Introduction

Rapidly growing cities with high anthropogenic pressure commonly face extensive infrastructural development in their land use planning while minimizing environmental impact and providing long-term sustainability. The subsurface soil conditions have become essential to support safe design of buildings, railway lines, pipelines, tunnels, bridges, dams, and roads. Geotechnical properties of soils influence the stability and economical design of structures and deemed necessary in the design of foundation, road pavement, retaining structures, and utilities to be safe, serviceable, sustainable, and economic for future construction projects.

City-scale 3D models are of great importance in all stages of a construction and help improve the planning and storing of the soil information data in databases for future use. This requires in-depth knowledge based on a comprehensive database of the soils upon which cities were built (Kolat et al. 2006, 2012; Donghee et al. 2012; Price, et al. 2018; He, et al. 2020) to assess soil suitability to meet planned uses and manage the proper design and construction, and also to avoid future risks at an early stage of design. This can also help prevent adverse environmental impact or structural failure and prevention of post construction problems.

Sound reliable geotechnical data is indispensible to achieve accurate site investigation formed commonly of a combination of in situ testing, site description, ancillary data, and soil and rock sampling for further laboratory tests. Soil data measurements are usually spaced to minimize cost of borehole drilling where appropriate interpolation techniques are applied to fill the area between the widely spaced data points. These can help anticipate unforeseen soil characteristics not only for design and economy but also for construction techniques. Unraveling the accurate soil spatial geotechnical variability is imperative in optimum cost, time, and safety and efficient setting of hazard mitigation measures that can play a decisive role to help efficient land suitability prioritization and land use management for future urban expansion projects (e.g., Das 2005; CGS 2006; Hack et al. 2006; De Rienzo, et al. 2008; Kolat, et al. 2012; Masoud 2015; Masoud, et al. 2016). This urges the use of a multidisciplinary and 3D modeling approach that can integrate the multivariate statistical and the geostatistical techniques.

The 3D modeling approach is commonly influenced by the spatial variability of soils that naturally results from many disparate sources dependent on nexus of factors related to the geological and hydrogeological conditions, prevailing seasonal temperature changes, wind, rainfall, and human practices (Chang et al. 2005; Phien-wej et al. 2006; Chrétien et al. 2007) which may lead to severe geotechnical problems in the 3D space. In the desert regions, wadi deposits are underlain by beds of hard rocks at various depths. This type of soil presents many problems during construction due to its high permeability and particularly arises where sound rock bed underlies the soil. Collapse of soil structure often takes place under prolonged exposure to moisture.

The 3D models are widely rendered in two forms: layers on the top and base boundaries in the form of borehole and as stochastic probabilistic models of regular shapes of volume elements (voxels) representing the interpolated properties (e.g., grain size, density, shear strength parameters, etc.) at and in-between the sampling points in the 3D space. Stochastic models are quantitative and objective, based on statistical probability of occurrence of a given layer or a specified physical property. Such deterministic models have been proven to be widely applicable to modeling of many single-solution environmental and geotechnical problems (Aldiss et al. 2012) of the shallow subsurface (< 100 m below ground level) formed mostly of the engineering soils or weak rocks where complexity related to geologic discontinuity structures is low.

The provision of geotechnical database in 3D is a central requirement of mainstreaming into a city’s master plan to optimize the soil use which is lacking in the literature and uncommon in desert regions. Therefore, in this research, the 3D modeling was appraised to improve the geotechnical investigations and the distribution of the measured soil properties and to tackle the inherent complex nature in the un-sampled areas. The prime objective is to locate and map the geotechnically at-risk areas to mitigate hazards by focusing future sustainable development plans to inform pre-development design and construction and to take suitable ameliorative and preventive measures. This will greatly intensify fairly accurate and economical geotechnical design since the cost of data collection, analysis, and mapping will be reduced using less dense boreholes.

Data and methods

Geotechnical data from ninety-two boreholes unevenly spatially distributed in the city with 189 soil samples were analyzed. Borehole index data recording names, geographic coordinates, elevation, soil layer types, and boundaries along with the depth of sampling data points and recorded corresponding properties are recorded in excel sheet. Models are built for the soil type variation, density classes of cohesive and cohessionless soils, rock quality designation (RQD), unconfined compression strength, shear stress parameters (Ø and c), Atterberg limits of plasticity, grain size analysis, and soil water chemistry. Spatial distribution of the geotechnical properties is rendered in Voxler 3 software. For the sake of visual clarity, the depth dimension is exaggerated 100 times in representing borehole log and 200 times for point data. Borehole coordinates were recorded and represented using the Universal Transverse Mercator (UTM) zone 37.

