Statistical Correlations between undrained shear ...

Statistical Correlations between undrained shear strength (CU) and both SPT- N value and net limit pressure (PL) for cohesive glacial tills Kanagaratnam Balachandran Exp Services Inc., Brampton, Ontario, Canada Jinyuan Liu Ryerson University, Toronto, Ontario, Canada Laifa Cao & Scott Peaker WSP Consultants Limited, Toronto, Ontario, Canada ABSTRACT: This paper presents a statistical analysis of the correlation between the undrained shear strength (CU) and both standard penetration test blow count (SPT-N) and net limit pressure (PL) value for cohesive glacial tills in the city of Toronto. The Cu values were derived from the field vane shear test (FVST) and PL values were derived from SPT-N. This study is based on the results of a comprehensive geotechnical investigation for the Eglinton Crosstown Light Rail Transit (LRT) project in Toronto. This study focused primarily on the statistical correlations between CU and both SPT-N and PL value for cohesive glacial tills with different textures, such as silty clay till and clayey silt till. In this paper, the correlation equations between SPT – (N) 60 values and CU, PL values and CU are suggested for cohesive glacial tills. Additionally, the range of SPT – (N) 60, CU, PL and the pressuremeter constant (β) factor for cohesive glacial tills is suggested. RÉSUMÉ: Cet article présente une analyse statistique de la corrélation entre la force de cisaillement non découpée/ drainée(CU) et le taux de détection de pénétration standard (SPT-N) et la pression de limite nette (PL) pour les calculs glaciaires cohésifs dans la ville de Toronto. Les valeurs de Cu ont été dérivées du test de cisaillement de la piste de champ (FVST) et les valeurs de PL ont été dérivées de SPT-N. Cette étude est basée sur les résultats d'une enquête géotechnique globale pour le projet Eglinton Crosstown Light Rail Transit (LRT) à Toronto. Cette étude portait principalement sur les corrélations statistiques entre la C U et la SPT-N et la valeur PL pour les labies glaciaires cohésives avec différentes textures, telles que la till d'argile et le till de limon argileux. Dans cet article, les équations de corrélation entre SPT - (N)60 valeurs et CU, PL valeurs et CU sont suggérées pour les cultures glaciaires cohésives. En outre, la gamme de SPT - (N)60, CU, PL et le facteur de constante de pressionmètre (β) pour les calculs glaciaires cohésifs est suggérée. . 1.0 INTRODUCTION Statistical correlations between in-situ soil testing results have become growingly more and more popular during the site investigations especially for being practical and economical. Hence, estimations of geotechnical parameters from in – situ test results hold a significant place in the geotechnical design practice. Keep that in mind, in this study also the statistical correlation between undrained shear strength (CU) from the field vane shear test (FVST) and both standard penetration test blow count (SPTN) and net limit pressure (PL) value for cohesive glacial tills were performed. The SPT is a well-established method for soil investigation. As many forms of the test are in use worldwide, standardization is essential in order to facilitate the comparison of results from different investigations, even at the same site (Thorburm 1986). In this paper, SPT was performed in

accordance with the ASTM D 1586 method. This means that the test was standardized using a 50 mm O.D. split spoon sampler, driven into the soil with a 64 kg weight having a free fall of 760 mm auto hammer was used exclusively on the project. The blows required to drive the split –barrel sample a distance of 305 mm, after an initial penetration of 152 mm, is referred to as the SPT –N value. This method has been accepted internationally and is useful in field investigation. The FVST is a moderately rapid and economical in situ method for determining the undrained shear strength of fully saturated clays without disturbance. The test is relatively simple, quick, and provides a cost-effective way of estimating the soil shear strength. Therefore, it is widely used and much more common in geotechnical investigations. The results of the test are not reliable if clay contains silt or sand. In this paper, FVST is performed in accordance with the ASTM D 2573 (1) method. This means that the test

