Consideration of oversurcharge effects on soft clay with vertical drains.

Wenyi, Yang ; Guangya, Kong ; Wang, Jeffrey 等

The effects of over surcharge on soft clay have been assessed in a term of "equivalent time". Based on the assumption of the uniform relationship of clay in effective stress-strain-time space (Bjerrum et al., 1967), the deformation of soft clay caused by the process of applying and removing overcharge is assessed by the additional elapsed time under the load without overcharge. Based on the results of theoretical analyses and laboratory tests, a simplified method of assessment of over surcharge effects of soft clay is proposed.

GENERAL

The main considerations involved in the design of over surcharge with vertical drains are the arrangement of vertical drains and procedures of over surcharges. The procedure of over surcharges is governed by the requirements of soil strength and settlement rate after treatment. The criteria of settlement rate might be a critical issue due to the possibility of mobilizing negative skin friction when piled foundation system is selected.

A problem might be encountered in the design is to predict the consolidation state of soft clay after the removal of over surcharge. In most cases, the backfilling material is stacked on top of soft clay and sand blanket stage by stage. Once one layer of the backfilling material is loaded on the sand blanket, soft clay is subjected to the process of consolidation under current weight of backfilling material. The next layer is then loaded prior to the end of primary consolidation under the previous loading. This process is repeated until the over surcharge is completely loaded.

Terzaghi's consolidation theory is traditional method to calculate the degree of consolidation under multiple stages of loading. The primary consolidation of soft clay under the over surcharge may not be completed prior to the removal of the over surcharge. In this case, soft clay is still subjected to further consolidation under current reduced surcharge. As Terzaghi's consolidation theory applies to constant load, the process of applying-and-removing over surcharge normally brings difficulties for the calculation of consolidation of soft clay. The concept of "equivalent time" in effective stress-strain-time space is proposed by the author to simplify the calculation of consolidation under the process of applying-and-removing over surcharge.

CONCEPT OF EQUIVALENT TIME

The deformation properties of soft clay under various loading conditions have been widely discussed since the establishment of Terzaghi's one-dimensional consolidation theory in 1925. The soft clay was found exhibiting time-independent and time-dependent deformation. The whole process of deformation can be defined as primary and secondary stages (Fig.1). Terzaghi's theory is now recognized only to reflect the deformation at primary stage rather than secondary stage.

[FIGURE 1 OMITTED]

The secondary deformation of soft clay is time-dependent and is found to be significant in the case of very soft clay. A series of studies on the secondary deformation have been carried out and a number of models proposed to describe the primary and secondary deformation of soft clay. The secondary deformation of clay under constant load is basically found to be a straight line in strain- logarithm time coordinates.

Bjerrum et al. (1967) have proposed a comprehensive model to describe the deformation properties of soft clay with assumption that void ratio of clay is function of effective stress and time. As shown in Fig. 2, the relationship of the effective stress, strain and time is represented by a set of paralleled straight lines. It is reasonably assumed that soft clay follows a uniform relationship in the effective stress-strain-time space, i.e.

R ([sigma'], [epsilon], t) = 0 (1)

where [sigma']' is effective stress of clay; [epsilon] is strain of clay; t is elapsed time

[FIGURE 2 OMITTED]

The effect of over surcharge can be assessed based on Bjerrum's assumption. As shown in Fig. 2, the initial state of clay after experience of deformation under load [P.sub.0] to [P.sub.1], the point in the diagram representing the state of clay is moved from point A to point B after time [t.sub.B]. Under this load, over surcharge [DELTA]P is applied and then removed. The point of soil state is moved to point D instead of point B, i.e. soil is subjected to residual deformation ([[epsilon].sub.D]--[[epsilon].sub.B]).

Above process can be understood in following way: once the load is increased from [P.sub.0] to [P.sub.1], and the point of soil state in the diagram is moved from point A to point B, the deformation of clay is to be continued under the load [P.sub.1]. With the additional elapsed time ([t.sub.B]--[t.sub.D]), the point of soil state is also moved to point D.

The above analysis of clay deformation clearly indicates that based on the assumption of uniform deformation curve of clay in effective stress-strain-time space, the residual deformation ([[epsilon].sub.D]--[[epsilon].sub.B]) due to the applying and removing over surcharge [DELTA]P is equal to the effect of additional elapsed time ([t.sub.B]--[t.sub.D]) under load [P.sub.1]. In other words, the effect of over surcharge can be assessed with additional elapsed time under previous loading (Fig. 3). For this reason, it is not irrational to defined the residual deformation ([[epsilon].sub.D]--[[epsilon].sub.B]) as additional deformation for [P.sub.1] and corresponding time difference ([t.sub.B]--[t.sub.D]) as "equivalent time" to additional deformation for P1 in effective stress-strain-time space. If secondary deformation is involved in the process of over surcharge, the additional deformation can be divided into two parts: i.e. "additional deformation in primary stage" and "additional deformation in secondary stage". The equivalent time could be defined as "equivalent time in primary stage" and "equivalent time in secondary stage".

[FIGURE 3 OMITTED]

If [t.sub.c] is supposed to be the elapsed time of end of primary consolidation (EOP), and [[epsilon].sub.c] is the deformation of clay at [t.sub.c] the equivalent time at primary stage and secondary stage can be calculated as follows:

(1) Equivalent time in primary stage

t = [H.sup.2] / [C.sub.v] ([T.sub.vc] - [T.sub.vb])

where

H is thickness of clayey layers; [C.sub.v] is consolidation coefficient; [T.sub.vc] is time factor corresponding to [t.sub.c]; [T.sub.vb] is time factor corresponding to [t.sub.B].

