573 | 0.675536 | 0.748775 | 1.759621 |

1.2 | 0.048 | 0.24726 | 2 | 0.469888 | 0.74094 | 0.804996 | 1.891739 |

1.4 | 0.056 | 0.267062 | 2 | 0.548203 | 0.793161 | 0.848399 | 1.993739 |

1.6 | 0.064 | 0.285487 | 2 | 0.626517 | 0.834855 | 0.882001 | 2.072703 |

1.8 | 0.072 | 0.302785 | 2 | 0.704832 | 0.868144 | 0.908068 | 2.13396 |

2 | 0.08 | 0.319139 | 2 | 0.783147 | 0894723 | 0.928321 | 2.181555 |

Table Example 12.8b Triangular spacing. | |||||||

Given B = 100 mm, T = 4 mm. So d._{w} = 2*(B+T)/3.14 = 66.24204 mm = 0.06624 m, H = 10 m. Ultimate settlement is 2.35 m. S = 2m triangular spacing | |||||||

d_{w} (m) | d_{e}(m) | N=d_{e}/d_{w} | ln (n) | n^{2} | A | C_{v}(m^{2}/yr) | |

0.06624 | 2.12 | 32.00483 | 3.465887 | 1024.309 | 2.719518 | 1 | |

Note: C_{h}=2 m^{2}/yr C_{v} | |||||||

Time (year) | T_{v} | U_{v} | C_{h} (m_{2}/yr) | T_{r} | U_{h} | U_{vr} | Settlement (m) |

0.2 | 0.008 | 0.1009508 | 2 | 0.0889996 | 0.230342806 | 0.30804035 | 0.723894823 |

0.4 | 0.016 | 0.1427657 | 2 | 0.1779993 | 0.407627804 | 0.492198206 | 1.156665784 |

0.6 | 0.024 | 0.1748503 | 2 | 0.2669989 | 0.544076478 | 0.623794833 | 1.465917858 |

0.8 | 0.032 | 0.2018971 | 2 | 0.3559986 | 0.649095181 | 0.719941862 | 1.691863376 |

1 | 0.04 | 0.2257234 | 2 | 0.4449982 | 0.729923582 | 0.79088614 | 1.858582429 |

1.2 | 0.048 | 0.2472605 | 2 | 0.5339979 | 0.792133742 | 0.843530854 | 1.982297507 |

1.4 | 0.056 | 0.2670615 | 2 | 0.6229975 | 0.840014239 | 0.882740282 | 2.074439664 |

1.6 | 0.064 | 0.2854865 | 2 | 0.7119972 | 0.876865808 | 0.912018963 | 2.143244563 |

1.8 | 0.072 | 0.3027853 | 2 | 0.8009968 | 0.905228884 | 0.933924182 | 2.194721829 |

2 | 0.08 | 0.3191394 | 2 | 0.8899964 | 0.927058728 | 0.950337159 | 2.233292323 |

## 12.7 SMEAR EFFECT DUE TO MANDREL PENETRATION

When PVDs are installed into the soft soil, the soil around the mandrel penetration point is disturbed and a smear zone occurs. Because of this disturbance and remolding of the soil in the smear zone, the soil parameter will change, especially its permeability. If the disturbance is significant, permeability caused by horizontal and vertical flows becomes equal, or both will become the same as remolded permeability.

Barron (1941) and Hansbo (1979 & 1981) have stated that smearing affects the performance of vertical drains. The actual smear zone in the field and the reduction of permeability caused by the smear effect of the mandrel penetration could be one or two orders higher than those found in

early literature (Buddhima Indraratna & Wayan Redna I 1997, Bo et al., 1998).

The reduction of permeability in the horizontal direction is generally expressed by a permeability reduction ratio, which is the ratio of horizontal permeability to the remolded soil *(K,/K*). In order to include smear terms, the function of drain spacing is changed to the following equation proposed by Hansbo (1981).

where *s* is the smear zone ratio and *d _{s}* is the diameter of the smear zone.

k_{s} is the coefficient of permeability of the soil in the smear zone.

*Example 12.9*

The soil model is the same as Example 12.8 but there is a smear zone of 2 times the effective drain diameter and a permeability reduction ratio of 2.5 due to mandrel penetration. Calculate the time rate of settlement for both square and triangular spacing, compared with the time rate of settlement without a smear effect.

