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22 TCN 262 - 2000 Page 1 of 40 I. GENERAL REQUIREMENTS I.1. This specification is applied as surveying and designing the motorway sub-grade on the soft ground, including the embankment for expressway and motorway at different classes. Besides, it is referred for embankment design of airport on the soft ground. This standard shall defines all regulations on topography survey, investigation and geotechnical test of the soft ground crossed by the route; as well as other requirements and specifications satisfied on designing embankment on the soft ground by the equivalent formation and calculation methods and alternatives and applicable scope of these methods for embankment work on the soft ground (except the other special methods such as soft ground treatment by penetration electricity, limestone piles, cement piles, concrete piles, and sand piles, etc…). I.2. Surveying and designing sub-grade on the soft ground shall not only conformed with the regulations stated in this standard but other specifications and general regulations on sub-grade design in TCVN 4054-1998 “Motorway – Design Requirements” and TCVN 5729-1997 “Expressway - Design Requirements”. The specifications on plastic board drain and geo-textiles solutions stated in this standard are same as the regulations in “Designing procedures for soft soil treatment by Plastic Board Drain in sub-grade construction – 22TCN 244-98” and “Specifications for detailed design and acceptance of geo-textiles in embankment work on soft ground – 22TCN 248-98”. Unless otherwise required in surveying and designing embankment on the soft ground, this standard shall be applied. I.3. In this specification, the soft ground determined in Section I.4 is to indicate type of soil with low shear strength and excessive deformation. Therefore, unless we do apply any measures, embankment on the soft ground shall lead to unstable wholly and deep settlement, the long duration settlement affects to the pavement, works on pavement and adjacent abutments. Hence, the objectives of the regulations in this standard is to ensure the dimension and geometric factors of the embankment on the soft ground (including sub-grade elevation) being as same as in the design during construction and exploitation later. I.4. Hang upon the formation causes, soft soil may become from mineral or organic matters I.4.1. The types having origin of mineral are usually clay or foamy clay at littoral, gulfs, lakes, plains; these types may be organo-mineral soils due to sediment period (the organic content may amount to 10-12%), thus they are brown, black, gray and have odor. These types are identified as soft soil at the physical status, their humidity shall be about or equal to the yield point, great void ratio (clay e 1.5, foamy clay e 1), cohesive force C complying with the quick shear result shall not discharge less than 0.15 daN/cm 2 , angle of internal friction φ from 0-10 o or cohesive force from the shear vane test at sit Cu 0.35 daN/cm 2 . Moreover, in the valleys, soft soil may be under the form of sandy peat, fine sandy peat (void ratio e > 1.0 and satiability G> 0.8). I.4.2. The types having origin of organic matters are usually formed in lakes ditches where there are stagnant water and high level underground water. Flora grows, decomposes and deposits, then it

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Page 1: 22TCN 262-2000_En

22 TCN 262 - 2000

Page 1 of 40

I. GENERAL REQUIREMENTS I.1. This specification is applied as surveying and designing the motorway sub-grade on the

soft ground, including the embankment for expressway and motorway at different classes. Besides, it is referred for embankment design of airport on the soft ground.

This standard shall defines all regulations on topography survey, investigation and geotechnical test of the soft ground crossed by the route; as well as other requirements and specifications satisfied on designing embankment on the soft ground by the equivalent formation and calculation methods and alternatives and applicable scope of these methods for embankment work on the soft ground (except the other special methods such as soft ground treatment by penetration electricity, limestone piles, cement piles, concrete piles, and sand piles, etc…).

I.2. Surveying and designing sub-grade on the soft ground shall not only conformed with the

regulations stated in this standard but other specifications and general regulations on sub-grade design in TCVN 4054-1998 “Motorway – Design Requirements” and TCVN 5729-1997 “Expressway - Design Requirements”.

The specifications on plastic board drain and geo-textiles solutions stated in this standard are same as the regulations in “Designing procedures for soft soil treatment by Plastic Board Drain in sub-grade construction – 22TCN 244-98” and “Specifications for detailed design and acceptance of geo-textiles in embankment work on soft ground – 22TCN 248-98”. Unless otherwise required in surveying and designing embankment on the soft ground, this standard shall be applied.

I.3. In this specification, the soft ground determined in Section I.4 is to indicate type of soil with

low shear strength and excessive deformation. Therefore, unless we do apply any measures, embankment on the soft ground shall lead to unstable wholly and deep settlement, the long duration settlement affects to the pavement, works on pavement and adjacent abutments. Hence, the objectives of the regulations in this standard is to ensure the dimension and geometric factors of the embankment on the soft ground (including sub-grade elevation) being as same as in the design during construction and exploitation later.

I.4. Hang upon the formation causes, soft soil may become from mineral or organic matters I.4.1. The types having origin of mineral are usually clay or foamy clay at littoral, gulfs, lakes, plains;

these types may be organo-mineral soils due to sediment period (the organic content may amount to 10-12%), thus they are brown, black, gray and have odor. These types are identified as soft soil at the physical status, their humidity shall be about or equal to the yield point, great void ratio (clay e ≥ 1.5, foamy clay e ≥ 1), cohesive force C complying with the quick shear result shall not discharge less than 0.15 daN/cm2, angle of internal friction φ from 0-10o or cohesive force from the shear vane test at sit Cu ≤ 0.35 daN/cm2.

Moreover, in the valleys, soft soil may be under the form of sandy peat, fine sandy peat (void ratio e > 1.0 and satiability G> 0.8).

I.4.2. The types having origin of organic matters are usually formed in lakes ditches where there are stagnant water and high level underground water. Flora grows, decomposes and deposits, then it

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becomes organo-mineral matters. It is usually called peat soil with the organic content of 20-80% in black or dark brown, coarse structure (due to flora remains). This type is determined as soft soil if void coefficient and shear strength satisfy the values mentioned in Section I.4.1.

Soft soil of peat soil shall be classified based on its organic content: - The organic content of 20-30%: Peaty soil - The organic content of 30-60%: Peat soil - The organic content of over 60%: Peat

I.5. Classification of soil physical state

For preliminary evaluation of soft soil characteristics, then consider the corresponding sub-grade design alternatives, based on its physical state the soft soil is classified as follows;

I.5.1. Clay or sandy clay of soft soil shall be classified in accordance with consistency B: W - Wd B = Wnh - Wd

In which: - W, Wd, Wnh : Moisture content at the physical state, plastic limit, and pasty limit of soft soil - If B>1, it shall be called peat - If 0.75<B<1, it shall be extremely high plastic peat

I.5.2. In terms of natural condition, peat soil is classified into 3 types as follows:

Type I: Viscosity of the soil type is stable. Soil will be classified as type I if vertical excavation is 1m in thickness and its stability is maintained in 1-2 days;

Type II: Viscosity of the soil type is unstable, so type II does not meet type I’s requirements, but peat soil is not in very soft condition;

Type III: Peat is in very soft condition.

I.6. If the route goes through the area of very soft soil and clayey mud as mentioned in

Articles I.4.1, I.5.1; the area of sandy mud and fine sandy mud as mentioned in Article I.4.1; the peat area as mentioned in Article I.5.2, it is necessary to prepare a correlative method of investigation for design (mentioned next parts of this specification) in order to ensure sub-grade stability in its strength and deformation, including non-soft soil layer under the soft soil one.

Especially for expressway works and other special construction works, if embankment height is from 8m to 10m and more, all kinds of clay and soft clayey mud (with viscosity B within 0.5-0.75) should apply methods for investigation for design as that in soft soil.

II. REQUIREMENTS AND SPECIFICATIONS ON DESIGN

OF EMBANKMENT ON SOFT SOIL

II.1. Requirements on embankment stability

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Embankment on soft soil should be stable, undamaged due to changes in the construction of embankment (embankment is carried out in accordance with design or carried out with elevation over the one in design for pre-loading) and in operation afterwards. To meet those requirements, the following specific standards should be gained at the same time:

II.1.1. Forecasted stability following calculation results for each embankment stage (embanking and

pre-loading) and for designed embankment (regarding maximum vehicle loading) is equal or over minimum stability as follows:

• In case of applying Stable Maths Method by classical splinter and circular displacement

surface bored deep in soft ground and calculation values determined by Item V.3, then minimum stability coefficient Kmin = 1.20 (as for using laboratory testing results of undrained accelerated shear for maths method, then Kmin = 1.10);

• In case of applying Bishop Method for Stable Maths Method, then minimum stability coefficient Kmin = 1.40.

II.1.2. In the construction of embankment and pre-loading, data for vertical settlement monitoring and

horizontally movable monitoring of the soft soil at two side of embankment shall not exceed the following value:

- At centerline, settlement velocity of the embankment bottom shall not exceed

10mm/calendar day. - Horizontally movable velocity of monitoring piles in both sides of embankment shall not

exceed 5mm/calendar day. - Arrangement of settlement monitoring and horizontally movable monitoring is clearly

stipulated in Articles II.3.1 and II.3.2. II.2. Requirements and specifications for settlement calculation II.2.1. Total settlement coefficient S shall be forecasted and calculated from the beginning of

embankment works until in full settlement in order to embank for settlement prevention (embankment shall be extended towards sub-grade width compared with the one in design). Extended width in both sides of sub-grade (bm) is determined in the following formula:

bm = S.m In which: 1/m – slope of designed embankment

S is calculated in accordance with the method in VI.2 and II.3 regarding two coefficients Si (instant settlement due to undrained transverse deflection, regarding unconfined capacity of the soft soil under the embankment) and consolidation settlement Sc (due to pore water and compressed soft soil under embankment loading)

II.2.2. In calculation of the captioned coefficient S, settlement loading consists of only designed

embankment loading including berm embanking (if any), excluding pre-loading (if any) and does not examine vehicle loading.

