An Investigation of Beirut Soil PropertiesElsy Ibrahim, Dalia Youssef Abdel Massih, and Jacque Harb

Department of Civil and Environmental EngineeringNotre Dame University, Louaize

Zouk Mosbeh, LebanonCorresponding Author Email: eibrahim@ndu.edu.lb

Abstract—The aim of this study is to set a foundation formapping Beirut soils using available soil reports obtained fromexcavations. With the availability of a certain number of exca-vations and soil reports, one could attempt to gather soil datain order to understand the subbase and map the stratigraphy ofthe city. However, only a limited number of boreholes and soildata are available. Consequently, the use of innovative methodsto analyze and assess limited numbers of heterogeneous data isnecessary for developing countries where data is generally scarce.The paper investigates the available soil report data, specificallysoil cohesion (c), soil friction angle (φ), and soil type classification.The results show that soil cohesion and the soil friction angle ofBeirut have a high negative correlation r2 = −0.71. Then, amixture of Gaussians (MG) clustering approach is utilized tofind meaningful patterns in the data, and thus resulting in threecategories according to which the soil is to be mapped in futurework. The categories are related to ranges in values of c and φand their corresponding soil types.

Keywords—soil; cohesion; friction; unsupervised; classification

I. INTRODUCTION

The Geology of Beirut is not well understood since verylittle investigation has been performed. The main applicationbeing reduced to surface stratigraphic interest for the purposeof shallow and deep foundations, it did not trigger any in-depth exploration. Nevertheless, this information is of a majorinterest in the understanding the response of structures to theunderlying base, especially when dynamic excitations occur.

Historically, very few geologic explorations of Beirut werecarried out. The only remaining source still in function is theDubertret [1] geologic map on surface geology. Few theses andstudies have been carried since then in major universities. Thework of Sanlaville in 1977 [2] is also a good reliable source.Since then, the reconstruction process of Beirut in the 1990after 15 years of a destructive war induced many changes inthe surface geology with the removal of dumping areas, fillingworks, land reclamation, implementation of major off shorestructures and marinas etc. The close proximity of structure totheir increasing heights induced the deeper excavations withshoring works.

Recent days have witnessed the proliferation of excavationin front of the real estate boom. A team of Civil engineersaffiliated to Notre Dame University (NDU) captured this op-portunity to gather data from existing excavations. The centralfocus of the data is on some sporadic laboratory testing andboreholes. This effort was not left without major barriers ofextracting information from geotechnical companies. In some

cases, students had to collect surface soil samples and analyzethem in the laboratories. Other types of difficulties resided inthe quality of the collected data that required serious filtration.

With the availability of a certain number of excavations andsoil reports, one could attempt to gather soil data in orderto understand the subbase and map the stratigraphy of thecity. However, only a limited number of boreholes and soildata are actually available for Beirut. Consequently, usinginnovative methods to analyze and assess limited numbersof heterogeneous data is necessary for developing countrieswhere data is generally scarce. It allows the possibility toobtain a powerful database with a limited amount of resources.Moreover, these innovative methods lead to the sustainabilityof such database and the prediction of important informationbased on data models.

Due to the huge boom of real estate in the city, variousexcavations for contraction have been carried out for the lastfew years. Typical soil reports of an excavation contain geo-logical descriptions of soil layers, grain size distribution andclassification based on the Unified Soil Classification System(USCS), the Rock Quality Design (RQD) for rock layers, theLiquid limit (LL), Plastic Limit (PL), soil cohesion (c), thesoil friction angle (φ), and the in-situ Standard PenetrationTest number (NSPT ) at several locations and depths. Thesereports, although are highly diverse in content and format, canbe a great source of information regarding the soil propertiesof Beirut city. Yet, due to the lack of consistency and tothe randomness of locations of the obtained reports, clearmethodology with advanced techniques is required to benefitfrom this available information.

The aim of this paper is to use data mining techniques toinvestigate and integrate limited amounts of soil data fromdistinct soil reports obtained from various excavations. Thestudy aims to be a preliminary insight into mapping Beirut’ssoil and stratigraphy using this challenging approach.