Standards of the American Society for Testing and Materials (ASTM) were applied for Sieve Analysis of Fine and Coarse Aggregates (C 136–96a); Liquid Limit, Plastic Limit, and Plasticity Index (ASTM D 4318–98); Maximum Index Density and Unit Weight Using a Vibratory Table (D 4253–00); Moisture Density Relationship ( D 1557 Method “C”); Specific Gravity and Water Absorption of Aggregate (C 127–88); Direct Shear Test for Soils Under Consolidated Drained Conditions (D 3080–98); and unconfined compression strength (ASTM D 2166).

Relative soil density is indicated by the Standard Penetration Test (SPT)-N value, the number of blows required to affect the last 300-mm penetration below the seating drive. In this test, a split spoon sampler (50 mm diameter) was driven 450 mm into the soil with a hammer (63.5 kg) falling freely a distance of 760 mm. The sampler was driven in two stages: the initial 150-mm penetration of the sampler (seating drive) and the last 300-mm penetration (test drive).

The 3D models are rendered as soil layer boundaries and their corresponding relative density and the underlying RQD parameters of rocks, as well as stochastic probabilistic models of voxels for the interpolated properties in the 3D space. Stochastic models are rendered as points, iso-surfaces of equal values from two opposite viewing directions, and as volumetric solid models.

Study area

The holy city of Medina was chosen, guided by the city’s master plan. This plan identifies environmental and sustainability goals as part of a series of planning measures to achieve the safe and efficient use of land. The prime objective is to provide the 3D spatial assessment of the soil geotechnical variability that contribute to the successful implementation of the future safe urban expansion plan that comprise mixed retail, residential, education, commercial, open space, and subsurface basement construction for car parking. The city is nearly flat elevated at 600–610 m surrounded by low to medium altitude hills/mountains (900–1100 m) and lava plateaus (620–750 m) with a gentle northwest slope. The most famous among these mountains are Uhud in the north and Ayr in the southwest (Fig. 1).

Fig. 1
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Location map and borehole distribution (Google Earth 2019)

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The city is located in the western part of the Precambrian Arabian Shield overlaid by lava plateaus (i.e., harrats) and sediments from the Tertiary and Quaternary ages. The area is covered by veneer of Wadi deposits composed of sand, gravels, and silt inter-bedded with clay that carry water for a few days, but most water is lost through direct infiltration and evaporation. Most of the groundwater wells are located in the basaltic aquifer to the east of wadi Aqiq. Water table in the area ranges from 50 to 80 m below the surface (Al-Shaibani, et al. 2007).

Geologically (Fig. 2), the upper Proterozoic rocks intrude the wadi deposits and compose mainly of mafic to silicic volcanic rock (e.g., Uhud Mountain) and derivative epiclastic and detrital sedimentary rock (Pellaton, 1981). The Al Ays Group is generally intruded by younger igneous intrusions including layered gabbro complex, granite batholiths, granodiorite and diorite, and isolated gabbro stocks. Tertiary and Quaternary basalt lava fields (known as Harrats) formed at the same time as the Red Sea rifting (Camp and Roobol 1991) composed of alkali olivine basalt typically derived from rift volcanism. Quaternary deposits in the study area comprise surficial deposits of varied fluvial, aeolian, and lacustrine origin and are commonly closely intermixed. Wadi alluvium of gravel, sand, and clay, these deposits follow the present-day drainage pattern.

Fig. 2
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Geological map of the study area (Modified after Pellaton 1981)

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Okasha and Abduljauwad (1992) reported that construction work carried out in the clayey soils of Al-Medinah city, in particular the greenish-brown clays, has met many problems. The soils are composed of quartz, feldspar, smectite, calcite, kaolinite, and some chlorite and were highly expansive indicated from Atterberg limits, clay fractions as well as from the axial free swelling, percentage of swell, and swelling procedure.