II.2.3. After completion of sub-grade construction in soft soil, the remaining consolidation settlement

∆S at centerline of the sub-grade is as in the table II-1 below:

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Remaining consolidation settlement ∆S at centerline of the sub-grade after construction completion

Table II-1

Highway classification

Embankment location on soft soil

Near abutment At the place of

culverts or under public highway

At normal embankment

1. Expressway and highway class 80 ≤ 10 cm ≤ 20 cm ≤ 30 cm

2. Highway under class 60 with surfacing class A1

≤ 20 cm ≤ 30 cm ≤ 40 cm

Note (Table II-1):

- The remaining consolidation settlement ∆S is unfinished ones after wearing course completion of embankment on soft soil. ∆S value is determined as in the formula (VI-9) depending on consolidation U at the time of wearing course completion.

- Length of sub-grade near abutment is 3 times of abutment footing length of the other abutment. Length of embankment with culverts and underpasses is 3 to 5 times of bedding width or pavement width.

- If the remaining consolidation settlement ∆S exceeds the values in Table II-1, it is necessary to have a method to decrease ∆S mentioned in items IV.3, IV.5, IV.6. If the values in Table II-1 are satisfied, it is no need to apply treatment methods for accelerating consolidation.

II.2.4. For highway with grade of 20, 40 and highway using soft wearing course A2 and below, ∆S in

design is not mentioned. II.2.5. Requirements on monitoring of settlement forecast

Besides forecast of settlement calculation mentioned in Article II.2.1 for proposing treatment methods for embankment structure in soft soil, it is necessary to rely on settlement monitoring results as in Articles II.3.1 and I.3.2 to compare and correct the forecast results to examine allowable settlement and settlement velocity as in Articles II.2.3 and II.1.2, as well as to determine soil mass or sand mass, actual settlement addition shall be done after completion of the construction.

Requirements in details of settlement monitoring are as follows: - To determine soil or sand mass that is settled in soft soil (compared with natural soil before

embanking). - To prepare diagram of total settlement S and time (clearly stated period of each stage of

embankment and pre-loading). To rely on this diagram to separately handle instant settlement (settlement that unexpectedly increases in each stage of embankment) and to prepare diagram of consolidation settlement Sc regarding time t since the completion of embankment and pre-loading.

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- To approximately describe St = f(t) in monitoring practice by using the following mathematical function St = Sc (1 – αe-ßt) in which α and ß are recurrent values of settlement monitoring data, and are the basic for forecasting the remaining consolidation settlement mentioned in Article II.2.3.

II.3. Requirements on design and arrangement of settlement monitoring system during

embankment execution on soft soil II.3.1. For construction works in soft soil, in all cases, settlement monitoring system shall be designed

in spite of applying whatever treatment methods, surveying or carefully calculating, except for applying methods of dredging soft soil in full, decreasing embankment bottom into non-soft soil layer. The system shall be arranged in accordance with the following regulations:

- Every section in embankment on soft soil is differently calculated and designed, or each

section that is separately constructed shall be separately monitored their settlement (which is different in embankment height, soft soil types with different properties and thickness of different soft soil layers).

- If length of each section is 100m or more, 3 settlement instruments shall be arranged at center of cross section (1 in centerline and the rests in the edges of pavement), if it is more than 100m, settlement monitoring of 2 cross sections shall be arranged in minimum, and every extra 100m shall be arranged 1 cross section (at ones where settlement is abundantly)

- Elevation point system for settlement monitoring shall be arranged at unsettlement place and shall be firmly fixed.

- Minimum dimension of settlement instruments is 50cm x 50cm with thickness of 3cm or more, which shall firmly connect to their rods. The rods are made by steel, their diameters are smaller than those of embankment casing (embankment soil shall not be contacted with the rods): the casing shall not be connected to settlement instruments. Rod with diameter of 4cm or more should be used. Rods and casing should be done by each section of 50-100cm for the convenience of connection to embankment height.

- Settlement instruments are placed at beginning elevation point of the embankment: they shall be arranged where soft soil is already dredged and excavated; or arranged on sand mat layer if any, or arranged on natural hard surface of soil layer if the surface is on soft soil one, or arranged on surface of geo-textile if any. In case of arranging the instruments in soft soil, the soil shall be excavated with a depth of 30cm within area of the instruments instead of sand, then the instruments are arranged.

- The instruments shall be protected for a long time until they are handed over. II.3.2. Settlement monitoring regulations shall be stipulated in design:

- To check elevation at the time of arranging settlement instruments and to measure settlement once a day in embanking and pre-loading; if embankment and pre-loading are done in several stages, each stage shall be daily monitored.

- At the time of embanking completion and 2 months after embanking, monitoring shall be weekly, then monthly done until completion of warranty period and hand-over of monitoring system to highway operation and management units (for their continuous monitoring if necessary).

- Settlement in mm is required for accuracy.

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II.3.3. When applying treatment method for embankment on soft soil that requires controlling embanking speed, it is necessary to prepare a horizontally movable monitoring system in order to monitor stability in embanking as in Article II.1.2, the system is as the follows:

- In each section of settlement monitoring, a row of horizontally movable monitoring piles

shall be arranged outside the slope 1m that is perpendicular to centerline about 3-4 piles with distance from 5m to 10m, piles or concrete piles with the section of 10x10cm are used that deeply stake in soft soil with minimum depth of 1.2m and minimum height of 0.5m over the soft soil (and more than 0.5m in case of excessive settlement and overflow); monitoring points shall be marked at the top of the piles. All the piles are required strongly driving in the soft soil.

- In construction of embankment and pre-loading (if any), it is necessary to daily check horizontal moving (that is perpendicular to centerline) of the monitoring points at the top of piles by Theolite in accordance with Triangle Measuring Method, with two fixed tops of the triangle outside the impact scope of embankment loading. Simultaneously, elevations of pile top are checked in order to see whether soft soil surface is emerged or not. After construction of embankment, it is necessary to continue daily monitoring until sub-grade is stable. The accuracy of Theolite must be ensured about interval errors of ± 5mm, about angle measuring of ± 2.5’’.

II.3.4. For large-scale and important embankment on soft soil or embankment with complicated

geology conditions such as big embankment height, which make the big difference between conditions in practice and conditions in stability and settlement calculation, pore pressure monitoring system is additionally arranged (together with underground water monitoring points) and settlement instruments at different depth (twist reeling equipment …). Owing to the monitoring equipment system, requirements in Article II.2.5 shall be easily carried out and therefore, construction period shall be shortened. In this case, design for installation arrangement of the above monitoring equipment system is specially carried out by specialist engineers and approved by employer.

II.4. Determination of calculated loads II.4.1. Calculated loads in checking stability and forecasting settlement of embankment on soft soil

include loads of embanking and pre-loading, vehicle load, earthquake load, as mentioned in Articles II.1.1 and II.2.2. Since calculation is converted to plane maths, calculated loads are determined correlative to its distribution scope in every 1m sub-grade length.

II.4.2. Loads of embanking and pre-loading are determined in accordance with embanking shape in

practice (trapezium with design slope, which berms may be added or if soft soil is digged before embanking, two lines of boundless berm loads at both side of embankment).

II.4.3. Vehicle loads is considered as loads of maximum weight of vehicles that fully park at the same

time in every 1m of highway length (formula II-1); the load is equivalently converted to embankment soil layer with height of hx that is determined as follows:

n.G hx = (II-1) γ.B.ℓ

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In which:

G – Weight of one vehicle (the heaviest one), ton n – Maximum number of vehicles parking in sub-grade width (as in vehicle arrangement plan in II.1)

γ – Natural weight of embankment soil, T/m3

ℓ - Longitudinal distribution scope of vehicle loads, m (as in II.1) If G = 13 tons, then ℓ = 4.2m; if G = 30 tons, then ℓ = 6.6m; if G = 80 tons, then ℓ = 4.5m.

Figure II.1. Vehicle arrangement plan to determination of vehicle load on soft soil

B is transverse distribution width of vehicle (m) determined as in figure II.1 in accordance with the following formula:

B = n.b+(n-1)d+e (II-2)

In which normally b = 1.8m for all kinds of car, b = 2.7m for motorcycle; d is minimum distance between vehicles (normally d = 1.3m); e is width of double-tyre or motorcycle track (normally e = 0.5 – 0.8m); and n does not exceed its value limit but it must ensure that B calculated in accordance with (II-2) is smaller than sub-grade width. Therefore, in case of calculation regarding vehicle loads, embankment load is supposedly calculated to a higher value as hx.

II.4.4. Earthquake loads in calculation and checking of embankment stability in soft soil is inertia

force due to earthquake of sliding block, the force is considered in direct ratio to the weight of sliding block:

Wi = Kc.Qc (II-3)

In which:

Wi – Impact of earthquake force on a sliding piece i (or sliding block i) (tons), Wi’s placed points is the piece’s gravity (or block’s gravity) and is transversal from sub-grade to embankment’s slope; Qi – Weight of sliding piece i (or sliding block i), Tons; Kc – Depending on earthquake level as in Table II-2.

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Ratio coefficient Kc Table II-2

Earthquake

Level 7 8 9 10 11 12

Coefficient Kc

0.025 0.05 0.1 0.25 0.5 0.5

Earthquake arrangement in Vietnam is shown on Specifications on Vietnam Construction. In the area where earthquake is from 7th level and more, then earthquake force is considered in calculation. Furthermore, calculation on earthquake force (for reference) is available in Industry Specification 22 TCN 221-95.

