Study on the Construction of a Nonlinear Creep Constitutive Model of Salt-Gypsum Rock in the Bayan Deep and the Critical Value of Wellbore Shrinkage Liquid Column Pressure

Abstract

Aiming at the problems of borehole shrinkage and pipe sticking caused by creep in salt-gypsum rock formations during deep well drilling, multi-field coupling creep experiments on deep salt-bearing gypsum mudstone were carried out. Furthermore, a nonlinear creep constitutive model was constructed based on the Drucker–Prager criterion, and the critical value of liquid column pressure for borehole shrinkage was determined through numerical simulation. Experiments show that at 140 °C, salt-gypsum rock is mainly subjected to brittle failure with single shear fracture, while at 180 °C, multiple sets of cross-cutting shear bands form, shifting to plastic flow-dominated composite failure. The coupling effect of confining pressure and deviatoric stress is temperature-dependent; the critical deviatoric stress is independent of confining pressure at 140 °C, but decreases significantly with increasing confining pressure at 180 °C, revealing that salt-gypsum rock is more prone to plastic flow under high temperatures and confining pressure. The creep constitutive equation was further determined, and fitting parameters show that the stress exponent m = 2–5 and the time exponent n decrease linearly with the increase in deviatoric stress, and the model can accurately describe the characteristics of three-stage creep. The numerical simulation found that there is a nonlinear relationship between the drilling fluid density and borehole shrinkage; the shrinkage rate exceeds 1.47% when the density is ≤2.0 g/cm³, and the expansion amount is >1.0 mm when ≥2.4 g/cm³. The critical safe density range is 2.1–2.3 g/cm³, which is consistent with the field data in the Bayan area. The research results provide an experimental basis and quantitative method for the dynamic regulation of drilling fluid density in deep gypsum rock formations, and have engineering guiding significance for preventing borehole wall instability.

1. Introduction

Borehole shrinkage and pipe sticking incidents induced by the pronounced creep behavior of salt-gypsum formations have emerged as a critical technical constraint on the efficient development of deep oil and gas resources [1]. Take the Keshen 9 Gas Field in the Tarim Basin as an example: its salt-gypsum layer has an average thickness of 500 m, a burial depth exceeding 8000 m, and a formation temperature of 180 °C. During drilling, pipe sticking accidents caused by borehole shrinkage occur frequently, with the longest single handling cycle reaching 45 days and the drilling cycle of some wells as long as 567 days, resulting in substantial economic losses [2]. Field experience confirms that dynamically matching the liquid column pressure with salt-gypsum creep parameters is essential for borehole stability. However, conventional theoretical models exhibit significant limitations in characterizing nonlinear creep behavior and time-dependent closure mechanisms [3]. Classical Maxwell and Kelvin models, for example, only describe decaying and steady-state creep stages. The abrupt strain-rate acceleration during tertiary creep necessitates empirical corrections, resulting in insufficient wellbore stability prediction accuracy [4]. As the development of ultra-deep wells and complex structural wells advances, establishing nonlinear constitutive models that integrate multi-field coupling effects and damage evolution mechanisms, while clarifying spatiotemporal evolution laws for critical liquid column pressure, has become an urgent engineering challenge.

Salt-gypsum creep demonstrates marked time-dependence, stress nonlinearity, and temperature sensitivity, challenging traditional theoretical frameworks. Zhang Yu et al. [5], through high confining pressure triaxial creep tests, revealed that the strain rate during accelerated creep in gypsum mudstone follows a power-law exponential relationship with deviatoric stress, a behavior unattainable with linear element models. Although Lü Aizhong et al. [6] proposed a parameter identification method for unsteady creep equations, its physical mechanisms lack clarity, and its engineering applicability remains limited. Recently, nonlinear constitutive models based on the Drucker–Prager criterion have gained attention for their ability to couple hydrostatic and deviatoric stress effects. Zhang Liangliang et al. [7], for example, integrated the Drucker–Prager yield function with viscoelastoplastic damage theory to develop a triaxial stress-path creep equation and validated it through sandstone experiments. Nevertheless, existing models typically neglect temperature-induced degradation of long-term creep parameters. Xu et al. [8] demonstrated that elevated temperatures accelerate damage accumulation by reducing intergranular cementation strength, an effect particularly critical in deep high-temperature formations that highlights the current models’ limitations in complex environments.

