Incorporating the Stress History Parameter KD of DMT into the Liquefaction Correlations in Clean Uncemented Sands

Marchetti, Silvano

doi:10.1061/(ASCE)GT.1943-5606.0001380

Open access

Technical Papers

Aug 12, 2015

Incorporating the Stress History Parameter $K_{D}$ of DMT into the Liquefaction Correlations in Clean Uncemented Sands

Author: Silvano Marchetti [email protected]Author Affiliations

Publication: Journal of Geotechnical and Geoenvironmental Engineering

Volume 142, Issue 2

https://doi.org/10.1061/(ASCE)GT.1943-5606.0001380

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Abstract

This paper analyzes the possibility of reducing the uncertainty of the cyclic resistance ratio (CRR) estimates by incorporating stress history into the liquefaction correlations. A way of obtaining this objective stems from the combination of two well-recognized notions: (1) sensitivity of the flat dilatometer test (DMT) parameter

K_{D}

to stress history, and (2) necessity of stress history information to obtain better estimates of the liquefaction resistance. The main aim of this paper is to develop a framework providing CRR estimates based not on the one-to-one correlations

CRR - Q_{c n}

or

CRR - K_{D}

, but on a correlation based at the same time on both

Q_{c n}

and

K_{D}

. A

Q_{c n} - K_{D} - CRR

correlation has been constructed by combining the current

CRR - Q_{c n}

and

CRR - K_{D}

correlations. It is expectable that an estimate based at the same time on two measured parameters is more accurate than estimates based on just one parameter. 'A chart is presented providing estimates of CRR based at the same time on both

Q_{c n}

and

K_{D}

.

Introduction

It is widely recognized that the cyclic resistance ratio (CRR) estimates by cone penetration test (CPT) are not always of a satisfactory reliability. For example, Robertson and Wride (1998) wrote “CRR by CPT may be adequate for low-risk projects. For high-risk projects estimate CRR by more than one method,” and Idriss and Boulanger (2006) wrote “The allure of relying on a single approach (e.g., CPT-only) should be avoided.” This uncertainty has stimulated a large number of studies, which however do not consider the addition of fresh collateral independent easily measured information on stress history.

This paper analyzes the possibility of reducing said uncertainty using the flat dilatometer (DMT) horizontal stress index

K_{D}

(often alternatively called stress history index).This possibility stems from the combination of two notions that are well recognized today: (1) sensitivity of

K_{D}

to stress history, and (2) necessity of stress history information to obtain better estimates of the liquefaction resistance.

1.

The higher sensitivity to stress history of

K_{D}

, compared with the sensitivity of

Q_{c n}

(normalized cone tip

Q_{c}

resistance), has been observed by numerous researchers, either in the calibration chamber (e.g., Jamiolkowski and Lo Presti 1998) or in the field (e.g., Schmertmann et al. 1986; Jendeby 1992; Marchetti 2010). An expressive example, clearly illustrating the different sensitivity, is shown in Fig. 1 (Lee et al. 2011). CPT and DMT were executed in the calibration chamber on 40 large specimens of Busan silica sand, partly normally consolidated (NC) and partly previously preconsolidated to overconsolidation ratio (OCR) in the range 1–8. Then the

Q_{c n}

and

K_{D}

obtained before and after the preconsolidation were compared. The two diagrams in Fig. 1 confirm that

K_{D}

is considerably more reactive to OCR than

Q_{c n}

. A consequence of Fig. 1 is that the same

Q_{c n}

can correspond to various values of

K_{D}

, as shown in the schematic example in Fig. 2. In the example Site 2 has the same

q_{c}

profile as Site 1, but has a higher

K_{D}

, suggesting higher stress history, and hence higher CRR. This benefit would not be detected by just the two identical profiles of

Q_{c n}

. Another interesting consequence of Fig. 1 is the necessity of both

Q_{c n}

and

K_{D}

to evaluate OCR in sand. If only

K_{D}

is known and is entered in Fig. 1(b), its value could be due to a low relative density

D_{r}

and a high OCR or to a high

D_{r}

and a low OCR. In order to evaluate OCR,

q_{c}

must also be available to provide an indication of

D_{r}

on the horizontal axis.

2.