involves pushing a four blade vane into a clay stratum and slowly rotating it while measuring the resisting torque. The peak torque which develops is related to the undrained shear strength of soil, CU at cylindrical failure surface, which is a function of the shape and dimensions of the vane. This undrained shear strength (CU) was derived for rectangular vane is 6 𝑇𝑀𝑎𝑥 𝐻 equal to for = 2. Where, T MAX is a maximum 3 7 𝐷 𝐷 value of measured torque corrected for apparatus and rod friction, D is vane diameter and H is a height of vane. The equation can be in any units as long as shear strength, torque, and diameter are in consistent units. It is very important that the measured vane strength has to be corrected prior to use in stability analyses involving embankments on soft ground, bearing capacity, and excavations in soft clays (Bjerrum, 1972). The corrected undrained shear strength (CU) is given by CU =  CU, where μ is an empirical vane shear correction factor that has been related to plasticity index (PI). The Bjerrum, (1972) suggested vane shear correction factor () based on plasticity index (PI). In our study, the plasticity index (PI) is less than 20%. Then  is equal to one is adopted in this paper according to Bjerrum, (1972). After the peak torque has been determined, the vane is rotated quickly about to ten times to remold the soils. The torque then is measured again to determine the remolded shear strength. The sensitivity (St) may be calculated as the ratio of the peak to remolded strength. Details are given in the ASTM D 2573 (1). In this study, an attempt was made to develop correlations between SPT- N values with CU, and PL values with CU were performed for cohesive glacial tills based on the extensive site investigation program conducted for the Eglinton Crosstown LRT Project in the city of Toronto. As emphasized by Phoon and Kulhawy (1999), local correlations that are developed within a specific geologic setting generally are preferable to generalize global correlations because they are significantly more accurate.

2.0 LITERATURE REVIEW The literature review was conducted on the statistical correlation between both SPT- N values and CU, PL values and CU in this paper. Information available from specific research studies on the statistical correlation between both SPT- N values and CU, PL values and CU is few, as only a few researchers have studied for clay, even rare for Toronto cohesive glacial tills. Such information, as it was considered very valuable, is presented in this section.

proposed correlation equation such as CU (kPa) = 6.25N. After Terzaghi & Peck, many studies have been done in this area by using unconfined compression (UC) test results. Sowers (1979), (adapted from NAVFAC DM 7.1, 1986) proposed a correlation with considering the plasticity of the clay. He concluded CU (kPa) = 3.63N for low plasticity clay, CU (kPa) = 7.25N for medium plasticity clay and CU (kPa) = 12.0N for high plasticity clay. Sivrikaya & Togrol (2007) evaluated a large data of SPT-N mainly obtained from different sites in Turkey with the results of various laboratory tests such as UC, triaxial test and FVST. Based on these studies, the results are differentiated according to the type of the laboratory tests. According to the results of the study, the relationships between SPT - Nf and CU are expressed such as CU = 4.30Nf from UC tests, 5-10 Nf from triaxial tests. Sivrikaya & Togrol (2007) clearly stated that the coefficients in the equations are highly dependent on the type of the laboratory test. In addition, the scatter of the data was found to be the largest for the UC tests. This result can be mainly related to disturbance and heterogeneity of the sample that influences the behavior. Especially, hard clay can be very sensitive to sampling and testing condition due to their fissured nature and brittle behaviour tendency. Stroud (1974) proposed one of the most popular relationships between SPT- N values and CU. In his study, SPT- N data were collected from many sites in the United Kingdom together with triaxial tests performed in insensitive stiff and hard clays. The relationships between SPT-N values and CU were recommended as CU (kPa) = f1 N60. Stroud (1974) stated that the factor f1 is not a constant value but changes with the plasticity index (PI) of the soil such as CU (kPa) = 4.2 N60 for PI>30, CU (kPa) = 4-5 N60 for 20200

2.1 The literature review on statistical correlation between SPT- N values and CU

2.2 The literature review on SPT- N correction

Approximate ranges of CU and corresponding SPT- N values for cohesive soils proposed by Terzaghi & Peck (1967) are given in Table1. Further they