II. THE STUDY AREA AND ITS GEOLOGY

The study area is Beirut City, Lebanon. It is the capitaland largest city in Lebanon with a population of about onemillion. The Peninsula of Beirut constitutes an accidentalfeature of the Lebanese coast line in the East-West orientation,advancing around 10km offshore. The oriental part drops inlevel, in between Nahr Beirut and the mountain at the BourjHammoud suburb. West of the river, on a 6 km length stretchand 2 km wide, the city of Beirut has accidental topography,

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characterized by two hills: the 102 m high eastern Ashrafiehhill and 95 m hight Tallet el-Khayyat western hill. Both hillsare separated by a 59 m high plateau following DamascusRoad. The axis of Corniche el Mazraa, Avenue Fouad Ist andCornice el Nahr drop in altitude with areas of sandy soil.

The Ashrafieh hill and the oriental part of the Beirutpeninsula west of Nahr Beirut are made of Helvetic Marls,subhorizontal north but dipping south along the shore of theriver, beneath Neogene conglomerates. The Tallet el-Khayyathill is carved into the Cenomanien limestone, slightly flexuredin a caving shape to the west, where the island of La Grotteaux Pigeons is made of Marly limestones with bedding ofSilex disappearing north, south, and east under compactedlimestones.

Beirut hills are cut by regular ledges separated by abruptcut in slopes similar to a stair-like shape, located at 10-20m, 40-60 m, and above 70m altitudes. These three levelsbecame confused with the proliferation of structures, bridgesand interchanges and the general topographic modification ofthe modern city.

The connection between Neogene and the Cenomanien isthrough a SSW-NNE fault extending from the Port area towardBasta El-Tahta, passing by Riad El-Solh. A Meridian faultextends between Ashrafieh hill and the mountainous front,following the Nahr Beirut section downstream [1]. At thesouth of Beirut area, the substratum disappears suddenly andboreholes show thick quaternary terrains of Ramleh sand andgravel. Red sand and Ramleh, sometimes very thick, cover thesouthern side of the occidental hill of Ashrafieh and climbsup to 75m.

III. AVAILABLE DATA

Out of the numerous excavations in the city, around 60soil reports are collected from different locations and aredistributed as shown in Figure 1. These reports comprisethe results of different geotechnical tests performed in var-ious periods of time and locations. After examining thesereports concerning the number of available parameters andtheir importance in terms of soil capacity for the use bya geotechnical and/or structural engineer, it is seen that alimited number of parameters should be considered for thispreliminary investigation. These parameters are shear strengthparameters i.e. the cohesion (c) and the angle of internalfriction (φ), the Standard Penetration number (NSPT ), and thesoil classification based on USCS. Figure 2 shows an exampleof collected excavations distribution over Achrafieh area.

Each excavation contains one or more borehole. At eachborehole, samples and measurements are collected at var-ious depths, and thus obtaining numerous data points perexcavation. Unfortunately, measured parameters vary over thevarious number of soil reports. Thus, only a selected numberof data points are chosen that included at least two of theconsidered variables namely c, φ, NSPT , and the USCS soiltypes. Depending the utilized parameters for an analysis, thenumber of useful data varies according to the availability ofthese variables.

0  2  4  6  8  

10  12  14  

Ain  El  M

reyseh

 Ashrafieh

 Ba

shou

ra  

Bir  H

asan  

Chiah  

Hamra  

Haret  H

reik  

Hazm

ieh  

Mar  Elias    

Mazraa  

Mdawar  

Minet  El  H

osn  

Mou

saytbe

h  Rm

eil  

Sayfe  

Sin  el  Fil  

Sode

co    

Verdun

 Zkak  El  Blat  

Num

ber  o

f  collected

 soil  repo

rts  

District  

Fig. 1. The number of soil reports gathered from various districts of Beirut

0 250125 Meters

³Fig. 2. The distribution of excavations in Achrafieh (marked in black dots)for which soil reports are obtained

The collected solid data of Beirut is comprised of 93 pointsof which 78, 91, and 92 contain c, φ, and NSPT respectively.The USCS classification is available for 143 data points thatalso contain at least one the three variables of interest. Thedistribution of these points is shown in Table II. Table I givesthe USCS definition of terms used in Table II

IV. METHODOLOGY

A. Background information on the considered parameters

1) Soil Shear strength parameters: A theory for failure insoils is proposed by Mohr in 1900 [3]. It stated that a criticalcombination of normal stress and shearing stress exists forwhich a soil material will fail. The relation between shear (τ )and normal stress (σ) on a failure plain is expressed by:

τf = c+ σtanφ (1)

Where c is the soil cohesion, φ is the angle of internalfriction of the soil and τf is the failure shear stress for agiven normal stress (σ).