Results

Soil descriptive statistics

Descriptive statistics of the city soil parameters of grain sizes, Atterberg limits, direct shear stress parameters (friction angle Ø and cohesion c), unconfined compression strength, and soil water chemistry (pH, Cl−, and SO3−) are shown in Table 1. Borehole total depth varied between 8 and 30 m from the ground surface. Grain size distribution of 128 samples indicated the dominance of the average content of sand (45.20%) followed by gravel (31.8%) and fines (23.55%). Out of the 189 samples, 174 were non-plastic while 15 samples showed an average liquid limit (LL) of 42.57% (22.9–71.3% range) and plasticity index average of 9.92 (3.75–19.5 range). Friction angle of shear test showed an average of 30.47° (27°–35° range) with cohesion, c, values averaged 0.11 (0.01 to 0.41 range) indicating the dominance of the cohessionless soils. Unconfined compressive stress averaged 609 kg cm−2 (0–1462 kg cm−2). Soil water chemistry clarified alkaline water (8–8.6 pH) with means of 0.1 for Cl− and SO32− contents. According to AASHTO classification, 56.5% showed A-1-b type, 19.5% A-2–4, 14% A-1-a, and 10% varied between A-7–5, A-4, A-2–6, A-3, and A-5.

Table 1 Descriptive statistics of soil properties
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Soil varieties and AASHTO types

Three-dimensional models of the soil varieties are shown on Fig. 3a. Cohessionless and cohesive soil classes according to their SPT soils are shown on Fig. 3b and c. Bedrocks of basalt, rhyolite/granite, and andesite and their relative strength classified according to their corresponding RQD% are shown on Fig. 3d. The main five soil varieties that are recognized ranged in size from clays to cobbles overlain by fills and underlain by basalt, rhyolite/granite, or andesite (Table 2).

Fig. 3
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Three-dimensional models of a the soil types and b their classification according to SPT of the cohessionless/c cohesive soils and d the RQD of bedrocks

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Table 2 Description of the monitored soil varieties with classes for the cohessionless and cohesive soils and the rock RQD
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The cohessionless soil contains little to no clay or fine particles while cohesive soils contain high amounts of clay and fine particles. Cohesive soils are those in which the surface forces of the soil particles are largely responsible for the soil strength (Scott 1963). Cohesive soils with clay and fine particular materials maintain a certain binding capacity that works to retain a soil’s shape and consistency. Cohessionless soils consist of large or irregular-sized soil particles with little to no clay content and tend to shift or change in consistency under different environmental conditions such as in rain and wind conditions commonly associated with water infiltration and evaporation.

The fill and the cohessive soils spread at shallow not exceeding 15 m depth. The swell potential of these soils clays, clayey silt, and silt is high and poses geotechnical problems accumulated east and west of Auhud mountain and north of Al-Manahil district. The cohessionless soils prevail on the surface at the periphery of the city and to a depth of more than 15 m elsewhere. Very dense to dense cohessionless soils predominate deep in the downtown area and change upward into medium dense to loose varieties (Fig. 3b). Cohesive soils are recorded in 7 boreholes and varied from hard to soft (Fig. 3c).

Fill varied in thickness from 0.5 to 4.5 m that ranged from dense to loose. The fill layer of clayey sandy silt with gravel reaches maximum of 4.5 m in some parts of the Prophet’s Holy Mosque area and decreases gradually to 1.5 m outward. Clay soils (1.5–6 m thick) were recorded in two boreholes and varied between loose cohessionless and stiff cohesive clays. Silts (0.5–7.5 m thick) were partly sandy, varied between loose to very dense cohessionless (14 samples) and soft to hard cohesive silts (17 samples). Sands (0.5–12.5 thick) were clayey to silty sand, and sand with silt, and gravel and/or cobbles ranged from medium to very dense cohessionless, plastic to non-plastic, and well to poorly graded (91 samples). Sand forms the top layer several meters thick over a wide area in the intermountain areas, west and along the foothills in the city, and decreases in thickness in the eastern area.

Gravels were sometimes silty to sandy, with silt, sand, and/or cobbles (0.5–8.5 m thick), medium to very dense cohessionless, plastic to non-plastic, and well to poorly graded (37 samples). Cobbles and boulders of vesicular basalt intermixed with sandy silt, silty sand, silty gravel, and gravel (0.5–10 m thick) of 10 samples proved very poor cohessionless. Cobbles and boulders commonly overlie the gravels in the city center that decrease in thickness and sometimes disappear at the peripheries. Sound bedrocks are represented mainly by vesicular basalt (33 boreholes) in the Harrat areas, rhyolite/granite (7 boreholes) close to the mountains, and andesite (1 boreholes) (Fig. 3d).

Basaltic vesicular lava (0.5 to 9 m thick) showed varying degrees of hardness, weathering, and fracturing and was excellent according to their RQD (69 samples). Rhyolite/granite bedrock (1–6 m thick) was excellent to very poor according to their corresponding RQD (14 samples). Andesite greenish grey bedrock of 1–1.5 m thick was recorded in one borehole and showed moderately hard, highly to intensely fractured, of poor to very poor RQD.