In the literature, most researchers express their concerns in regards to energy correction which was elaborated as follows. The energy delivered to the rods during a SPT expressed as a ratio of the

theoretical free fall potential energy, can vary from 30% to 90% (Kovacs and Salomone 1982 and Robertson et al. 1983). Schmertmann and Palacios (1979) have shown that the SPT blow count is inversely proportional to the delivered energy. Kovacs et al. (1984), Seed et al. (1984) and Robertson et al. (1983) have recommended that the SPT-N value has to be corrected to an energy level of 60% (CFEM 2006). The SPT N-values corresponding to 60% efficiency is termed as N60. The practice in the United States/Canada the SPT N-value measured to an average energy ratio of 60% (ERR=60%) according to ASTM D1586-11 (2014). In this study energy ratio of 60% (ERR=60%) is adopted. 2.3 The literature review on statistical correlation between PL values and CU In the literature, most researchers expressed that Pressuremeter test (PMT) is a commonly suitable test to estimate the undrained shear strength of cohesive soils. There are different approaches for the estimation of undrained shear strength which can be listed as limit pressure method, yield pressure method and shear curve method etc. Yield pressure method uses the yield pressure result and employs the following equation for the estimation of CU such as CU = py - 𝑜ℎ , where py - yield pressure and 𝑜ℎ - total horizontal stress at rest. However, yield pressure method is not recommended because yield pressure is generally a large value that may lead to overestimated results (Briaud 1992). Shear curve method, on the other hand, uses a graphical solution for the entire shear stress and strain graph is derived from the test. This method is also not recommended for being a graphical solution and leading high undrained shear strength estimations. The limit pressure method is commonly accepted in the practice which uses the theoretical expression such 𝑃 as CU = 𝐿 stated by Cassan (1972) (cited in Clarke 

1995). Factor  is referred as pressuremeter constant. According to many researchers such as Cassan (1972) and Briaud (1992),  value ranges between 5.5 and 7.5 with an average of 6.5. Similarly, Clarke (1995) presented a summary of  factors proposed in the literature which is given in Table 2. The variation of factor  can be related to uncertainties involved in the measurement of 𝑜ℎ , differences in reference strength, an influence of disturbance and anisotropy (Clarke1995). Table 2. Proposed values of the  factors in the literature (Clarke1995) Soil Type All clays Soft to firm clays Firm to stiff clays

 factors 2 -5 5.5 8

Source Menard 1957 Cassan 1972, Amar & Jezequel 1972

Stiff to very stiff clays Stiff clays

15 6.8

All clays

5.1

Stiff clays

10

Marsland & Randolph 1977 Lukas and Le Clerc de Bussy 1976 Martin & Drahos 1986

Other non – linear relationships were recommended by Baguelin et al. (1978) and Bozbey et al. (2010) between CU and PL. The Baguelin et al. (1978) and Bozbey et al. (2010) suggested the  factor varies between 5.5 and 10 and 5.5 and 15 respectively. Currently, there is no such relationship available for cohesive glacial tills in the city of Toronto. This study is performed based on an extensive site investigation conducted for the Eglinton Crosstown LRT project for the Toronto Transit Commission and Metrolinx.

3.0 ENGINEERING BACKGROUND The site is situated along Eglinton Avenue from the existing Kennedy subway station in the east to the Mount Dennis station in the west, in Toronto, Ontario, Canada. The Toronto area acquired at least three glacial and two interglacial periods from the published geological data (Karrow 1967 and Sharpe 1980). The geological history of the Toronto area has included several advances and retreats of glaciers of Illinoian and Wisconsinan ages (Karrow and White 1998). The glacial tills in this area were generally deposited during the early to late Wisconsinan period, represented by the Sunnybrook, Seminary, Meadowcliffe, Newmarket and Halton tills (Sharpe 1999). The glacial till deposits in Toronto can be divided into low plasticity cohesive glacial tills (silty clay to clayey silt glacial till) and cohesionless glacial tills (sandy silt to silty sand glacial till) (Manzari et al. 2014). This kind of soil is derived due to the wearing away and entrainment of material as a result of the moving ice of a glacier. As shown in Figure 1, this type of soil can be described as high variability materials in both horizontal and vertical axis, and it normally contains complex non-linear stress-strain characteristics (Baker et al. 1998). In addition to that, the tills consist of a heterogeneous mixture of gravel, sand, silt and clay size particles in varying proportions. Cobbles and boulders are common in these deposits (Robert et al. 2011). However, the behaviour of glacial tills in southern Ontario is not fully understood.

Figure 1. Typical glacial till (Source-Mark Clark, (http://www.free-stockillustration.com)

The proposed Eglinton Crosstown LRT is approximately 33 km in length and located approximately 7 km north of Lake Ontario. There are 25 proposed stations along the alignment as shown in Figure 2.