III. REQUIREMENTS ON SURVEY FOR DESIGN OF SUB-GRADE

ON SOFT GROUND III.1. General Requirements III.1.1. Distribution scope of soft soil areas regarding distribution area, depth and cross slope of the

bottom of soft soil layer shall be investigated and determined to examine alternatives for bypass or for alignment through soft soil layer that is in the least adverse areas. Causes for wet areas, drainage, as well as location and operation capacity of soil quarry for embanking should be determined.

III.1.2. Samples shall be taken, laboratory testing shall be carried out and necessary testing at site on

geo-textile shall be done in order to determine:

• Types and properties of soil as mentioned in Articles I.5.1, I.4.1 and I.5.2 to confirm go-through alignment area be a soil area and to determine type of soft soil for treatment;

• Properties for calculation and checking embankment stability on soft soil in details as follows: undrained resistance against shear that is determined by Vane Shear Test Method at site (or by Accelerated Shear Test Method in laboratory, if vane shear equipment is not available at site), natural weight γ and underground water level (to determine soft soil area bearing buoyancy). Those properties shall be separately determined for different soft soil layers. Besides, properties of cohesion C, angle of interior friction and natural weight of soil for embankment (corresponding to wet and density condition of embankment soil) shall be determined;

• Properties for forecast and calculation of total settlement and consolidation settlement according to testing time determining settlement compression in unconfined compression test, initial void coefficient eo, settlement compression Cr and Cc, vertical consolidation coefficient Cv (cm2/ second) and pre-consolidation pressure σp. Those properties shall be separately determined for different soft soil layers (please see sign explanation of the above properties in Item VI).

III.2. Requirements on topographical survey III.2.1. In preparation of feasibility project, plan with scale of 1:500 ÷ 1:1000 compared with difference

in contour line 0.5m along alignment alternatives through soft soil area shall be measured and

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made. In case of considerable distribution of soft soil area (such as lagoon area …), methods of aeronautic measurement for topographical survey for the whole area shall be applied. In this stage, profile and cross section for embankment calculation on soft soil for design are determined by the topographical plan.

III.2.2. In preparation of technical design and design for working drawing stage, profile and cross

section along design alignment together with detailed piles with suitable distance in each stage shall be measured, besides, piles at exploratory drilling location shall be added, samples on soft soil shall be taken and monitoring system shall be arranged at expected locations (as mentioned in Item II.3).

III.3. Requirements on geotechnical survey and tests III.3.1. To meet requirements as mentioned in Articles III.1.1 and III.1.2, it is necessary to combine

exploratory drilling with sampling (carried out by drilling machine for undisturbed samples and tested in laboratory) and that with not sampling (carried out by spiral drilling machine, penetration or vane shear equipment at site) so as to be the most economic way. Due to considerable exploratory area in feasibility study stage, taking full advantages of exploratory methods for not sampling should combine with exploratory methods for sampling. In preparation of technical design and detailed design stage, drilling methods for sampling should be used, drilling methods for not sampling shall added when necessary (in case of expansion of exploratory area or insufficiency exploratory for not sampling in feasibility study as mentioned in Article III.3.2). Locations and quantities of exploratory areas shall be decided by project manager after expected design alternatives is submitted.

In exploration by drilling, penetration or vane shear, it is necessary to refer to the following specifications:

o Specification for Geological Exploratory Drilling 22 TCN 259 - 2000 o Vane Shear Test: ASTM D2573 and TCXD 205 – 1998 o Penetration Test: ASTM D1586

III.3.2.

o Feasibility project stage: After normal drilling, if soft soil is discovered, boreholes shall be localized and arranged in centerline with the distance from 250m to 500m (if necessary exploratory points shall be added such as: vane shear, penetration … in order to discover soft soil area, but the additional exploration shall not be for sampling). Drilling in cross section is proposed by consultant and approved by employer.

o Technical design stage: Geological exploratory works is carried out by boreholes which each borehole are normally arranged from 50m to 100m to each other in centerline (including boreholes in the first stage). + In some special circumstances, the distance may be shortened. + Every 100-150m shall be arranged 1 geological cross section perpendicular to centerline in which is 3 boreholes. There are at least 2 geological cross sections on each soft soil area.

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+ Exploratory drilling depth should reach the bottom of the soft soil layer and 2 more meters on non-soft soil layer, if depth of the soft soil layer is considerable, drilling should reach the impact area of embanking loads. The area is determined correlative with its depth where stress is caused by embanking loads (or by embankment or preloading if any) by 0.15 of the stress (pressure) due to soft soil (in consideration of buoyancy in case of existence of underground water). + In case of carrying out vane shear test at site, this test shall be independently carried out or in boreholes.

o Investigation stage for working drawing preparation is to use borehole or testing results at site in technical design stage. Investigation quantity is an additional one for on-going technical design stage. If extra soft soil area is discovered, then geological investigation quantity may increase, which is proposed by consultant and approved by employer; however, the quantity does not exceed 20% of the quantity in technical design stage.

III.3.3. Section to vane shear exploratory and drilling for sampling shall be arranged in the relatively

highest embankment and in the most specific soft soil layer. III.3.4. In each borehole mentioned in Article III.3.2, soft soil length depends on:

• If soft soil length up to 200m, every 1-2m soil in thickness shall be taken a disturbed sample.

• If soft soil length is more than 200m, sample quantity is proposed by project manager and approved by employer, but at least, soft soil between each layer shall be taken undisturbed sample.

Methods for undisturbed sampling, packing, hauling and preservation are in accordance with regulations in Vietnam Standards TCVN 2683-91

III.3.5. Testing for determination of soft soil’s physio-mechanical properties mentioned in III.1.2

should be carried out with all undisturbed samples in accordance with the following:

• Testing for determine resistance against shear properties (cohesion force C and friction angle φ) is in accordance with methods and regulations in Vietnam Standards TCVN 4199-95, in which method for accelerated shear and accelerated shear for consolidation is also determined (accelerated shear properties are for determination of embankment stability in embanking and the others are for determination of embankment in operation);

• Testing for determination of settlement compression in confined compression condition is carried out in accordance with Vietnam Standards TCVN 4200-95. Determination of pressure value for pre-consolidation σpz is carried out as instructions in Appendix I of this Specification;

• Other properties are determined in accordance with equivalent Vietnam Standards. III.3.6. Testing for determination of physio-mechanical properties of embankment soil and sand is

carried out in accordance with equivalent standards mentioned in Article III.3.5 with samples by embankment material from soil quarries or sand pits which their density and moisture are as that in practice. Resistance against shear properties shall apply accelerated shear method.

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III.3.7. For calculation of each property, at least 6 testing datum and calculation values shall be determined as in the following formula:

∆t = ∆tb ± δ (III-1) In which: ∆t – Calculation value of the property

∆tb – Arithmetic average value of testing data δ – Average square declination

In which: Ai – Determined value of the property in each testing time n – Testing time towards each property

In choosing calculation value of each property, it is necessary to carefully analyze actual conditions having impacts on quality of soft soil samples before testing as well as adverse impacts of these properties on calculation results.

Besides, geo-technical specialists’ experience should be considered in choosing calculation value.

III.3.8. Testing data at site carried out by penetration or vane shear equipment is also processed towards

calculation value mentioned in Article III.3.7 (for more information, please refer to Specifications and Standards mentioned in Article III.3.1, in combination with geo-technical specialists’ experience).

IV. APPLICABLE ALTERNATIVES FOR DESIGN OF EMBANKMENT

ON SOFT GROUND IV.1. General Requirements for embankment structure on soft ground IV.1.1. Embankment structure on soft soil must mitigate adverse impacts from flood water and

underground water:

• soil for embankment must be a soil type with good water stability, it is unaccepted to use those soil types (which are classified in TCVN 5747-1993);

• density, minimum embankment height in flood water and underground water levels as well as other requirements of sub-grade structure (as talus embankment when sub-grade body is sand ...) shall conform to specifications defined in TCVN 4054-1998 and TCVN 5729-1997.

IV.1.2. Within 20m from slope foot of embankment outwards each side, sag locations (ponds, lakes)

shall be fully filled up and it is strictly prohibited to carry out excavation for soil collection within this area.

IV.1.3. An effort is made to reduce embankment height for creating easy conditions for soil

stabilization and settlement decrease; however, except for temporary roads, minimum embankment height shall be from 1.2 – 1,5m away from the position connected to soft soil, or 0.8 – 1m away from surface of sandy buffer stratum (if any) so as to ensure effective area of sub

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grade excluding soft soil area. The former value of the above mentioned minimum height of embankment shall be applied for embankments of expressway and roads for many heavy trucks, the later one for embankment of other road types.

IV.2. Direct embanking on soft soil IV.2.1. During calculation of stability and settlement of direct embankment on natural ground

(including soft soil under it) or on soft soil, we can apply alternative of direct embankment (without using any other treatment measure) but it shall satisfy all requirements and conform to specifications stated in II.1 and II.2. Method of stability calculation is defined in V, that of settlement one in VI of this Specification.

In all cases, if direct embankment is conducted on soft soil, there should be a sandy buffer layer at least 50cm in thickness and 0.5 – 1.0m wider than embankment toe.

IV.2.2. Direct embanking shall be applied for the cases as follows:

• On soft soil area, there is no soft soil as classified in I.4 and I.5 (it is actually called covering layer on soft soil surface). If the covering layer is 1-2m, height of direct embankment might be up to 2-3m, if it is 2m thicker, the height might be 3-4m;

• On grade I peat or soft and viscous soil area with peat thickness of less than 1-2m; • On sandy mud or fine sandy mud area (normally, as this type has big consolidation

coefficient, settlement occurs quickly.