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TABLE IDEFINITION OF USCS TERMS

USCS Soil descriptionGW Well graded gravel, sandy gravel, with little or no finesGP Poorly graded gravel, sandy gravel, with little or no finesGM Silty gravels, silty sandy gravelsGC Clayey gravels, clayey sandy gravelsSW Well graded sands, gravelly sands, with little or no finesSP Poorly graded sands, gravelly sands, with little or no finesSM Silty sandsSC Clayey sandsML Inorganic silts, silty or clayey fine sands, with slight plasticityCL Inorganic clays, silty clays, sandy clays of low plasticityOL Organic silts and organic silty clays of low plasticityMH Inorganic silts of high plasticityCH Inorganic clays of high plasticityOH Organic clays of high plasticityPT Peat and other highly organic soils

TABLE IITHE DISTRIBUTION OF THE SOIL DATA ACCORDING TO USCS

CLASSIFICATION

Type No. of data points Type No. of data pointsSC 21 GC 6

SP-SM 20 ML 3CL 18 GM 3SP 17 CL-SC 3SM 16 CL-ML 1CH 15 SW-SM 1

ML-CH 9 GM-SC 1SM-SC 7 GW 1

A dataset of c and (φ) values is compiled from the varioussoil reports. The correlations between these different variablesare investigated. This is essential to assess dependence be-tween these aspects and understand the various obtained resultsin the study.

The cohesion comes from cementation between particles.This component of shear strength is independent of normalstress on shear plane. However, the internal friction angle ofthe soil depends on the normal stress. Some typical values of cand φ are presented in the Table III depending on the soil typeand USCS soil classification and for non-compacted soil [4],[5] and compacted soil [6]. Table I gives the USCS definitionof terms in Table III

2) Correlation between soil shear strength parameters:The coefficient of correlation between two soil parametersrepresents the degree of dependence between them. Variousreferences indicated correlations between soil shear strengthparameters c and φ. The correlation coefficient r(c, φ) rangesfrom: -0.7 to -0.37 [7] and -0.49 and -0.24 [8]. In otherreferences, it appears to be -0.47 [9] and -0.61 [10].

B. Unsupervised classification

1) Mixture of Gaussians approach: Classification is a basicdata mining tool to investigate hidden entities and a dataset.Unsupervised classification groups the data into meaningfulclusters while maximizing inter-class variability and mini-mizing intra-class variability. Yet, this is carried out withoutreference to any pre-set thresholds or limits - contrary tosupervised classification. The basic aim of a classification is

TABLE IIITYPICAL VALUES OF C AND φ FROM LITERATURE DEPENDING ON THE

SOIL TYPE AND USCS SOIL CLASSIFICATION FOR NON-COMPACTED SOIL[4], [5] AND COMPACTED SOIL [6]

USCS φ (o) c (kPa)GW 40±5 [4]; 30-35 [5]; >38 [6] 0 [4], [6]GP 38 ± 6 [4]; >37 [6] 0 [4], [6]GM 36 ± 4 [4]; >34 [6] 0 [4], [6]GC 34 ± 4 [4]; >31 [6] 0 [4], [6]SW 38 ± 5 [4]; 38 [6] 0 [4], [6]SP 36 ± 6 [4]; 30-35 [5]; 37 [6] 0 [4], [5], [6]SM 34 ± 3 [4]; 34 [6] 0[4], 50 [6]SC 32 ± 4 [4]; 31 [6] 0 [4]; 74 [6]ML 33 ± 4 [4]; 32 [6] 0 [4]; 67 [6]CL 27 ± 4 [4], 28 [6] 20 ± 10 [4], 86.18 [6]OL 25 ± 4 [4] 10 ± 5 [4]MH 24± 6 [4]; 25 [6] 5 ± 5 [4]; 71.82 [6]CH 22 ± 4 [4]; 19 [6] 25 ±10 [4]; 103 [6]OH 22 ± 4 [4] 10 ±5 [4]PT 0-10 [5] 0-10 [4]

for an unclassified vector xk, belonging to a data set X, to beaffiliated to one of several specified groups. The first step isto find the probability of this vector to belong to each group.These probabilities are conditional and are referred to as aposteriori probabilities [11]. Depending on the classificationapproach, a classifier computes either the maximum of theseprobabilities or the maximum of a defined function of them.An unclassified feature vector is then assigned to belong tothe group corresponding to this maximum.