The necessity of stress history information for assessing liquefaction resistance CRR has long since been recognized (e.g., Youd and Idriss 2001; Salgado et al. 1997; Monaco and Schmertmann 2007; Harada et al. 2008). Even before, Jamiolkowski et al. (1985), based on extensive calibration chamber studies, had warned “Reliable predictions of liquefaction resistance of sand deposits having complex stress-strain history require the development of some new in situ device [other than CPT or SPT] much more sensitive to the effects of past stress-strain histories, because stress history produces a small increase in penetration resistance, but a significant increase in CRR and in stiffness of a cohesionless soil.”

Fig. 1. Sensitivity of CPT and DMT to stress history: (a) CPT; (b) DMT (Reprinted from Engineering Geology, Vol. 117, No. 3-4, Moon-Joo Lee, Sung-Kun Choi, Min-Tae Kim, Woojin Lee, “Effect of stress history on CPT and DMT results in sand”, pp. 259-265, Copyright (2011), with permission from Elsevier)

Fig. 2. Schematic profiles of two sites having the same $q_{c}$ but different $K_{D}$

Construction of a $Q_{c n} - K_{D} - CRR$ Correlation

The main aim of this paper is to develop a framework providing CRR estimates based not on the one-to-one correlations of

CRR - Q_{c n}

or

CRR - K_{D}

, but on a correlation based at the same time on both

Q_{c n}

and

K_{D}

. This

Q_{c n} - K_{D} - CRR

correlation, as shown in this section, has been constructed by combining the current

CRR - Q_{c n}

and

CRR - K_{D}

correlations.

$CRR - Q_{c n}$ Correlation

Today’s standard practice for evaluating the liquefaction resistance CRR is to use the well-known correlations

CRR - Q_{c n}

described in numerous papers (e.g., Youd and Idriss 2001; Robertson and Wride 1998; Idriss and Boulanger 2006). The

CRR - Q_{c n}

correlations, despite various uncertainties, are the result of a large number of documented real earthquake data. The

CRR - Q_{c n}

correlation adopted in this paper, Eq. (1a) ahead in the paper, is the Idriss and Boulanger (2006) correlation (somewhat more conservative than the previous Robertson and Wride correlation).

$CRR - K_{D}$ Correlation

CRR estimates are also made using

CRR - K_{D}

correlations. This section provides some background on these correlations. The first

CRR - K_{D}

correlations go back to Marchetti (1982) and Robertson and Campanella (1986). Since then, numerous updated curves have been produced (e.g., Reyna and Chameau 1991; Monaco et al. 2005; Tsai et al. 2009; Robertson 2012). These research efforts have been stimulated by the fact that the factors increasing

K_{D}

of a sand also increase its liquefaction resistance. For example, Robertson and Campanella (1986) listed the following factors: (1) relative density, (2) in situ

K_{o}

, (3) stress history and prestressing, (4) aging, and (5) cementation. Robertson and Campanella (1986) also pointed out that it is not possible to identify the individual contribution of each factor to

K_{D}

. On the other hand, when

K_{D}

is low, none of these factors is high, that is the sand is loose, uncemented, in a low horizontal stress environment, and has little stress history. A sand under these conditions may be prone to liquefaction. In this paper, the term stress history is meant to globally include any factor making the sand more stable than a freshly deposited sand.

•

Sensitivity of

K_{D}

to OCR: Schmertmann et al. (1986) observed that, upon compaction (which increases OCR), the percentage increase of

M_{DMT}

(the constrained modulus by DMT) was twice the percentage increase of

q_{c}

(the increase of

M_{DMT}

is primarily due to the increase of

K_{D}

). More recently numerous compaction jobs include before-after CPTs and DMTs. The presentation of the comparisons often includes the before-after

M_{DMT} / q_{c}

versus

z

profiles [Figs. 3(a and b)]. The fact that

M_{DMT} / q_{c}

increases with compaction indicates that

M_{DMT}

(and hence

K_{D}

) increases with OCR at a faster rate than

q_{c}

, confirming the Schmertmann et al. (1986) observation, and is in agreement with Fig. 1. The

M_{DMT} / q_{c}

profiles also permit an evaluation of the achieved OCR increase, using, e.g., the Monaco et al. (2014) equation OCR -

M_{DMT} / q_{c}

in Fig. 3(c).

•

Sensitivity of

K_{D}

to pure prestressing:

K_{D}

has been found to be substantially more sensitive than penetration resistance to pure prestressing, consisting in cycles of loading-unloading along the

K_{o}

line, followed by unloading to the initial vertical and horizontal stress, without locked-in horizontal stresses (Jamiolkowski and Lo Presti 1998; Marchetti 1982).