In addition, in case, an embankment is expected to be few and quick settlement but if the embankment is filled up promptly until designed height, which shall not ensure the stability in accordance with the specifications stated in Article II.1.1, can adopt alternative of direct embankment together with method of filling speed control (filling is conducted in many times, between each interval, there is waiting time for consolidation) so as to secure the stability requirements (see Article II.1.2) except when the filling speed control leads to overtime lasting, which does not ensure requirements of construction schedule for the whole road engineering, it is necessary to consider other treatment measures.

IV.2.3. Filling method shall be conducted from natural ground of non-soft soil to soft soil ground for direct embankment on soft soil.

During implementation of the filling method, the following conditions must be satisfied: • Embanking banks, drying water on soft soil surface; • Embankment materials shall be good water-reserving ones such as sand, cobbles, stones or

industrial scraps… • Embankment section is situated under natural soft soil, so compaction shall be conducted by

using from light (bull dozer…) to heavy equipments (heavy-duty roller) until embankment materials do not make any settlement into soft soil, i.e. until firm space is created for construction on soft soil ground.

• Embankment from natural ground upwards must be filled up as layer by layer and satisfactory with requirements of compaction.

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IV.2.4. For convenience of implementation of direct embankment on soft soil (good conditions for traffic on soft soil and firm compaction of the first layer), geo-textile can be used to cover the soft soil prior to embankment as instructed in Table IV.1 bellow:

Selection of geo-textile and structure of temporary roads

for traffic on soft soil area Table IV.1

Materials for road

embankment

Structure of

temporary roads

Required Properties for geo-textile

Stressing strength (kN/m)

Stretch (%)

Tearing strength

(kN)

Permeable coefficient

m/s m

Filter hole diameter Φ95 (µm)

I. Sand, mixture of sand and natural gravels

1. One layer of geo-

textile above 50cm

embankment

≥ 12 ≤ 25 ≥ 0.8

≥ 0.1

≤ 125

2. Two geo-textile layers above each

25cm embankment

≥ 8 15 - 80 ≥ 0.3 ≥ 0.1 ≤ 125

3. One layer of geo-

textile above 15cm

embankment

≥ 16 15 - 80 ≥ 0.5 ≥ 0.1 80 - 200

II. Good aggregate

1. One layer of geo-

textile above 30cm

embankment

≥ 25 ≤ 25 ≥ 1.2 ≥ 0.1 ≤ 200

2. One layer of geo-

textile above 50cm

embankment

≥ 12 ≤ 25 ≥ 0.8 ≥ 5.10-2 ≤ 200

3. Two geo-textile layers above each

15cm embankment

≥ 20 15 - 80 ≥ 1.2 ≥ 5.10-2 ≤ 200

Note on Table IV.1:

• Permeable coefficient with s-1 as m/s per unit of trial geo-textile thickness;

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• Filter hole diameter is equivalent to the biggest material grain which can follow water to go through the geo-textile; the grain size is equal to D95 (this is grain diameter that composition of smaller grains obtains 95%);

• Geo-textile shall be horizontally laid (perpendicular to alignment) and overlapped at least 0.5m or sewed with 10cm overlap;

To ensure compaction quality, right at the first embankment layer, geo-textile with stressing strength at least 25kN/m shall be selected.

IV.3. Partial or total excavation of soft soil IV.3.1. This method has advantages such as stability increase, settlement and settlement time reduce;

thus, except that there is a hard crust on soft soil, for all other cases, designer must give priority to consideration of application or combination of the partial excavation and other methods. Soft soil, which has smaller thickness than affected area of embankment load, will be an especially appropriate case. Using method of soft soil excavation by chained excavator, each excavated section shall be filled up promptly; the depth of excavation might reach 2-3m. Major point is to prepare properly construction lay-out for convenience of quick embankment after forming rows of excavation; excavated soft soil shall be dumped on two sides of the embankment to create berm. If necessary, the excavation depth can be defined by calculating as instructed in V.2.6 and meeting requirements stated in II.1 and II.2.

IV.3.2. Cross section of soft soil section shall be trapezium with small bottom under equal width of

sub-grade surface; the big bottom above equal closure width between embankment and soft soil surface when it has not been dug (between two toes of embankment). It means that excavation depth of soft soil can only fit sub-grade width, on two embankment toes, the depth can be reduced gradually.

IV.3.3. The following cases are suitable for partial or total excavation of soft soil:

• Maximum thickness of soft soil is 2m (in this case, the whole soft soil section shall be dug so that sub-grade bottom is closely contacted to firm soil stratum);

• Soft soil is grade I peat or clay, viscid sandy clay, very loose sandy clay; if thickness of soft soil is more than 4-5m, partial excavation shall be conduced so as for maximum thickness equal ½ - 1/3 of embankment height (including sub-merged embankment inside soft soil).

IV.3.4. In the case that soft soil has less than 3m in thickness and too low intensity, during excavation,

it is not enough time for embankment, such as grade II, grade III peat, clayey mud (viscosity B>1) or fine sandy mud; method of filling stones down into soft soil bottom or combination of stones and overloading filling so that the ground itself can settle down to the bottom of soft soil. This option is especially suitable for extension of existing embankment during road rehabilitation and upgrade on soft soil area.

Rocks with 0,3m diameter or bigger shall be used and dumped outwards so as to push soft soil out, until rocks emerge on the soft soil surface, after that sand or small rocks shall be scattered on and compacted from lightly to heavily. If rocks are small, barrels, steel or polyethylene gabions can be used to put stones inside them for embankment.

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IV.3.5. Bamboo stakes shall be driven, 25 stakes/m2; this is an alternative to replace excavation of soft soil within stake setting depth (the stakes can be set into 2 – 2,5m depth). Bamboo stakes should be more than 7cm diameter for big end, 4cm for small end and will not be broken or out of shape. After filling one soil layer of 30cm on bamboo stake tops, geo-textile (or equivalent geo-grids) shall be laid on them (as described in IV.2.4) to arrange embankment load evenly on the bamboo stakes.

Similarly, cajuput stakes with 12cm diameter of big end and 5cm of small end can be used, set up 3-5cm in depth with the interval of 16 stakes/m2.

IV.4. Embankment of berm IV.4.1. This option is only used when direct embankment on soft soil in order to increase stability of

sub-grade to prevent its displacement and swelling and to satisfy the requirements in II.1 during both embankment period and long-term operation. If embankment and berm are done at the same time, it is no necessary to control falling speed thus, construction can be implemented quickly. However, this option is not only able to reduce consolidation settlement time but also increase the settlement (due to added load of berms on both sides). Furthermore, its advantage is large embankment mass and large land acquisition area. This option is also not suitable for soft soil types such as grade III mud and clayey mud.

IV.4.2. Structure of berm

• Materials of berm are normal soils or sands; if there is a lack of these types, organic soil can be used.

• Berm width on each side should exceed scope of the most dangerous displacement curve from 1-3m (the most dangerous displacement curve shall be calculated in accordance with the method described in V.1 and V.2). Top surface of berm must create horizontal slope 2% outwards.

• Berm height shall not be too big so not to cause in swelling displacement (instability) for berm embankment itself; when designing, it is expected that berm height is 1/3 – ½ of embankment height and then calculation of stability shall be done according to method of circular displacement surface as described in section V. If the calculation results satisfy the requirements in Article II.1.1, they are accepted.

• Density of soil for berm embankment should be K≥0.9 (standard compaction). IV.5. Buffering sand layer IV.5.1. Buffering sand layer shall be arranged between soft soil layer and embankment in order to

increase consolidation drainage capacity under the soft soil layer upwards natural ground by effect of embankment loading capacity.

The buffering sand layer should be adopted for direct embankment on soft soil (IV.2.1 and IV.2.2) and it is obligatory to be applied for vertical consolidation drainage (in section IV.6).

IV.5.2. Sand used in buffering layer must satisfy the following requirements:

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Sand shall have organic content < 5%, more than 50% of 0,25mm grain, 5% of 0,08mm grain size, and it shall satisfy one of the two conditions as follows:

D60

> 6 (IV-1) D10 (D30)2

1 < < 3 (IV-2) D10 . D60

In which: D30 – grain size, content of its smaller grains obtain 30%. D10 – grain diameter, content of its smaller grains obtain 10%.

IV.5.3. Thickness of buffering sand layer at least shall be equal to the total settlement S stated in II.2.1 but not less than 50cm. Its compaction density is required to obtain 0.9 of standard compaction density (for construction equipments on upper layers).

IV.5.4. Width of buffering sand layer surface shall be at least 0.5 ÷1m wider than embankment bottom;

slopes and widening sections on both sides of the buffering sand layer shall be designed to have vertical filtering layer so as not to drift sand out when consolidation water drains, especially when being settled and submerged into soft soil, the water still can and, if required, the water can be pumped out without damage of the buffering sand layer.

The vertical filtering layer can be normally designed (stone blinding with 20÷25cm in thickness) or by geo-textile which should be laid on soft soil ground, and then embanked by buffering sand layer, after that the geo-textile shall cover the slope and its widening section for its function of vertical drainage. This geo-textile layer shall cover embankment bottom at least 2m. It should make use of the geo-textile for other functions such as enhancing stability during embankment (see IV.7) or the functions described in IV.2.4.

IV.5.5. If geo-textile performs as the vertical filter layer as described in IV.5.4, filtering hole diameter shall satisfy the conditions as follows:

Of ≤ C.D85 (IV- 3) In which:

Of – filtering hole diameter to be selected (µm) D85 – grain diameter of buffering sand layer, volume of its smaller grains obtains 85% (µm) C – Coefficient taken equally to 0.64

If the geo-textile performs plural functions, its technical properties shall meet the equivalent requirements.