When used for the soil data, the resulting clusters representthe main distinguishable types of soil with respect to theconsidered variables. Such classification has been used forsoil data [12], [13], [14]. For example, k-means and fuzzyc-means clustering have been utilized to classify fine grainedsoils in terms of shear strength and plasticity index parameters[13]. Although these two methods are high powerful clusteringtechniques, the mixture modeling approach has been shownto be even more powerful due to its high flexibility inrepresenting each cluster[15]. Consequently, the Mixture ofGuassians (MG) approach is used in this paper where modelssuitable for describing each cluster are used. Such an approachoptimizes the fit between a cluster of data and a specifiedmodel, whereby clusters are considered as various Gaussiandistributions centered according to their covariance structure[16], [17], [18], [19]. Therefore, soil data xk, of n dimensions,belonging to X, are assumed to arise from a probability distri-bution of the density [20] indicated below. To find the mixturecomponents, the expectation-maximization algorithm (EM) isutilized [21], where it assigns the a posteriori probabilitiesto each component density of the mixed Gaussian modelwith respect to the various variables. Clusters are assignedby selecting the component that maximizes the a posterioriprobabilities.

f(xk; θ) =I∑i=1

Piϕ(xk; νi, covi) (2)

Pi are the mixing proportions where Pi ≥ 0, and∑Ii=1 Pi = 1. Each proportion denotes the prior probability

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that a data point is generated by a mixture component i. νiand covi denote the mean and the covariance matrix of thedistribution. The vector parameters to be estimated are denotedby θ, i.e. θ = (Pi, ..., PI , νi, ..., νI , covi, ..., covI).ϕ(xk; νi, covi) is of an n-dimensional density Gaussian

distribution representing density component i:

ϕ(xk; νi, covi) =1√

(2π)n | covi |exp(m)

(3)

where

m = −1

2(xk − νTi cov−1

i )(xk − νi) (4)

This Gaussian density model leads to (hyper)ellipsoidalclusters, whose geometric characteristics are based on theeigenvalue decomposition of the covariance matrix. Dependingon the parameterization of the covariance matrix, modelsallow the fixing of cluster properties (i.e. the shape, size,and orientation) in various combinations, resulting in differentmodel types [22], [20]. Bayesian Information Criterion (BIC)is used to choose the most descriptive of those models. It isa commonly used criterion to compare models with differentparameterization and/or components since it effectively de-scribes the data without the use of too many parameters [23].Therefore, the model with the smallest BIC value was chosenas the most suitable using a threshold of 10−4 for the relativechange of the likelihood criterion.

MG approach in this paper is performed using the MixtureModeling software (MIXMOD) by [20]. The algorithm isinitiated with the selection of random seed values. Due to theheuristic nature of the approach, the classification is carriedout 10 times, and the most suitable initiation is chosen basedon the lowest BIC values.

2) Number of clusters: The number of clusters to whichthe data needs to be grouped into can vary between 1 andthe smallest integer larger than N0.3, where N is the numberdata points [24], [20], [25]. This is a rule of thumb thattries to ensure that the number of required parameters of themixture models do not exceed the number of available data.The normalized entropy criterion (NEC) [20] can be used forMG to choose the most suitable number of clusters in a data,whereby it measures the separation of the resulting clusterswith respect to different number of clusters. The minimumvalues of NEC would indicate an appropriate clustering [26].

3) Unsupervised classification assessment: The dataset isdivided into two parts where two-third is clustered and re-vealed patterns in the dataset. The distribution of each datapoint is assessed per variable. Based on these distributions,significant thresholds could be chosen per property, represent-ing the distinction of each cluster. Consequently, the remainingone third is utilized to assess the accuracy of the these patterns,in the sense that, how applicable they are to randomly selecteddata which is not utilized to set up these patterns.

Fig. 3. Description of considered parameters and their pair-wise correlations

V. RESULTS

A. Classification and categorization

The collected solid data of Beirut have the following prop-erties, as shown in Figure 3. These points show a considerablenegative Pearson’s correlation of r2 = −0.71 between c andφ. This is consistent with the correlations found in literatureand described earlier in the paper. On the other hand, no realdirect correlation is revealed between NSPT and c nor NSPTand φ. Due to that reason, only c and φ are considered furtherin the investigation presented in this paper.