By applying Equation 12.19

For square spacing

*F _{s(n)}* = 3.81826

For triangular spacing

*F _{s(n)}* = 3.74661

Details of the results are shown in Table Example 12.9.

As can be seen in Figure Example 12.9, the time rate of settlement is much slower.

Table Example 12.9 Time rate of settlement with vertical drain consideration of smear effect. | |

C_{v} (m^{2}/year) | 1 |

C_{h} (m^{2}/year) | 2 |

H(m) | 10 |

width(a)(m) | 0.1 |

Thickness (b) (m) | 0.004 |

Spacing (m) | 2 |

d_{w} (m) | 0.066208 |

d_{e} (Square Spacing) (m) | 2.256 |

d_{e} (Triangular Spacing) (m) | 2.1 |

N (Square spacing) | 34.07428 |

N (Triangular spacing) | 31.71808 |

Ln(n/s) (Square spacing) | 2.835396 |

Ln(n/s) (triangular spacing) | 2.76374 |

N^{2} (square spacing) | 1161.056 |

N^{2}(triangular spacing) | 1006.036 |

Dia. of smear zone (d_{s})(Sq) | 4.512 |

Dia. of smear zone (d_{s}) (Tri) | 4.2 |

Smear zone ratio (s) (Sq) | 2 |

Smear zone ratio (s) (Tri) | 2 |

Ln(s) (Square spacing) | 0.693147 |

Ln(s) (triangular spacing) | 0.693147 |

Permeability reduction ratio (sq) | 2.5 |

Permeability reduction ratio (Tri) | 2.5 |

F(n) (Square spacing) | 3.818264 |

F(n) (Triangular spacing) | 3.746608 |

Ultimate Settlement (m) | 2.35 |

Table Example 12.9 Settlement (m). | ||||||||||

Time (yr) | T_{v} | U_{v} | T_{h} (square) | T_{h} (Tri) | U_{h} (square) | U_{h} (Tri) | U_{vh} (Square) | U_{vh} (Tri) | (Square) | (Triangular) |

0.1 | 0.004 | 0.0714 | 0.0392963 | 0.04535 | 0.07903511 | 0.092296 | 0.1447764 | 0.15709 | 0.3402245 | 0.369164044 |

0.2 | 0.008 | 0.101 | 0.0785926 | 0.0907 | 0.15182368 | 0.176074 | 0.2374478 | 0.25925 | 0.5580023 | 0.609238035 |

0.35 | 0.014 | 0.1335 | 0.1375371 | 0.15873 | 0.25036345 | 0.287468 | 0.3504738 | 0.38262 | 0.8236134 | 0.89916527 |

0.5 | 0.02 | 0.1596 | 0.1964816 | 0.22676 | 0.33745503 | 0.383802 | 0.44320807 | 0.48216 | 1.041539 | 1.133069829 |

0.75 | 0.03 | 0.1955 | 0.2947223 | 0.34014 | 0.46070917 | 0.516295 | 0.56613341 | 0.61085 | 1.3304135 | 1.435504936 |

1 | 0.04 | 0.2257 | 0.3929631 | 0.45351 | 0.56103417 | 0.6203 | 0.66011901 | 0.70601 | 1.5512797 | 1.659117068 |

1.25 | 0.05 | 0.2524 | 0.4912039 | 0.56689 | 0.64269557 | 0.701942 | 0.73286384 | 0.77716 | 1.72223 | 1.826323966 |

1.5 | 0.06 | 0.2764 | 0.5894447 | 0.68027 | 0.7091654 | 0.76603 | 0.78956036 | 0.83071 | 1.8554668 | 1.952158571 |

2 | 0.08 | 0.3191 | 0.7859263 | 0.90703 | 0.807309 | 0.855828 | 0.86880428 | 0.90184 | 2.0416901 | 2.119321568 |

2 | 0.08 | 0.3191 | 0.7859263 | 0.90703 | 0.807309 | 0.855828 | 0.86880428 | 0.90184 | 2.0416901 | 2.119321568 |

4 | 0.16 | 0.4505 | 1.5718525 | 1.81406 | 0.96287018 | 0.979214 | 0.97959835 | 0.98858 | 2.3020561 | 2.323160645 |

5 | 0.2 | 0.5028 | 1.9648157 | 2.26757 | 0.98370128 | 0.992108 | 0.99189652 | 0.99608 | 2.3309568 | 2.340778787 |

## 12.8 WELL RESISTANCE

It is well known that vertical drains never perform as perfect drainage systems. The performance of vertical drains is reduced because of decreased discharge capacity caused by well resistance (Barron 1948, Yoshikuni 1967, Hansbo 1981 and Bo et al. 1997b).