The glacial tills are interbedded with silty clay, clayey silt, sandy silt, sand and silt and silty sand. SPTs conducted near the FVSTs at similar depths were selected to develop the relationship between SPT-N values and CU in this paper for the following stations such as Bermondsey, Keel, Victoria Park, West portal. The pairs of readings (SPT-N and CU) for silty clay till and clayey silt till were collected from these tests in this study. Silty clayey till from the above stations contains 1 to 19% gravels, 9 to 41% sand, 36 to 62% silt and 14 to 31% clay size particles based on grain size analysis. The water contents are generally between 6 3 to 31% and unit weight is from 20.6 – 23.7 kg/m . Based on the consistency (Atterberg) limits test the range of LL is 17 to 28%, PL is 7 to 17% and PI is 7 to 14. These values are shown in Table 3. Clayey silt till from the above stations contains 1 to 13% gravels, 22 to 44% sand, 37 to 60% silt and 11 to 22% clay size particles based on grain size analysis. The water contents are generally between 6 to 31% 3 and unit weight is from 21.7 – 23.1 kg/m . Based on the consistency (Atterberg) limits test the range of LL is 15 to 22%, PL is 10 to 16% and PI is 4 to 7. These values are shown in Table 3. Overall cohesive glacial till from the above stations contains 1 to 19% gravels, 9 to 44% sand, 36 to 62% silt and 11 to 31% clay size particles based on grain size analysis. The water contents are generally between 6 to 31% and unit weight is from 20.6 – 23.7 3 kg/m . Based on the consistency (Atterberg) limits test the range of LL is 15 to 28%, PL is 7 to 17% and PI is 4 to 14. These values are shown in Table 3.

Table 3. Properties of cohesive glacial tills

Figure 2. Crosstown route map (http://www.thecrosstown.ca/the-project)

A series of laboratory and in-situ tests were conducted in advance at the stations above. The insitu tests included SPTs, FVSTs, pre-bored TEXAM PMT and seismic tests. The laboratory tests included density and moisture content measurements, grain size and hydrometer analysis, consistency (Atterberg) limit tests, consolidation tests, consolidated undrained and drained triaxial compression tests. Based on these tests, the soil was classified as a glacial till which further classified as low plasticity cohesive glacial till and cohesionless glacial till according to the current version of TTC Geo-technical Standards (2014). In this area, the low plasticity cohesive glacial till mostly consists of the following soil types such as (i) silty clay till (ii) clayey silt till. The cohesionless glacial till mostly consists of following soil types such as (iii) sandy silt till (iv) silty sand till.

Gravel (%) Sand (%) Silt (%) Clay size particles (%) Water contents (%) Unit weight 3 (kg/m ) LL (%) PL (%) PI (%)

Silty clayey till 1 - 19 9 - 41 36 - 62 14 - 31

Clayey silt till 1 - 13 22 - 44 37 - 60 11 - 22

All soil 1 - 19 9 - 44 36 - 62 11 - 31

6 - 31

6 - 31

6 - 31

20.6 – 23.7 17 - 28 7 - 17 7 - 14

21.7 – 23.1 15 - 22 10 - 16 4-7

20.6 – 23.7 15 - 28 7 -17 4 - 14

4.0 CORRELATION BETWEEN SPT-(𝑁) 60, CU AND PL The statistical analysis is carried out in this paper to investigate the relationship between SPT-N value with CU, and PL value with CU. The first step is to collect the pairs of field vane shear strength (CU) and SPT-N value at the same depths in the same boreholes. The

(1) The data situated far from the trend line was discarded by visual inspection compared to other data. (2) In such cases the same SPT-(𝑁) 60 values was associated with different values of CU and this pair of readings was omitted. 4.1 General Range of SPT--(𝑁) cohesive glacial tills

60,

CU and PL for

C Range (kPa)

58%

U

100

95%

65%

50

Silty clay till

Clayey silt till

All soil

Figure 4. Range of CU values for cohesive glacial tills

2000 1500

L

1000

73%

65%

75%

Silty clay till

Clayey silt till

All soil

500 0

Figure 5. Range of PL values for cohesive glacial tills Table 4. Approximate range of SPT--(𝑁) for cohesive glacial tills Soil type Silty clay till Clayey silt till All soil

60,

CU and PL

SPT--(𝑁) 60 2 - 16 5 - 12

CU (kPa) 18 - 197 78 - 93

PL (kPa) 184 - 1840 520 - 1248

2 - 16

18 - 197

184 - 1840

4.2 Correlation between SPT--(𝑁) 60 values and CU The correlation between SPT--(𝑁) 60 values and CU for a cohesive glacial till is shown in Figure 6. The correlation functions and correlation coefficients are given in Table 5.