A 2-D matrix of c and φ is classified in an unsupervisedmanner using the MG clustering approach. Then, the USCSclassification is used to assess the existence of certain patternsin data, aiming at attaining a number of important and districtcategories that can represent most aspects of the data. Asindicated in the methodology, two third of the data is randomlyselected. The NEC criterion revealed that the data could besplit into five statistically meaningful clusters. Therefore, thedata is clustered as such (Figure 4 ), and the distribution ofvalues of c and φ is shown in Figure 5 and Figure 6.

These five clusters are assessed with respect to the soilclassification data and the following distinctive patterns areobtained: a) Referring to Figure 5 and Figure 6 a distinctionbetween three patterns is found in ”c”, namely between 0 and20 kPa, 20 and 30 kPa, and higher than 30 kPa; b) Clearcut-off of values for φ is revealed to be around 23o, and thus,leading to two patterns; c)The dominant soil types of thesepatterns lead to three distinct categories shown in Table IV.

The categories clearly retrieved two essential properties,namely the high negative correlation between c and φ andthe essential role of the presence of sand and clay in the soil.An assessment of these categories is carried out using theremaining one third of the data. As indicated in the categoriesand as expected, the SC soil types cannot be classified usingonly the considered variables. Therefore, the soil types ofSC are excluded from the accuracy assessment. The achievedaccuracy is 83% of ”correct” categorization of the data.

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Fig. 4. The five clusters obtained from ”c” and ”φ”

Fig. 5. The distribution of values of ”c” within the clusters (mean andstandard deviation)

Fig. 6. The distribution of values of ”φ” within the clusters (mean andstandard deviation)

TABLE IVTHE THREE SOIL CATEGORIES REVEALED BY MG AND USCS

CLASSIFICATION

category c (kPa) φ (o) soil typeI 0 < c < 20 >= 23 SP, SM, SP-SM, and traces of SCII 20 <= c < 30 >= 23 ML-CH, SC-SM, and traces of SPIII c >= 30 < 23 CL, CH, and traces of SC

B. Practical applicationAs the categorization in Table IV is obtained, one is

able to reference the data points with missing information.

Fig. 7. Ashrafieh district with examples of classified parcels based on thethree categories

Therefore, although a few soil reports indicate c, φ, and the soilclassification simultaneously, the category of a data point canbe obtained by knowing one or two of the considered variables.Yet, data points with SC as their soil type are referred to asunidentified since their mixture of sand and clay does not allowtheir categorization in the three considered groups.

In order to carry out these categorizations of the soil data,the work is required to be on the parcel level of the cadastralmap. As mentioned earlier, each soil report refers to a parcelnumber with one or more boreholes. Furthermore, at eachborehole, soil information is obtained at various depths. Asan illustration, the soil information at the surface (up to 3m)is considered and only parcels with homogenous measure fromvarious boreholes are retained. An example of the applicationis shown in the figures below. Figure 7 shows an example ofa few parcels in Ashrafieh district of Beirut that can now beclassified into the set categories. Using the soil reports, thesurface soil layer of a total of 45 parcels were categorized, ofwhich 15 parcels contained c, φ, and USCS classification, and35 parcels contained at least one of the variables.

VI. CONCLUSION AND FUTURE WORK

Due to the lack of soil data for Beirut, it is essential to obtaina Beirut soil map. With the low amount of resources to carryout a city-wide study, soil reports are collected from variousexcavations with the aim to map Beirut soil types and otheraspects of importance in soil stability. This paper is a first stepin building the soil map where the attained soil categories arethe basis of this map. These categories are based on c, φ, andUSCS classification. Using these categories, the top soil layer

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of 45 parcels of Beirut are classified, of which 15 containedc, φ, and USCS classification, and 30 contained at least oneof the variables.

Although the categorization is obtained with high accuracy,it is essential to the note the low number of data points usedfor this analysis. Therefore, prior to proceeding with the useof the retrieved categories, additional soil reports that covervarious parts of the city are required. Then, the categoriesand their accuracy assessment can be fine-tuned accordingly.These categories are then to be used as a foundation to assessunclassified parcels. Spatial statistics will be used to estimateunknown lots using the categorized ones while consideringvarious soil layer individually. Finally, a soil map of Beirutwould be obtained which covers Beirut spatially and maps itsstratigraphy.

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