According to AASHTO classification (Fig. 4), 56.5% of soil samples showed A-1-b type, 19.5% A-2–4, 14% A-1-a, and 10% varied between A-7–5, A-4, A-2–6, A-3, and A-5. Soil types of A-1-b and A-2–4 dominate the area. A-1-b type consists of coarse-grained silty sand with gravel (50% 0.425 mm no. 40 and 25% 0.075 mm no. 200). A-2–4 type consists of coarse-grained silty clayey sand with gravel (35% 0.075 mm no. 200) with LL% < 40% and PI < 10.

Fig. 4
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Soil types according to AASHTO classification

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Stochastic 3D geotechnical soil models

Grain size distribution varied in the 3D space (Fig. 5). Gravel reached 48% east of Ayr and Wairah mountains. Sand exceeded 60% in the wadi deposits west of Makhit and Kinana mountains. Fines have been maximum east and west of Uhud Mountain and in Al-Manahil district. Atterberg limits of LL and PI decrease upward at the southern boundary and reaches maximum in the area surrounding Auhud Mountain (Fig. 6).

Fig. 5
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Grain size distribution 3D models of the a gravel, b sand, and c fines

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Fig. 6
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Liquid limit (LL%) and plasticity index (PI)

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Shear strength of soils is an important aspect to stability of shallow foundations and piles, slopes of dams and embankments, and lateral earth pressure on retaining walls. The most common laboratory methods employed to obtain shear strength parameters are direct shear test, tri-axial compression test, and unconfined compression test. The shear strength of cohessionless soils is affected by the internal friction: friction resistance to sliding and rolling of particles and interlocking. That is, estimated by the angle of internal friction, ϕ, and cohesion, c. Shear stress ϕ and c were largest in SW and NE (Fig. 7).

Fig. 7
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Shear strength friction angle (Ø) and c index

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The unconfined compression strength showed largest values in the area surrounding Ayr Mountain and the northernmost occurrence of the Harrats (Fig. 8). Soil water chemistry 3D models are shown on Fig. 9. The pH clarified alkalinity with increase toward the south. Gradual southeastward increase of SO3− points to its possible source, the Harrat. Chlorides showed plumes east of Ayr Mountain and in the northern and western areas. Harrat is a major source of chloride and sulfates in the soil water. The high chloride and sulfate require protective measure for the reinforcement and concrete of the foundation.

Fig. 8
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Unconfined compression strength (UCS kg cm−2)

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Fig. 9
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Soil water a pH, b SO3−, and c Cl−

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Conclusions

The first insights from the 3D modeling of the geotechnical properties of soils in Medina proved potential in deciphering the complex subsurface for supporting subsoil future planning. It provides a future basis for integration with city master planning to ensure that the most efficient use of underground geo-assets is made to achieve optimal land sustainability. The methodology for building 3D models is now well established from the case study area that highlights their potential use in site appraisal before ground investigation and to identify underground resource potential based on the soil properties. The built models provide a relative assessment of ground suitability for safe construction based on sound assessment of their potential geotechnical properties and depth-related spatial zoning consistent with international standards and protocols. The geo-referenced database enhances the dynamicity of city-scale deterministic 3D models that can continuously be updated throughout all stages of development where the accuracy, scale, and resolution can be maximized by increasing the density of the borehole data.

The results of this research can enable city planners to prioritize areas with risks or over-costs for civil engineering projects. Specifically, the results can be used by geotechnicians, urban planners, or civil engineers for (a) evaluation and planning of urban areas according to the engineering conditions and the geohazard zones, (b) selection of engineering geological investigations areas of construction, (c) selection of a suitable foundation type and construction design, and (d) suppose changing of the engineering conditions and prediction of hazardous soil phenomena.

According to AASHTO classification, 90% of the soils were dominated by A-1-b (56.5%), A-2–4 (19.5%), and A-1-a (14%), and 10% varied between A-7–5, A-4, A-2–6, A-3, and A-5. Five main soil varieties were detected varied in grain sizes from clays to cobbles, sometimes overlain by dense to loose fills (0.5–4.5 m thick) and underlain, in some boreholes, by basalt, rhyolite/granite, or andesite.

Results are expected to foster future land-use optimization that identifies the most suitable soil use based on its geotechnical properties to support integrated and sustainable urban planning.