•

Sensitivity of

K_{D}

to aging: Results shown by Monaco and Schmertmann (2007) and in the various references mentioned by them, by Marchetti (2010) and by Kurek and Balachowski (2015), indicate that

K_{D}

is substantially more sensitive to aging than penetration resistance.

The

CRR - K_{D}

correlation adopted in this paper is the Idriss and Boulanger (2006) correlation combined with

Q_{c n} \approx 25 K_{D}

, following a procedure suggested by Robertson (2012). Thus the adopted

CRR - K_{D}

correlation is given by the combination of Eqs. (1a) and (1b)

CRR = \exp [(Q_{c n} / 540) + {(Q_{c n} / 67)}^{2} - {(Q_{c n} / 80)}^{3} + {(Q_{c n} / 114)}^{4} - 3]

(1a)

with Q_{c n} = 25 K_{D}

(1b)

Fig. 3. (a) $M_{DMT} / q_{c}$ before and after compaction (data from Jendeby 1992); (b) $M_{DMT} / q_{c}$ ratio before and after compaction (data from Balachowski and Kurek 2015); (c) correlation OCR versus $M_{DMT} / q_{c}$ (Monaco et al. 2014)

Combining the $CRR - Q_{c n}$ Correlation and the $CRR - K_{D}$ Correlation

A combined correlation for estimating CRR based on

Q_{c n}

and

K_{D}

has been obtained by adopting as CRR the geometric average between a first CRR estimate obtained from

Q_{c n}

[Eq. (1a)] and a second CRR estimate obtained from

K_{D}

[Eqs. (1a) and (1b)], namely

Average CRR = {[(CRR from Q_{c n}) \times (CRR from K_{D})]}^{0.5}

(2)

Eq. (2) has been plotted in Fig. 4 as a function of

Q_{c n}

.

Fig. 4. Chart for estimating CRR in clean sand based on $Q_{c n}$ and $K_{D}$

$K_{D} - Q_{c n} \approx 25$ Relation

Eq. (1b), suggested by Robertson (2012), used in the previous sections, is highly approximate. It was obtained by Robertson by interpolating a straight line through the Tsai et al. (2009) data points [Fig. 5(a)]. Figs. 5(b–d) have been added in Fig. 5 as additional examples of the

Q_{c n} - K_{D}

correlation in clean sand. All data are for a DMT material index

Id > 3

, i.e., for clean sand. The three added figures essentially confirm both the average value 25, and the considerable dispersion. The high observed dispersion in the

K_{D} - Q_{c n}

relation is, to a large extent, the consequence of the higher reactivity of

K_{D}

to stress history (Fig. 1). If the scatter were small, it would mean that

Q_{c n}

and

K_{D}

contain equivalent information, which is negated by Fig. 1. The high scatter indicates that

K_{D}

contributes fresh collateral independent information to the characterization of the sand.

Fig. 5. $K_{D} - Q_{c n}$ relations: (a) from five Taiwan sand sites [reprinted from Engineering Geology, Vol. 103, No. 1-2, Pai-Hsiang Tsai, Der-Her Lee,Gordon Tung-Chin Kung, C. Hsein Juang, “Simplified DMT-based methods for evaluating liquefaction resistance of soils”, pp. 13-22, Copyright (2009), with permission from Elsevier]; (b) from Treporti research site; (c) from calibration chamber results (data from Baldi et al. 1986); (d) derived from Fig. 1

Comments on the $Q_{c n} - K_{D} - CRR$ Chart in Fig. 4

•

A plot similar to Fig. 4 was proposed by Harada et al. (2008), who suggested using

K_{o}

as a parameter in the curves. It is observed that

K_{o}

in sand can be estimated, e.g., by the correlations developed by Baldi et al. (1986) expressing

K_{o}

as a function of

K_{D}

and

Q_{c n}

, but these estimates are often uncertain and subjective, while

K_{D}

is accurately, easily, and unequivocally determined. Moreover,

K_{D}

is a cumulative parameter reflecting, besides

K_{o}

, other stress history factors increasing CRR.

•

The essence of Fig. 4 is to estimate CRR from

Q_{c n}

by the everyday CPT correlations. Then if

K_{D}

is higher than average (

K_{D} > Q_{c n} / 25

), increase CRR; if

K_{D}

is lower than average, reduce CRR. Described in this way Fig. 4 appears to be common sense, supporting the expectation that the real earthquake data points will plot not far from the curves.