25 20 15 10

150

0

65%

62%

60%

200

All soil

(kPa)

5

values for cohesive

C

60

SPT- (N) Range

The ranges of SPT- (𝑁) 60, CU and PL values are determined for cohesive glacial tills of the data are collected from in-situ tests. The ranges of (𝑁) 60, CU and PL values of cohesive glacial tills are shown in Figure 3 to 5 and Table 4 respectively. The percentages (%) marked in Figure 3 to 5 represents most of the range values that belong to the thick portion of the range diagrams.

200

P Range (kPa)

field measured SPT-N values are corrected according to the CFEM (2006). Because of the variability in equipment and operating conditions, direct use of SPT-N values for geotechnical design is not recommended. As a result, many corrections shall be done on the field SPT-N values. Those corrections are rod length, borehole diameter, sampler, energy and overburden described in CFEM (2006). The practice in the Canada the SPT N-value measured to an average energy ratio of 60% (ERR=60%) according to ASTM D1586-11 (2014). In this study energy ratio of 60% (ERR=60%) is adopted. In the case of cohesive glacial tills, overburden correction is not accommodated in this study. In these situations, the SPT-N became SPT-(𝑁) 60. Then the net limit pressure (PL) value is predicted according to Balachandran et al. (2016) equation for that particular SPT-(𝑁)60 values. After corrected the SPT-N, the pair of data were collected for both SPT- (N) 60 values and CU, PL values and CU for cohesive glacial tills. In order to analyze more accurately, the compiled data were filtered by using the following methodology:

0 Clayey silt till

100

U

Silty clay till

150

Figure 3. Range of SPT- (N) glacial tills

60

Silty clay till Clayey silt till All soil

50 0 0

5

10 15 SPT - (N)

60

20

25

Figure 6. Correlation between CU vs SPT- (N) 60 for cohesive glacial tills

4.3 Correlation between PL values and CU The correlation between PL values and CU for cohesive glacial till is shown in Figure 7. The correlation functions, correlation coefficients and “” factors are given in Table 5.

CU (kPa) = 8.32(N) 60

2

R = 0.79

[1]

The predicted CU values were calculated by using “Equation 1” and the measured CU and predicted CU values also presented in Figure 8.

2000 1500

y= 1000

200

L

P (kPa)

(1974) and Stroud and Butler’s (1975) were plotted in Figure 8 with the studied data. In this comparison, a linear best fit line was plotted for the studied corrected and filtered data due to the available linear literature model. For the preliminary estimation of the CU for the cohesive glacial tills, the CU can be estimated from the SPT- (N) 60 value using the following relationship:

Silty clay till Clayey silt till All soil 50

100 C (kPa)

150

200

U

Figure 7. Correlation between PL vs CU for cohesive glacial tills

100

Soil type Silty clay till Clayey silt till All soil

2

Correlation equation (R ) CU (kPa) PL (kPa) 8.42 (N) 60 (0.80) 10.52 CU (0.80)

“”

8.22 (N) 60 (0.34)

11.70 CU (0.62)

12

8.32 (N) 60 (0.79)

10.83 CU (0.76)

11

11

5.0 DISCUSSIONS

60

values and CU

The approximate correlation between SPT- (N) 60 and CU proposed by Terzaghi & peck (1967), Stroud

5.9

2

m1 Chisq

5

10 15 20 25 SPT - (N) 60 y = 10.521x Figure 8. Correlation between SPT(N) 60 and CU for y = 11.695x cohesive glacial tills (Linear relationship) y = 10.834x In this comparison, there is good agreement with Stroud (1974) and Stroud and Butler’s (1975). Stroud and Butler’s (1975) expressed CU = 8N for low plasticity clay (PI =15%) and Stroud (1974) expressed CU=6-7(N) 60 for PI