IV.5.6. Consolidated water from buffering sand layer through vertical filtering layer need to be drained quickly out of the area adjacent sub-grade. It is necessary to design drainage pipes available and a pump shall be used to dry water, if necessary (especially when buffering sand layer settles down completely into soft soil).

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IV.6. Vertical consolidated water drainage (using sand drain or PBD) IV.6.1. Thank to arrangement of vertical drainage means (sand pipe or PBD), consolidated water

deeply inside soft soil stratum shall be drained quickly by loading capacity of embankment (horizontal drainage through sand pipes or PBDs, and then on natural ground). However, for this effective drainage, minimum height of embankment should be 4m, and satisfactory with the conditions stated in (IV-4a), (IV – 4b) as follows:

σvz + σz ≥ (1.2 ~1.5) σpz (IV – 4a) lg (σvz + σz) - σpz

η = > 6 (IV – 4b) lg (σvz + σz) - σpz

In which:

σvz - Vertical strength (pressure) caused by weight of soft soil layers themselves at the depth z (Mpa).

σvz = Σγi . hi (IV – 5)

γi and hi – volume weight and thickness of soil layer i within contact surface between soft soil and embankment bottom (z=0) down to the depth z inside soft soil; note that for soil layers are located lower than underground water level, γi shall use weight of emerging and pushing volume (minus 1). σz – Vertical strength (pressure) caused by embankment loading capacity (embankment and pre-load (surcharge) embankment , if any, excluding embankment height hx converted from loading capacity of vehicles) at the depth z inside soft soil from embankment bottom (MPa); σz shall be calculated by mathematical model Osterberg as stated in Appendix I. The conditions (IV-4a) and (IV-4b) shall be satisfactory with every depth z within embankment bottom down completely to depth of sand piles or PBD installation. If the abovementioned conditions are not satisfactory, a combination with pre-load method as stated in IV.6.8.shall apply for an increase of σz.

IV.6.2. Vertical consolidated drainage method is normally adopted when soft soil layer is thick (its thickness is excessive to width of embankment bottom) and embankment ground is high. Due to high construction cost, this method is only applied when other methods cannot secure standards on remaining consolidated settlement ΔS as stated in II.2.3 within required construction period.

IV.6.3. When using the vertical consolidated drainage method, it is necessary to set up a buffering sand

layer in conformity to the requirements defined in IV.5.2, IV.5.3, IV.5.4, IV.5.5 and IV.5.6. if using sand piles, its top shall contact directly buffering sand layer. If using PBD, it shall be driven through the buffering sand layer and additional length shall be at least 20cm higher than top upper surface of the buffering sand layer.

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IV.6.4. Sand used in sand piles shall satisfy the requirements defined in IV.5.2 as well as the conditions of IV.2 and IV.3.

IV.6.5. PBD used for vertical consolidated drainage must satisfy the following requirements:

• Filtering hole size of PBD: (in accordance with Specifications of ASTM D4571): O95 ≤ 75µm

• Permeable coefficient of filter cover (ASTM D4491) : ≥ 1.10-4 m/sec • Drainage capacity of PBD with pressure 350kN/m2 (ASTM D4716): qw ≥ 60.10-6 m3/sec. • Stretching Strength correlatively with less than 10% stretch (ASTM 4595) for

discontinuation resistance during installation of PBD: ≥ 1kN/PBD. • Width of PBD (for its suitability with standardized PBD installation equipment): 100mm ±

0,05mm. IV.6.6. It is advised to use sand piles with 35-45mm diameter arranged alternatively with the interval

equally to 8-10 folds of sand pile diameter. If using PBD, its arrangement shall be done the same with the interval no less than 1.3m and no more than 2.2m.

IV.6.7. Decision on depth of sand drain or PBD is an economic-technical issue that requires designer to

take it in consideration. This depends on settlement range of soft soil layers’ depth under impacts of embanking load for each specific design circumstance. It is unneccesary to arrange sand drains or PBDs to reach the area that is under impacts of embanking load as mentioned in Article III.3.2, but they need to arrange to a certain depth with consolidated settlement value of soft soil layers; from this depth to upper, the ratio shall be gained compared with consolidated settlement value Sc so that remaining consolidated settlement shall meet requirements as mentioned in Article II.2.3 within construction period if consolidation velocity within arrangement of sand drains or PBDs is accelerated. Thus, the designer must provide alternatives for various arrangements of sand piles or PBDs (on depth and interval). Depth alternative must satisfy requirements given in (IV-4a) and (IV-4b).

IV.6.8. When using vertical drainage method, it should be combined with pre-loading method and time

for embankment loading keeping should be not less than 6 months. Any soil types (even organic soil) can be used for pre-loading embankment. Grade of pre-loading embankment shall be 1:0.75 and compaction density is required to obtain K = 0.9 (standard compaction).

IV.7. Using PBDs for strengthening embankment stability on soft soil IV.7.1. When PBD is arranged between soft soil and embankment as shown in Figure IV.1, friction

between embankment soil and upper surface of geo-textile shall create a force to keep displacement block (regardless friction soft soil and lower surface of geo-textile) so embankment stability shall be increased.

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Figure IV.1

I - Active area (displacement block) II - Passive area (geo-textile keeps a role of anchorage) F- Stretching force that geo-textile bears (T/m) Y - Momen arm of force F for the most dangerous displacement center. Using this alternative, calculation for design must satisfy the following conditions:

F ≤ Fcp In which:

F - Stretching force that geo-textile bears (T/m) Fcp - Acceptable stretching force of geo-textile of 1m in width (T/m)

IV.7.2. Acceptable stretching force of geo-textile Fcp shall be determined in accordance with

requirements as follows: • Durability of geo-textile:

Fmax Fcp =

k In which:

Fmax – Shear strength of geotextile with 1m in width. (T/m) k – Safety coefficient; k = 2 if geo-textile is made of polyester and k = 5 if it is polypylene or polyethylene.

• Conditions for acceptable friction force of geo-textile laid directly on soft soil:

In which: l 1 and l 2 – length of geo-textile within active area and passive area (see Figure IV.1). γd – natural weight of embankment soil;

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f’’ – acceptable friction coefficient between embankment soil and geo-textile for calculation. hi – embankment height on geo-textile (changes within l 1 and l 2 , from hi = h to hi = 0 (see Figure IV.1.);

The expression IV.8 and IV.9 are total friction on geo-textile within active and passive area: 2

f’ = k’ tgφ 3

In which: φ – Internal friction angle of embankment soil shall be determined correlatively with factual density of embankment foundation or sand buffering layer, if any; k’ – reserve coefficient on friction, equally 0,66.

Determination of l 1 and l 2 shall be done at the same time with stability control as stated in V.1: suppose that F force shall make minimum stability coefficient satisfy the requirements in II.1.1 and it is compared to the conditions (IV-7) whether it satisfies both (IV-7), (IV-8) and (IV-9) or not; if it does, based on smallest value of Fcp according to the abovementioned relationships in order to select geo-textile with equivalent Fmax.

IV.7.3. Geo-textile, which is used for stabilizing embankment on soft soil, can be arranged into one or

more layers (1-4 layers); a 15-30cm sand layer shall come between two geo-textile layers, depending on compaction capability. Total shear strength of geo-textile layers shall be selected equally to value of Fmax determined as in IV.7.2.

Note: upper geo-textile layers situated in sand (both upper and lower surface are in contact with sand), value of Fcp shall be calculated by the expression (IV-8) and (IV-9) and then multiplied with 2, from which the total acceptable friction force of geo-textile layers shall be found out.

IV.7.4. If adopting this alternative, it is advisable to select woven geo-textile with minimum shear strength of 25kN/m as stated in IV.2.4 so as to ensure soil compaction efficiency on geo-textile with purpose of creating high friction coefficient between soil and the geo-textile. For other properties of geo-textile, refer to Table IV-1. If geo-textile performs as filter layer, the filter hole diameter must satisfy requirements defined in IV.5.5.

IV.8. Rules and procedures for selection of design alternatives IV.8.1. Procedures:

To be base for proposal of design alternatives, firstly, the Consultant must evaluate stability level and settlement development for direct embankment on soft soil (without applying any other treatments) according to instructions stated V and VI. Calculation and evaluation shall be conducted for specific section with various embankment dimension, structures as well as technical characteristics of various soft soil types. If the calculation results realize that requirements and specifications defined in II and IV.1 are not satisfactory, proposals of treatment methods for that section shall be prepared, firstly they are the simplest methods (including alternative of changing embankment dimensions in height and talus slope), or

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combination of some of the alternatives stated in IV and others unmentioned in this specification (for example, alternative of approach road extension over soft soil ground…). For each proposed alternative, it is necessary to calculate and evaluate stability and settlement as well as analysis, calculation and comparison on economy and technique so as to select the applicable alternative. During analysis, it should concern settlement affection of embankment on the existing engineering works.

IV.8.2. In all cases, it is necessary to make use of the whole acceptable construction period: Embankment on soft soil must be commenced earliest. If necessary, the last due in the general schedule shall be maximum extended or embankment shall be divided into many times, embankment shall be conducted while waiting for its consolidation. Such method is an option that gains significant economic and technical efficiency, thus, it should be applied in combination with other treatment measures at the same time.

IV.8.3. During actual construction, monitoring results shall be reviewed (II.3) and compared to

requirements of stability and deformation control stated in II.1.2 and II.2 so as to adjust embankment speed, if necessary, and design alternative regarding technical and economic benefits against the basic design. Especially, based on actual settlement monitoring as stated in II.2.5, remaining consolidated settlement shall be forecasted when determining construction time of work items related to requirements for settlement control of embankment on soft soil (the forecast of settlement obtained by calculation is only used for proposing design alternatives).