•

The

K_{D}

= constant lines have a limited length because, for any given

K_{D}

, only a limited range of

Q_{c n}

exists, as can be seen in Fig. 5.

•

The CRR provided graphically by Fig. 4 can alternatively be calculated using Eq. (2), where CRR from

Q_{c n}

is Eq. (1a) and CRR from

K_{D}

is the combination Eqs. (1a) and (1b).

•

Fig. 4 requires considerable real earthquake verification. It is to be regarded as an initial framework for initiating the accumulation of colocated

Q_{c n} - K_{D} - CRR

data points.

Concluding Remarks

•

Numerous studies have shown that

K_{D}

is an effective indicator of stress history and that information on stress history is necessary to obtain reasonable estimates of CRR. This paper analyzes the possibility of reducing the uncertainty in estimating CRR by incorporating the DMT stress history index

K_{D}

into the liquefaction correlations.

•

By combining the commonly used

CRR - Q_{c n}

and

CRR - K_{D}

correlations to estimate CRR, a plot has been constructed (Fig. 4) providing estimates of CRR based at the same time on both

Q_{c n}

and

K_{D}

. It is expectable that an estimate based at the same time on two measured parameters is more accurate than estimates based on just one parameter.

•

The essence of Fig. 4 is estimating CRR from

Q_{c n}

by the everyday CPT correlations. Then, if

K_{D}

is higher than average (

K_{D} > Q_{c n} / 25

), increase CRR; if

K_{D}

is lower than average, reduce CRR. Described in this way Fig. 4 appears to be common sense, supporting the expectation that the real earthquake data points will plot not far from the curves.

•

Fig. 4 was constructed with clean uncemented sand in mind. If the sand contains fines or is cemented, estimating CRR is much more complex. For example, the cementation can be ductile (toothpastelike) or fragile (glasslike), a quality that affects either

Q_{c n}

or

K_{D}

and the sand liquefaction behavior. Fine content may possibly have effects similar to a ductile cementation. Clearly the unknowns are too many and it may be not sufficient to add the

K_{D}

information to

Q_{c n}

. The knowledge of

G_{o}

(small-strain shear modulus) could possibly help, because high

G_{o} / q_{c}

and/or high

G_{o} / M_{DMT}

(Schnaid et al. 2004; Cruz et al. 2012) are also indicators of cementation. Even the dilatometer modulus

E_{D}

from DMT could possibly help. Considerable additional study is clearly necessary if the sand is not a clean uncemented sand.

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Journal of Geotechnical and Geoenvironmental Engineering

Volume 142 • Issue 2 • February 2016

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This work is made available under the terms of the Creative Commons Attribution 4.0 International license, http://creativecommons.org/licenses/by/4.0/.

History

Received: Nov 6, 2014

Accepted: Jun 4, 2015

Published online: Aug 12, 2015

Discussion open until: Jan 12, 2016

Published in print: Feb 1, 2016

Authors

Affiliations

Silvano Marchetti [email protected]

Professor, Dept. of Civil, Architectural and Environmental Engineering, Univ. of L’Aquila, 67100 L’Aquila, Italy. E-mail: [email protected]

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Incorporating the Stress History Parameter $K_{D}$ of DMT into the Liquefaction Correlations in Clean Uncemented Sands

Abstract

Introduction

Construction of a $Q_{c n} - K_{D} - CRR$ Correlation

$CRR - Q_{c n}$ Correlation

$CRR - K_{D}$ Correlation

Combining the $CRR - Q_{c n}$ Correlation and the $CRR - K_{D}$ Correlation

$K_{D} - Q_{c n} \approx 25$ Relation

Comments on the $Q_{c n} - K_{D} - CRR$ Chart in Fig. 4

Concluding Remarks

References

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Abstract

Introduction

Construction of a Qcn-KD-CRR Correlation

CRR-Qcn Correlation

CRR-KD Correlation

Combining the CRR-Qcn Correlation and the CRR-KD Correlation

KD-Qcn≈25 Relation

Comments on the Qcn-KD-CRR Chart in Fig. 4

Concluding Remarks

References

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Construction of a $Q_{c n} - K_{D} - CRR$ Correlation

$CRR - Q_{c n}$ Correlation

$CRR - K_{D}$ Correlation

Combining the $CRR - Q_{c n}$ Correlation and the $CRR - K_{D}$ Correlation

$K_{D} - Q_{c n} \approx 25$ Relation

Comments on the $Q_{c n} - K_{D} - CRR$ Chart in Fig. 4