To address classical model constraints, researchers have pursued multi-scale improvements. The Burgers model (configured as a Maxwell–Kelvin series) captures instantaneous elasticity and steady-state creep but fails to reflect damage acceleration during tertiary creep [9]. Han Yang et al. [10] enhanced this model using a time-weakening elastic modulus, effectively simulating the deep surrounding rock’s long-term rheology. Liu Wenbo et al. [11] introduced damage variables and fractional derivatives to establish a tertiary-creep-capable model. Parameter sensitivity analysis identified the acceleration onset time parameter *k* as critical for closure prediction accuracy. Internationally, Wang and Li’s [12] fractional-order soft matter model employs fractional derivatives to describe material memory and path dependence, offering novel creep modeling insights. Notably, these models’ universality under complex stress paths requires further verification, particularly regarding intermediate principal stress effects on damage evolution, where consensus is lacking [13]. Despite considering stress-path dependence, Zhang Liangliang et al.’s [14] Drucker–Prager-based viscoelastoplastic damage model was validated only under isothermal conditions, omitting the temperature-confining pressure-deviatoric stress coupling mechanism.

While the Drucker–Prager criterion provides a theoretical framework for deep formation stability analysis, its adaptability to multi-field coupling requires refinement. This criterion incorporates the stress deviator’s second invariant and spherical stress components to better characterize intermediate principal stress effects on material yielding [15]. However, studies predominantly focus on single stress conditions, lacking systematic experimental validation of parameter evolution under coupled temperature-confining pressure-deviatoric stress. For example, Lin Yuanhua et al.’s [16] Heard model simulation of Tarbei salt-gypsum shrinkage ignored the temperature gradients’ nonlinear creep acceleration, yielding overly conservative liquid column pressures in theengineering design. Viscoelastic analysis of Well Wangxie 781 revealed that at 2.4 g/cm³ drilling fluid density, theoretical shrinkage was zero, yet field measurements influenced by thermal degradation often fell below predictions [17].

Spatiotemporal evolution of borehole shrinkage governs dynamic liquid column pressure design, yet its kinetics remain inadequately understood. Zou Ming et al. [18] observed in hydraulic fill layers that closure progresses linearly initially before accelerating nonlinearly, a pattern mirroring salt-gypsum rheology. Liu Wenbo et al. [19] developed a kinetics model based on creep curve symmetry using parameter *j* to control the acceleration rate and *k* to define the onset time, enabling quantitative closure prediction. Critically, conventional theories overlook the time-dependent degradation of salt-gypsum creep parameters. Jiang Haifei et al. [20] demonstrated through high pore pressure creep tests that seepage accelerates microcrack propagation, causing the critical liquid column pressure to decline dynamically with drilling cycles. While this explains field theory deviations, integrating seepage-creep coupling into constitutive models remains unresolved.

To address these gaps, this study employs a high-temperature/high-pressure triaxial multi-field coupling creep system to conduct long-term experiments on deep salt-gypsum, elucidating its failure modes. Building on the Drucker–Prager criterion, we integrate fractional derivative theory and damage evolution to establish a nonlinear viscoelastoplastic constitutive model. An ABAQUS 2022-based borehole shrinkage numerical model is developed, and drilling fluid density is dynamically optimized using field data. This work provides theoretical and engineering foundations for liquid column pressure management in deep salt-gypsum drilling.

2. Long-Term Creep Experiment of Deep Rocks

2.1. Preparation of Rock Specimens

The salt-bearing gypsum mudstone specimens used in the experiment were taken from the Hetao Basin, Inner Mongolia Autonomous Region. In compliance with the specimen preparation guidelines outlined in the Test Code for Rocks in Water Conservancy and Hydropower Engineering (SL/T264-2020) [21] and the Standard for Test Methods of Engineering Rock Mass (GB/T50266-2013) [22], eight standard cores were fabricated via wire electrical discharge machining (EDM) technology. The morphology of the specimens is shown in Figure 1.

2.2. Experimental Scheme

The long-term creep test on deep rocks was conducted with a high-temperature and high-pressure triaxial multi-field coupling creep testing system. This system is composed of an axial loading module, a confining pressure loading module, and a data acquisition module. The axial loading system achieves a maximum axial pressure of 200 MPa with an accuracy of ±1%FS; the confining pressure system reaches a maximum of 100 MPa with an accuracy of ±0.5%FS; and the data acquisition system operates at a sampling frequency of 10 Hz. The schematic configuration of the system is illustrated in Figure 2. The experiment employed the following stepwise loading protocol: the confining pressure was first applied to the target value and held constant, after which the axial load was increased in 10 MPa increments, with each load stage maintained for 24 h while synchronously recording axial and hoop strain data. Specimen failure was identified, and the test was terminated when the axial strain rate abruptly increased or the load maintenance failed. The test scenarios included multi-field coupling conditions with confining pressures ranging from 60 to 100 MPa and temperatures from 140 to 180 °C; detailed parameters are presented in

Table 1. Basic parameters of long-term creep in cores.