IV.8.4. If at least 500m route length with technical characteristics through soft soil ground, 30-50m trial

embankment should be constructed on site (no less than two folds of embankment bottom width) with arrangement of monitoring instruments as stated in II.3. Based on the monitoring results, design alternatives shall be made accurate before the whole construction. The trial embankment must be conducted during technical design and adjustment after the trial work shall be done during drawing design for detailed construction. If the embankment height is low, it is more necessary to carry out the trial embankment. Observation time for the trial work should be from 6-12 months.

V. CALCULATION FOR EMBANKMENT STABILITY ON SOFT GROUND

V.1. Calculation method V.1.1. Classic or Bishop Method with circular displacement surface deepening down into soft soil

shall be adopted as the basic method for calculation of embankment stability on soft soil. V.1.2. The classic method shall be calculated according to Figure V.1 and stability coefficient Kj

equivalent to one circular displacement with center Oj shall de determined by the formula V-1:

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Figure V.1. Stability Diagram according to the classic method with circular displacement; (hx is height equivalent traffic loading capacity defined by the formula II.1)

In Figure (V.1), sliding piece i in width di is affected by load of Di , earthquake load Wi (if required); furthermore, if geo-textile is used for stability improvement, the whole sliding block shall be under affection of maintaining force F (see Figure IV.1 and Article IV.7.1). Wi shall be determined in conformity to Article II.4.4, F is defined as specified in Article IV.7.1 and IV.7.2. These forces have Yi (force Wi) and Y (force F) in comparison with sliding center Oi. For a circular sliding surface with center Oi, Yi will change according center of gravity position of sliding piece, Y shall not change.

l i – length of sliding curve within piece i. n – Number of sliding pieces ramified within sliding block. αi – angle between normal of l i and direction of force Qi (Figure V.1). Rj- diameter of sliding curve

ci and φi unit adhesive force and internal friction angle of the soil layer containing sliding curve l i of sliding piece i (if l i is within embankment area, using unit adhesive force and internal friction angle of embankment soil). For soft soil areas, when using on-site Vane Shear Test results, φi = 0, ci shall be equal to calculated shear strength Ci

u (see V.3.2).

V.1.3. Calculated by Bishop Method, stability coefficient Kj correlatively to circular sliding surface with center Oj (Figure V.1) shall be determined according to the formula below:

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With:

Symbols in (V.2) and (V.3) have the same meaning as in (V.1) on Figure V.1. The way to specify them is totally as same as calculation according to the classic method. Only difference is that the calculation by (V-2) and (V-3) is step by step one, as mi in (V-3) depends on Kj; thus if using the Bishop method, it is obligatory to use computer software programs.

V.2. Attention should be paid when using the classic and Bishop Calculation methods V.2.1. Width of sliding piece di shall not be more than 2m and length of sliding curve within each

piece l i must be located on the same soil layer.

Each sliding piece consists of all soil layers counted from sliding surfaces upwards (including buffer sand layer, submerged embankment in soft soil, embankment of berm, preloading embankment and embankment height with equivalent vehicle loading capacity).

V.2.2. Self-weight of each sliding piece Qi is determined as follows:

In which: hk is height of sliding piece i within various soil layers with various dry volume γk (N is number of various soil layers within i). For soft soil layers are located under underground water levels, values of γk shall be calculated by using volumetric weight of float minus 1. Note that, for sliding pieces within sub-grade width, when Qi is calculated regarding equivalent height of vehicle hx which is defined by the formula (II-1) shown in Figure V.1 and preloading embankment height (if any).

V.2.3. Calculation of various circular sliding surfaces (Oj, Rj) shall be conducted to determine the most dangerous sliding surface and smallest stability coefficient Kj min (Kmin for short). The coefficient Kmin is used to evaluate requirements of stability against resurfacing as stated in II.1). Note that, it must determine position of the most dangerous sliding surface forecasted by calculation for the base of design alternatives of treatment measures such as width of berm (Article IV.2.4), depth of vertical drainage arrangement (Article IV.6.7) or for determination of

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active area stabilized by PBD (Figure IV.1). If the soil is soft and thin, sliding surface may consist of circular curve sections in combination with a straight section at the bottom of soft soil (especially the bottom with grade more than 100).

V.2.4. If the most dangerous sliding surface is not calculated by computer model, it can be found out

by letting position of center Oj changed within area of “the most dangerous sliding center” as shown in Figure V.2.

Figure V.2. Diagram to determine dangerous sliding center (I is slope centerline, C is slope foot)

If embankment is made from sand (bondage force c = 0), cross point between the most dangerous sliding surface and sub-grade width may change on the whole scope of AB, if the bondage force is large, the point often passes through point A or near A (from A to the centerline of embankment).

V.2.5. Computer models for determination of stability coefficient Kj and finding out Kmin must be able to satisfy requirements of calculation defined in Articles V.1, V.2.1, V.2.3.

V.2.6. When evaluating embankment stability on soft soil, in addition to application of different

treatment measures as stated in IV.2, IV.3, IV.4, IV.6, IV.7, the methods described in V.1 and requirements in V.2 (especially V.2.1 and V.2.2) shall be adopted. This requires that prior to supposition of sliding surfaces and calculation, cross section of embankment must be drawn with fully natural underground strata and structures as required by the equivalent treatment measures (excavation depth of soft soil, buffer sand layer, berm in form of preload embankment, arrangement of PBDs), the embankment height shall be added by equivalent height of vehicles loading capacity.

V.2.7. If adopting embankment method divided into many times, acceptable embankment height shall

be determined as follows: • To suppose a height of embankment. • To calculate embankment stability at this height according to the methods stated in V.1 and

V.2 correlatively with different shear strength of soft soil for each embankment time (see Part V.3). If results of mathematical model satisfies the requirements stated in II.1.1 and Kmin value is not very high (Kmin = 1,2 should be adopted), the supposed height shall be accepted for design height of each embankment time, if not, the supposition of height will be repeated until the results of mathematical model provides Kmin = 1,2.

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It is acceptable to use mathematical models with availability of limited embankment height Hgh or formulas for calculation of limited loading capacity Pgh, depending on characteristics of shear strength, quickly find out values of the supposed embankment height. After that, it will be tested by mathematical model as method of circular sliding surface stated in V.1 and V.1 (note that Pgh = γd . Hgh with γd is natural weight of soil for embankment of sub-grade or preloading). If using mathematical models available on computer, it can suppose 3-4 of embankment height value and then run the program to determine value of Kmin equivalent to that height and by relation between Kmin = f (Hembankment) to determine acceptable embankment height equivalent to Kmin =1,2.

V.3. Calculation of stability and its correlative parameter V.3.1. There are calculations of stability with requirement of using calculated shear strength at various

states as follows:

1. Case I: embankment is constructed when the soft soil has not been consolidated or consolidated insignificantly as the following specific cases: • Calculation and evaluation of stability for proposal of design alternatives as stated in Article

IV.8.1; • Application of direct embankments, embankment with arrangement of PBDs (IV.2 and

IV.7), partial excavation of soft soil (IV.3), berm (IV.4); • First sub-grade embankment time in the method of embankment in many times (IV.8.2 and

V.2.7), adopting method of Buffer sand layer (IV.5) and vertical drainage (IV.6).

2. Case II: After completion, embankment on soft soil is taken into operation; the soft soil’s consolidation below has reached at least 90%. 3. Case III: if embankment is divided into many times, both embanking and waiting for soil’s consolidation (IV.8.2), the consolidation of soft soil will increase regularly during the second or third embankment. If results of stability calculation according to the case I satisfy the requirements in II.1.1, height in one embankment is equal to designed embankment height, whether any treatment measures are adopted, it is not necessary to regard the calculation according to Case II and Case III.

V.3.2. For Case I, characteristics of shear strength serve calculation as follows: • For embankment and sand buffer layer: values of bondage force c and friction angle φ shall

be determined by samples with factual density and moisture through fast shear test without water drainage in lab. If the ground is in water the sample shall be at the most disadvantaged moisture.

• For natural soft or non-soft soil layers under the embankment: using on-site vane shear test results and calculated bondage force values Cu which are determined according to the formula below (φ = 0):

Ciu = µ.Ss (MPa) (V- 5)

In which: Ss – Undisturbed shear strength (MPa) without water drainage from on-site vane shear test.

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µ - adjustment coefficient (according to Bjerum) regarding non-isotropous affection of soil, shear velocity and continuous destruction of soil ground depending on soil plastic index as shown in Table V-1.

µ depends on plastic index Ip Table V-1

IP 10 20 30 40 50 60 70

µ 1.09 1.0 0.925 0.86 0.80 0.75 0.70

(The first class interpolate among intervals in the table)

• Only when there is no equipment for implementation of on-site vane shear test, it can use the characteristics of shear strength according to fast shear test results in lab (ci , φi).

V.3.3. For Case II: characteristics of soft or non-soft soil layers under the embankment (C and φ) shall

be determined by undisturbed samples through consolidated fast shear test in lab; embankment soil layers (including sand buffer layer, if any) shall be also defined as Case I.

V.3.4. For Case III: characteristics of shear strength of soil layers and embankment shall be

determined as Case I but Ss in the formula V-5 shall be replaced by Su as follows: Su = U [0.22.σz + Ss (σpz /σvz)0.2] (V-6)

In which: U – Forecasted consolidation level can be gained from the beginning of first embankment until that of the second one: U is calculated by decimal number of … (e.g. soil consolidated 50%, U = 0.5) and according to the method stated in Article VI.3.1.