Therefore, well resistance parameter “*L”* was introduced in the calculation by applying Yoshikuni and Nakanido’s (1974) equation:

where *k h * is the coefficient of permeability in the horizontal direction in m/s

*k _{w}* is the cross-plane coefficient of the permeability of vertical drain

filters in the case of prefabricated vertical drains, and permeability of sand in the case of sand drains

*L* is the characteristic length of the drain, which is half the drain length for open drains and the entire length for closed drains. Therefore, the equation becomes (Yoshikuni and Nakanido [1974])

*Example 12.10*

The soil model is the same as Example 12.9, but the smear effect of well resistance is taken into consideration in this case, where the characteristic drain length (*L*) is 9.5 m, *K _{h}* is 1x10

^{9}m/s and the permeability of the PVD filter is 1x10

^{4}m/s. Calculate the time rate of settlement and compare this with perfect drain conditions, and smear effect.

Calculate the well resistance parameter (*L*) using Equation 12.20

Calculate *U _{h}* using Equation 12.21

Table Example 12.10 shows the resulting values, and Figure Example 12.10 shows the time rate of settlement with well resistance.

**Vertical drain design with well resistance**

*Given B = 100 mm, T = 4 mm. So d = 2*(B+T)/3.14 = 66.24204 mm =* 0.06624 m,H=10 m

Ultimate settlement is 2.35m (2.35m is used for comparison purposes). S = 2m square spacing

Table Example 12.10a Vertical drain design with well resistance. | ||||||||||

d 0.06624 | D 2.26 | n=D/d 34.1184 | In(n) 3.5298 | n^{2}1164.06 | a 2.78309 | C_{v}1 | K_{7}0.0001 | K_{h}0.000000001 | I 19 | L 0.0093 |

Time (year) | T_{v} | U_{v} | C_{h}(m^{2}/yr) | T_{r} | U_{h} | U_{vr} | Settlement (m) | |||

0 | 0 | |||||||||

0.2 | 0.08 | 0.10095 | 2 | 0.07831 | 0.2011 | 0.28175 | 0.6621056 | |||

0.4 | 0.016 | 0.14277 | 2 | 0.15663 | 0.36252 | 0.45353 | 1.0657959 | |||

0.6 | 0.024 | 0.17485 | 2 | 0.23494 | 0.49102 | 0.58002 | 1.3630377 | |||

0.8 | 0.032 | 0.2019 | 2 | 0.31326 | 0.59362 | 0.67567 | 1.5878157 | |||

1 | 0.04 | 0.22572 | 2 | 0.39157 | 0.67554 | 0.74878 | 1.7596214 | |||

1.2 | 0.048 | 0.24726 | 2 | 0.46989 | 0.74094 | 0.805 | 1.8917395 | |||

1.4 | 0.056 | 0.26706 | 2 | 0.5482 | 0.79316 | 0.8484 | 1.9937388 | |||

1.6 | 0.064 | 0.28549 | 2 | 0.62652 | 0.83485 | 0.882 | 2.0727032 | |||

1.8 | 0.072 | 0.30279 | 2 | 0.70483 | 0.86814 | 0.90807 | 2.13396 | |||

2 | 0.08 | 0.31914 | 2 | 0.78315 | 0.89472 | 0.92832 | 2.1815546 |

Table Example 12.10b

**Vertical drain design with well resistance**

*Given B = 100 mm, T = 4 mm. So d = 2*(B+T)/3.14 = 66.24204 mm = 0.06624 m*

Ultimate settlement is 2.35 m.