(2) Equivalent time in secondary stage

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where

[[DELTA].sub.D] - [[DELTA].sub.C] is additional deformation at secondary stage;

[C.sub.[alpha][epsilon]] is secondary consolidation coefficient

LABORATORY TEST RESULTS

A serious laboratory tests (total 19 number) were carried out using the standard odometers to verify above concept. The samples were selected from the same tube to minimize the discrepancy of soil properties. Two different loading procedure were adopted as shown in Fig.4. The results of tests are summarized in Table 1.

[FIGURE 4 OMITTED]

It could be seen from the results of tests that clay samples subjected to loading scheme A and B had two different types of consolidation curves (Fig.5). Coefficient of consolidation [C.sub.v] was apparently influenced by the type of loading schemes, with roughly 1.8 to 1.7 times difference. Meanwhile, values of [t.sub.90] also showed significant difference which indicates that the effect of [DELTA]P. Under loading scheme B, the load increment [DELTA]P caused additional deformation to the clay samples, hence equivalent to the additional lapsed time under the previous loading which reflected in the reduced of values of [t.sub.90].

[FIGURE 5 OMITTED]

APPLICATION OF THE CONCEPT OF EQUIVALENT TIME

As discussed above, the effects of over surcharge can be measured as a term of equivalent

time corresponding to additional deformation of clay under the over surcharge. The additional deformation can be estimated based on the magnitude of over surcharge and soil properties. The corresponding time can be calculated based on this additional deformation. The effects of over surcharge can be assessed according to calculated equivalent time:

(1) to calculate the final settlement [DELTA] of clay layer under the load of surcharge at designed final backfilling level;

(2) to calculate the settlement [DELTA] of clay layer prior to the application of over surcharge under the load of surcharge;

(3) to calculate the settlement s of clay layer due to over surcharge after the removal of over surcharge;

(4) to compare [DELTA]f and ([DELTA]p+[DELTA]s). if ([DELTA]p+[DELTA]s) is equal or large than [DELTA]f , the primary settlement of clay is considered completed and both of equivalent time in primary and secondary stage are to be assessed;

(5) to calculate the equivalent time according to the additional settlement of clay caused by over surcharge. The equivalent time in primary stage can be estimated by assuming time factor Tv=0.9 if ([DELTA]p+[DELTA]s) is larger than [DELTA]f.

The method discussed above was already used in a project in Singapore. In the said project, about 8m to 13m depth of very soft clay was to be improved by using vertical drains. According to the contract requirements, this soil improvement work must be completed within 40 weeks. In addition, the settlement rate of clay after improvement was required to be less than 20mm per year.

Vertical drains with over surcharge were used for this project. To ensure that the results of soil improvement can meet the contract requirements, the loading procedure of over surcharge was checked based on the method of equivalent time. The settlement rate of soft clay after removal of surcharge was estimated according to the values of additional settlement and equivalent time of consolidation. The actual loading procedure of applying-removing backfilling was adjusted depending on the calculation and monitoring results. The results of application are proven by the monitoring results to be satisfactory. In addition, it was also noticed that the proposed method is reliable and quite easy to use.

CONCLUSIONS

The effects of over surcharge on soft clay could be assessed in a term of "equivalent time" corresponding to the additional deformation in effective stress--strain--time space. The deformation of clay caused by the process of applying-and-removing of over surcharge is considered as equal effect as additional elapsed time of clay under the load without over surcharge. The results of laboratory tests of undisturbed samples by using two loading schemes with and without preloading (preloading to cause additional deformation of clay) indicate that the process of applying-and-removing of loads apparently reduces the consolidation time of clay, which provides evidence of the concept of equivalent time. According to the theoretical analysis and laboratory tests, a simplified method to assess the effect of over surcharge on soft clay with vertical drains was proposed and successfully applied in relative projects

REFERENCES

Bjerrum, L.(1967), "Engineering geology of Norwegian normally consolidated marine clays as related to settlement of buildings", Geotechnique (Seventh Rankine Lecture), Vol.17, No.2 81-118.

Lowe III, J. (1974). "New concept on the consolidation and settlement analysis", Journal Of Geotech. Eng. Div., Asce GT6, 574-612.

Leroueil, S., Kabbaj, M., Travenas, F. & Bouchard, R. (1985). "Stress-strain-strain rate relation for the compressibility of sensitive natural clay", Geotechnique, Vol. 35 No.2 ,159-180.

YANG WENYI

Tiandi Science and Technology Co. Ltd, China

KONG GUANGYA

Tiandi Science and Technology Co. Ltd, China

JEFFREY WANG

Tritech Consultants Pte Ltd, Singapore

Table 1. Comparison of test results of undisturbed clay samples
under two loading schemes.

Sampling Depth Coefficient of consolidation
Tube No. (m) Scheme A
 No. of [C.sub.v1]
 Tested (x [10.sup.3]))
 samples ([cm.sup.2]/sec.)

1 7.6 2 3.146
2 15.4 2 1.403
3 19.6 2 2.122
4 24.7 4 6.124
5 28.1 2 13.63

Sampling Depth Coefficient of consolidation [C.sub.v2]/
Tube No. (m) Scheme B [C.sub.v2] [C.sub.v1]
 No. of (x [10.sup.3]))
 tested ([cm.sup.2]/sec.)
 samples

1 7.6 2 7.543 2.4
2 15.4 2 5.088 1.8
3 19.6 2 16.43 7.7
4 24.7 1 27.09 4.4
5 28.1 - - -