Ss means the same as in the formula (V-5) with on-site fast shear test at the normal ground (natural state of soil) σz ,σpz ,σvz have the same meaning and determination as in the formula (IV-5 and IV-6) with loading capacity of the first embankment. With Su calculated according to (V-6), from that bondage force (calculated shear strength) Ci

u be found out by the formula (V-5), depending on consolidation level of soft soil after the first embankment. The calculated values of shear strength with U = 1 shall be less than shear strength values of Case II.

Su ≤ (σz + σvz ) . tgφi + ci (V-7) In which:

ci and φi are determined by consolidated fast shear test as stated in V.3.3. If value of Cu calculated by the formula (V-5 and V-6) is higher than values of the right side of the formula (V-7), just use the values of the right side of the formula (V-7) for calculation.

If results of fast shear test in lab will be used for calculation, equivalent to gained consolidation U, shear strength of soft soil i is considered to be added by Δci.

Δci = σz . U.tgφi (V- 8) and bondage force coefficient calculated according to the formulas (V-1) or (V-3) will be ci

u = ci + Δci . Calculated shear strength values with φi and ci

u must satisfy the requirements in (V-7).

V.3.5. Calculation of stability by determining shear strength as the abovementioned calculation only serves design alternatives. In Case I and Case II, to ensure stable ground during embankment, it

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is necessary to conform sufficiently to all requirements of settlement and transversal displacement as stated in II.3.

VI. CALCULATION OF EMBANKMENT SETTLEMENT ON SOFT GROUND

VI.1. Calculation of consolidation settlement Sc

VI.1.1. Consolidation settlement Sc is estimated according to the following formula:

In which:

Hi – Thickness of the i soil layer for settlement calculation (n layers with various deformation characteristics), i from 1 to n layers; Hi ≤ 2.0m; ei

o – void coefficient of the i soil layer at initial natural state (without embankment on it). Ci

o – settlement index or slope of settlement curve (under performance of e ~ lgσ) within σi > σi

pz (as shown in Figure 1, Appendix 1). σi

vz , σipz , σi

z – Pressure (vertical compression strength) due to weight of natural soil layers on the i layer, pre-consolidated pressure at the i layer and pressure caused by embankment loading capacity on the i layer (determining these pressures correlatively with the depth z in the middle of the soft soil i).

Note: a) When σi

vz > σipz (soil at incompletely consolidated state under affection of weight

loading capacity) and when σivz = σi

pz (soil at normal consolidated state), the formula (VI-1) only remains the following term (no existing of the term with Ci

r). b) When σi

vz < σipz (soil at excessively consolidated state), calculation of consolidated

settlement Sc according to VI-1 with two cases: § If σi

z > σipz - σi

vz , apply the formula (VI-1) with both of terms. § If σi

z < σipz - σi

vz , apply the formula below:

VI.1.2. Determination of calculation parameters and values in the formula for calculation of pre-settlement (VI-1) • Parameters Ci

r , Cic and σi

pz shall be determined by confined compression test with undisturbed samples which are representatives for the soft soil i in conformity to Instructions in TCVN 4200 – 95 and supplementations in Appendix I of this Specification and in Article III.3.5 and III.3.7.

• Strength value (pressure) σivz shall be determined as instructed in Article IV.6.1 (the

formula IV-6).

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• Strength value σiz shall be calculated according to mathematical model Osterberg in

Appendix II as mentioned in (IV.6.1), but it is only correlative to designed embankment loading capacity (Article II.2.2) and concerning pre-settlement as mentioned in VI.2.3.

VI.1.3. Settlement depth of soft soil under affection of embankment loading capacity or scope of

affection by embankment loading capacity za shall be determined in accordance with the conditions as follow:

σza = 0.15. σvza (VI-2) In which:

σza – Stress caused by embankment loading capacity at the depth Za σvza – Stress caused by weight of upper soil layers at the depth Za (with concerning of pushing pressure if these layers are located under underground water level).

VI.2. Estimation of total settlement S and instant settlement Si

VI.2.1. Total settlement is estimated according to the following experience: S = m.Ss (VI-3)

with m = 1.1 ÷ 1.4; if there are measures for prevention soft soil from transversal sliding by embankment loading capacity (such as berm or PBD), m = 1.1 shall be used; in addition, the higher embankment and the softer soil are, the bigger value of m is.

VI.2.2. Instant settlement Si mentioned in II.2.1 shall be estimated according to the relation below: Si = (m-1).Sc (VI-4)

with meaning and determination of m is as same as in VI.2.1. VI.2.3. Procedures of settlement calculation on soft soil

To calculate the total settlement S according to the formula (VI-3), results of consolidated settlement Sc according to (VI-1) or (VI-1’) must be found out; e.g. coefficients and parameters mentioned in VI.1.2 must be determined, σi

z depends on embankment loading capacity, this loading capacity consists of settlement embankment in soft soil S. As S is unknown, settlement calculation is a repeated and trial calculation by the procedures as follows: • Suppose that total settlement Sgt (Sgt = 5-10% of soft soil thickness or depth of soft soil

under settlement bearing za; if peat is excessive settlement, suppose that Sgt = 20-30% of the abovementioned depth);

• Calculation of settlement distribution σiz is done by the mathematical model Osterberg, with

designed embankment height concerning settlement estimate H’tk = Htk + Sgt (H’tk is designed embankment height: if it is direct embankment, the height is from natural ground to margin of road shoulder; if there is excavation of soft soil, it is from elevation of soft soil after excavation.

• With H’tk, we can calculate consolidated settlement Sc by the formula (VI-1) or (VI-1’), it depends on each case:

Sgt If Sc satisfies conditions in (VI-3), e.i. Sc = m , the result is accepted and Sc and Sgt are determined; if it does not satisfy, S shall be supposed again and the calculation shall be repeated.

VI.2.4. Designed embankment height with settlement estimate H’tk shall de determined by: H’tk = Htk + S (VI-5)

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So, elevation of embankment on soft soil shall be designed higher than S for settlement estimate. Embankment width at the elevation correlative with H’tk shall be equal the designed embankment width.

VI.3. Consolidated settlement estimate by time in the case of vertical one-way drainage VI.3.1. In this case, consolidation U, which is obtained after the time t since completion of

embankment of designed sub-grade and preloading (if any), shall be determined depending on Tv as shown in Table VI-1.

Ctb

v Tv = t (VI-6) H2

In which: Ctb

v – average vertical consolidation coefficient of soft soil layers within settlement bearing depth za (see its meaning in VI.1.3)

with hi is thickness of soft soil layers within za (za = Σhi) with different consolidation coefficient Cvi. Cvi shall be determined by unconfined compression test with undisturbed in accordance with TCVN 4200-95 correlative with average pressure 2σi

vz + σiz from which the soft soil has to

bear during consolidation. 2 H is depth of vertical consolidated drainage, if there is only one drainage surface, H = za’ if there are two on both above and below (under sand) H= 1/2za.

Consolidation obtained depending on Tv; Uv= f (T) Table VI-1

TV 0.004 0.008 0.012 0.020 0.028 0.036 0.048

UV 0.080 0.104 0.125 0.160 0.189 0.214 0.247

TV 0.060 0.072 0.100 0.125 0.167 0.200 0.250

UV 0.276 0.303 0.357 0.399 0.461 0.504 0.562

TV 0.300 0.350 0.400 0.500 0.600 0.800 1.000

UV 0.631 0.650 0.698 0.764 0.816 0.887 0.931

TV 2.000

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UV 0.994

Note: if Cv is calculated in cm2/sec, hi and H shall be calculated in cm and t in sec (second).

VI.3.2. Consolidated settlement of embankment on soft soil shall be determined as follows: St = Sc.Uv (VI-8)

In which: Sc is determined as instructed in VI.2.3, U done as in VI.3.1. The remaining consolidated settlement after the time t, ΔS will be:

ΔS = (1-U).Sc (VI-9) VI.3.3. Depending on relation (VI-6, VI-7) and Table VI-1, designer can determine the waiting time

after embanking (including wearing course construction) so that remaining consolidated settlement after completion of wearing course construction shall be within the allowable scope as mentioned in Article II.2.3, then considers whether methods for accelerating settlement should apply or not.

VI.4. Estimation of consolidated settlement by time in case of two-way drainage system (with

application of sand drain or PBD) VI.4.1. In this case, consolidation U by time t is determined by this formula: U = 1 – (1 – Uv) (1 – Uh) (VI-10) In which:

- Uv – Vertical consolidation is determined as mentioned in Article VI.3.1 - Uh – Transverse consolidation due to impact of sand drain or PBD (as stated in

Article VI.4.2) VI.4.2. Transverse consolidation Uh is determined as follows:

In which:

- Th – Time by transverse direction:

ℓ is the distance between sand drains or PBDs: + If sand drain or PBD is arranged by square, then: ℓ = 1.13D (VI-13) + If they are arranged by triangle, then: ℓ = 1.05D (VI-14)

- D – The distance between drain centers or PBD centers Transverse consolidation coefficient Ch (cm2/sec) is determined by means of compression test for undisturbed samples by transverse direction in accordance with the Standard TCVN 4200-95. If soft soil layer including soil layers with different Ch, the value for calculation is Ch followed by depth of the captioned different layers.

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In feasibility study stage, the following formula is temporarily used to determine the value Ch: Ch = (2 ÷ 5) Ctb

v (VI-15) In which Ctb

v is determined as mentioned in Article VI.3.1.

F(n) which is the factor affected on the distance between sand drains or PBDs is determined depending on n = ℓ/d (d is diameter of sand drain or equivalent diamater of PBDs) by the following formula:

Fs – Factor that determines the impacts of soil area around the PBDs (that decrease permeability coefficient in the area).

Fr – Factor that determines the impacts of PBDs’ obstruction.