*S=2m triangular spacing*

Table Example 12.10a Vertical drain design with well resistance. | ||||||||||

d 0.06624 | D 2.12 | n=D/d 32.0048 | In(n) 3.46589 | n^{2}1024.31 | a 2.71952 | C_{v}1 | K_{7}0.0001 | K_{h}0.000000001 | I 19 | L 0.0093 |

Time (year) | T_{v} | U_{v} | C_{h}(m^{2}/yr) | T_{r} | U_{h} | U_{vr} | Settlement (m) | |||

0 | 0 | |||||||||

0.2 | 0.008 | 0.10095 | 2 | 0.089 | 0.22979 | 0.30755 | 0.722732885 | |||

0.4 | 0.016 | 0.14277 | 2 | 0.178 | 0.40763 | 0.4922 | 1.156665784 | |||

0.6 | 0.024 | 0.17485 | 2 | 0.267 | 0.54408 | 0.62379 | 1.465917858 | |||

0.8 | 0.032 | 0.2019 | 2 | 0.356 | 0.6491 | 0.71994 | 1.691863376 | |||

1 | 0.04 | 0.22572 | 2 | 0.445 | 0.72992 | 0.79089 | 1.858582429 | |||

1.2 | 0.048 | 0.24726 | 2 | 0.534 | 0.79213 | 0.84353 | 1.982297507 | |||

1.4 | 0.056 | 0.26706 | 2 | 0.623 | 0.84001 | 0.88274 | 2.074439664 | |||

1.6 | 0.064 | 0.28549 | 2 | 0.712 | 0.87687 | 0.91202 | 2.143244563 | |||

1.8 | 0.072 | 0.30279 | 2 | 0.801 | 0.90523 | 0.93392 | 2.194721829 | |||

2 | 0.08 | 0.31914 | 2 | 0.89 | 0.92706 | 0.95034 | 2.233292323 |

## 12.9 SOFTWARE AVAILABLE FOR CONSOLIDATION ANALYSIS

There are several softwares available for predicting the magnitude and time rate of consolidation. Among others CONSOL99 developed by Wong and Duncan (1988) is an interesting software. It has several useful features, such as:

- — it permits intermediate drainage due to the presence of a sand layer.
- — it computes the reduction in stress as the overlying fill submerges below the water table with time (that is, buoyancy effect).

- — it computes stress due to changes in the ground water level.
- — it computes stress due to placement or removal of a layer of large area fill.
- — it computes stress due to strip fill.
- — it computes stress due to a circular area fill.

Details on the application of CONSOL99 are found in Wong and Duncan (1988). However, this program only calculates without vertical drain conditions. It is possible to calculate with vertical drain conditions by introducing a drainage layer at every boundary, the distance of which is equivalent to the vertical drain boundary.

In addition to its special features explained above, it also takes into account the large strain consolidation by updating the change in thickness from one time step to another, and also the change of geotechnical parameters such as void ratio from one time step to another.

Because it takes into consideration the submergence effect, and updates the thickness and void ratio, it usually predicts a lower magnitude of settlement and a faster rate of consolidation than conventional calculation. A comparison of the predicted magnitude and time rate of settlement using CONSOL99 and the conventional method is shown in Figure 12.3. The effect of submergence, large strain and non-linear strain on time rate of consolidation and the effect of a multi-layer system are explained through Figures 12.4 to 12.6. A comparison with the conventional method and all its effects is shown in Figure 12.7. The details can be found in Wong and Choa (1980).

Other software available for prediction of magnitude and time rate of consolidation using finite element methods are SAGE CRISP and PLAXIS. Details are found in the SAGE CRISP and PLAXIS manuals. Both software can create models with and without vertical drain conditions. Another software which applies a different method is the Visual Basic program VDRAIN99 developed by B.K. Low, details of which can be found in the soil improvement textbook written by Bo et al. (2003a).

Some examples of magnitude and time rates of settlement carried out by some computer programs are shown in Figures 12.8 to 12.11 together with conventional analyses.

It can be seen that most computer software predict faster rates of settlement than conventional calculation (Figure 12.8). Figure 12.9 shows a comparison of time rates of settlement calculated for perfect drainage, with PVD and with smear effect. It can be seen in Figures 12.10 and 12.11, that the time rate of settlement calculated with perfect drainage by conventional and with PLAXIS software are almost the same under perfect drain and smear conditions.

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# Design Process for Land Reclamation and Soil Improvement

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**Design Process for Land Reclamation and Soil Improvement**