In case of applying sand drains, the two factors shall not be determined (it means that Fs = 0 and Fr = 0); and in case of applying PBDs, they shall be determined as mentioned in Article VI.4.3.

VI.4.3. In case of applying PBDs as vertical drainage system, then F(n), Fs and Fr in the formula (VI-

11) are determined as follows:

F(n) as in formula (VI-16) with equivalent diameter of a PBD d shall be determined as follows: a + b d = (VI-17) 2

In which: a – Width b – Thickness of PBD

Because d is small, normally n is considerable and n2 >>1, so F(n) is determined by the following formula:

F(n) = ln(n) – 3/4 (VI-18)

• Factor determined oscillation: Fs = (kh/ks – 1) . ln (ds/d) (VI-19)

In which kh and ks are vertical permeability coefficient of the soft soil before applying PBDs (when soft soil are not oscillated) and after applying PBDs; ks < kh and normally ks = kh that kv is vertical permeability coefficient of the soil. In practice, the following calculation is normally applied:

kh kh Ch = = = 2 ÷ 5 (VI-20)

ks kv Cr Ch and Cv – Vertical and transverse consolidation coefficient of soft soil

ds/d – Ratio between equivalent diameter of the soil area around PBDs and equivalent diameter of PBDs. In practice, the following calculation is normally applied:

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ds = 2 ÷ 3 (VI-21)

d • Factor determined resistance force of PBDs:

2 kh Fr = πL2 (VI-22)

3 qw In which:

L – Length of PBDs (m); if there is only one-way drainage at the top, L is equal to the depth of PBDs; if there is two-way drainage (upper and lower), L is a half of the PBDs’ depth; kh – Horizontal permeability coefficient of soft soil can be approximately determined according to (VI-20) by vertical permeability coefficient kv or by direct permeability test with horizontal samples (m/s). qw (m3/sec) – PBD drainage correlative to hydraulic gradient = 1; this is from its certificate at manufacture. In practice, it is allowed to obtain the ratio kh/qw = 0.00001 ÷ 0.001 m-2 for clayey or loamy soft soil; kh/qw = 0.001 ÷ 0.01 for peat and kh/qw = 0.01 ÷ 0.1 for sandy mud.

VI.4.4. In case of applying sand drain, it is possible to directly use the Abac (VI.1) in order to present

relation between (VI-11) and F(n) according to (VI-16) and Fs = Fr = 0.

Figure VI.1. Abac to determine horizontal consolidation Uh by Th and n.

VI.4.5. The obtained settlement St and remaining settlement ∆S after time t in case of two-way

consolidation drainage are also determined as in formulas (VI-8) and (VI-9), but Uv is replaced by U to calculate (VI-10).

VI.5. Notice for settlement estimation

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VI.5.1. To examine the effects of construction period on settlement changes of the embankment on soft soil, it is possible to use the method as in Figure VI.2 with the assumption that embankment load increases linear.

• First, draw a consolidated settlement curve by time St = ScU in case embankment load is

immediately affected (discontinuous curve, line 2 in Figure VI.2).

Figure VI.2. Settlement changes by time with consideration of construction period

• Settlement at the end of construction period (at the time tc when being finished) is determined

by the settlement in line 2 at the time of half embankment tc/2. In FigureVI.2, from point 1/2tc draw a vertical line that meets line 2 at H, then from H draw a horizontal line that meets the vertical line from tc at E.

• Similarly, settlement at the time t is determined by point K (settlement at the time t/2 of the line 2), from the point, draw a horizontal line to get point N, connect ON to cut the vertical line from t at M. As a result, settlement estimation curve with in consideration of construction period is presented (curve 1 through OME in Figure VI.1).

VI.5.2. Because of some assumptions on theory and on input data, the result of settlement estimation

and consolidation is used as mentioned in Item II.2.5. In trial construction (VI.8.4) and construction in practice, result of actual settlement monitoring shall be presented to evaluate, correct methods and interpretation steps as mentioned in II.2.5 and IV.8.3.

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APPENDIX I

DETERMINATION OF PRE-CONSOLIDATION PRESSURE VALUE σPZ AND COMPRESSION PROPERTIES OF SOFT SOIL

Procedures are as follows:

1. Test to determine confined compression of undisturbed soil samples in the depth z is carried out in accordance with the Standard TCVN 4200-95, including unloading test after the final loading level as mentioned in Article 4.9 of the Standard. Accelerated compression test shall not be carried out.

2. Depending on testing result of drawing compression curve e – lgp (Figure 1), in which e is void coefficient respectively with pressure levels p. This compression curve is also drawn as lge – lgp.

3. Determination of pre-consolidation pressure value σp a. In the curve e – lgp, point A is shown where the biggest curvature (with minimum

radius) exists. From point A, draw a horizontal line and a tangential line to compression curve. Draw a bisector of an angle between the above horizontal line and tangential line through A. Intersection point of the bisector and tangential line at the end of compressive curve (the lengthened line) shall determine the point that is respectively with pre-consolidation pressure value P (see Figure 1).

b. In the curve lge – lgp, if a broken point is formed, then it is the point that is respectively with pre-consolidation pressure value (see Figure 2).

c. In two ways of determination of pre-consolidation pressure value, which value is higher is the usage value.

4. Determination of compression values Pre-consolidation pressure value divides compression curve e – lgp into 2 parts respectively with σ < σp line (in the left) and σ > σp line (in the right). Then compression values are determined as follows:

a. Compression value Cr in σ < σp line: e1 - ep

Cr = lg σp - lg σ1

In which: ep – Void coefficient respectively with pre-consolidation pressure value. e1 – Void coefficient correlative to compression pressure σ1. Selection of the value 1 depends on loading in practice of soil layer i that needs to calculate its settlement. σ1 = 0.1kG/cm2 is normally taken respectively with pressure level in the first test in accordance with the Standard TCVN 4200-95 for soft soil. Cr can also be calculated according to unloading line in Figure 1.

b. Compression value Cr in σ > σp line: ep – e2

Cc = lg σ2 - lg σp

- The meaning of ep, σ2p are as (a) of this part and e2 is void coefficient respectively to pressure value σ2. Selection of the value σ2 depends on loading in practice of soil

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layer i that needs to calculate its settlement and so that σivz + σi

z in the formula (VI-1) is between σp and σ2.

- In compression test, if the highest pressure level is selected as mentioned in Article 1.7 of the Standard TCVN 4200-95, then value σ2 is equal to the value of that level.

5. From the testing result to determine of pre-consolidation pressure at different soil layer i, diagram σp – z (depth) can be drawn as in the Figure 3. Line σv.z – z (pressure due to weight of soft soil layers themselves), line σz – z (pressure due to embankment loading) and line σv.z + σo = f(z) shall be drawn in order to check (IV.5a) and (IV.5b) as in the Figure 3. If (IV.5a) and (IV.5b) are not be satisfied, methods for vertical consolidation drainage (sand drain or plastic board drain) should not apply.

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COMPRESSION TEST Project: …………………………………………………………………………………….. Borehole: …………………Sampling depth: …………………………………………. (m) Sample No.: ………………Number of Test: ……………………………………………...

Pressure level – σ (kG/cm2)

Pre-consolidation pressure : σp = 0.620 (kG/cm2) Initial void coefficient : eo = 1.188

Appendix 1 – Figure 1

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Pressure level – P (kG/cm2)

Pre-consolidation pressure : σp = 0.68 (kG/cm2) Initial void coefficient : eo = 1.188

Appendix 1 – Figure 2. Determination of pre-consolidation pressure in the graph lge – lgp

(Testing data as in Figure 1)

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Stress (T/m2)

Appendix 1 – Figure 3. Condition checking (IV-5a)

-------------------- Stress due to weight _____________ Stress due to embankment load ………………… Maximum stress in the past (Pre-consolidation pressure)

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APPENDIX II

CALCULATION OF VERTICAL COMPRESSION STRESS (PRESSURE) σzi DUE TO EMBANKMENT LOAD OR BERM LOAD UNDERGROUND

ACCORDING TO OSTERBERG ABAC

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a. The Abac is to determine vertical compression stress caused by underground embankment b. Loading diagram and example of using Osterberg Abac (in case of rectangular load, it is

considered as trapezium with ratio a/z = 0 ≈ 0.01); Dimension of number used in the Figure is stated in m. For example: b’’= a = 2m; b’= b’’+ a + b1 + b2 = 8m Example of Osterberg Abac: 1. Determination of stress σzi of M1:

a. For load in the left: a 2 b1 1 = = 1 and = = 0.5 z 2 z 2

According to the Abac: It = 0.397 b. For the load in the right:

a 2 b2 3 = = 1 and = = 1.5 z 2 z 2

According to the Abac: If = 0.478 Then: σzi = (0.397 + 0.478)q = 0.875q

2. Determination of stress at M3: σz3 = (It + If)q

a/z = 0 and b/z = 0.5, then It is determined; a/z = 0 and b/z = 1, then If is determined. Then σz3 = (0.278 + 0.410)q = 0.688q

3. Determination of stress at M2 (for calculating stress due to berm block at central point of the embankment at the depth z):

σz2 = (Ilmnk – Ilrsk)q Ilmnk – Trapezium load at the right of M2 Ilrsk – Rectangular load at the right of M2

a. Calculating Ilmnk : a 2 b 8 = = 1 and = = 4 z 2 z 2

In the Abac: Ilmnk = 0.5

b. Calculating Ilrsk : a b b’’+ a/2 2 + 1 = 0 (rectangle) and = = = 1.5 z z z 2

In the Abac: Ilrsk = 0.46 Then: σz2 = (0.5 – 0.46)q = 0.04q