Numbered	Block	Depth (m)	Length (mm)	Diameter (mm)	Temperature (°C)	Confining Pressure (MPa)
LC1	Xinghua	5600	41.23	25.44	140	60
LC2	Xinghua	5600	50.46	25.26	140	80
LC3	Xinghua	5600	50.29	25.22	140	100
LC4	Hetan	7044.96	44.93	25.1	180	60
LC5	Hetan	7044.79	38.37	25.1	180	70
LC6	Hetan	7039.56	46.14	25.32	180	90

(confining pressure, temperature, and other experimental conditions for different scenarios).

2.3. Analysis of Experimental Results

Multiple sets of experimental data systematically reveal the creep failure mechanisms of deep salt-gypsum rock under different stress environments. As shown in Figure 3, the failure morphology of the specimens exhibits significant temperature-dependent differences. At 140 °C, the failure patterns of specimens LC1–LC3 were primarily characterized by a single shear fracture surface aligned with the loading direction. At the elevated temperature of 180 °C, specimens LC4–LC6 generally exhibited multiple sets of intersecting shear bands. This observation suggests that a high temperature substantially modifies the deformation mechanism of salt-gypsum rock, inducing a shift from brittle shear failure to plastic flow-dominated complex failure.

The time-axial strain curve (Figure 4) quantitatively characterizes the correlation between specimen failure time and critical deviatoric stress, providing data support for analyzing the coupling effect of confining pressure and deviatoric stress.

Table 2. Experimental results.

Numbered	Temperature	Confining Pressure	Eccentric Stress During Failure	Days
	(°C)	(MPa)	(MPa)	(Day)
LC1	140	60	60	7
LC2	140	80	100	9.7
LC3	140	100	75	7
LC4	180	60	210	15.4
LC5	180	70	130	9
LC6	180	90	100	7.3

describes the eccentric stress and the time of failure of each group of specimens at the time of failure. The study reveals that temperature significantly regulates the correlation between confining pressure and deviatoric stress. Under the 140 °C condition, there was no obvious correlation between the critical deviatoric stress at specimen failure and confining pressure; under the high-temperature condition of 180 °C, the two exhibited a strong negative correlation, meaning that as confining pressure increased, the critical deviatoric stress required for specimen failure decreased significantly. Taking specimen LC4 as an example, when the confining pressure was 60 MPa, its critical deviatoric stress at failure reached 210 MPa, which was significantly higher than that of other specimen groups. This phenomenon is attributed to the enhanced viscous flow of the material under high-temperature conditions, which effectively disperses stress concentration and improves the material’s bearing capacity. Although high confining pressure delays the initiation of initial damage by constraining lateral deformation, it exacerbates grain sliding and grain boundary creep, causing the salt-gypsum rock to more easily enter a plastic flow state under high temperature and confining pressure, ultimately leading to a reduction in critical failure stress.

The deviatoric stress-creep rate and creep strain curve (Figure 5) further reveal the nonlinear regulatory mechanism of stress level on the deformation behavior of salt-gypsum rock. Under the moderate-temperature condition of 140 °C, the correlation between deviatoric stress and creep rate/creep strain was weak, and the deformation rate exhibited a linear growth trend with increasing stress. Under the high-temperature condition of 180 °C, a significant negative correlation was observed between the two, meaning that with the increase in confining pressure, the variation amplitude of creep rate and creep strain under the same deviatoric stress increment significantly decreased, indicating that confining pressure effectively reduces the material’s sensitivity to stress changes by inhibiting microcrack propagation.

Analysis of curve characteristics shows that when the deviatoric stress approaches the specimen failure stress threshold, both the creep rate and creep strain exhibit sudden increase characteristics. This phenomenon indicates that salt-gypsum rock enters an accelerated creep stage near failure, with deformation behavior rapidly transitioning from steady-state creep to unstable failure, providing a key basis for determining the critical stress threshold in borehole shrinkage prediction.

3. Construction of a Nonlinear Creep Constitutive Model for Deep Salt-Gypsum Rock

3.1. Total Strain Decomposition and Mechanical Mechanism

The deformation behavior of deep salt-gypsum rock in the complex downhole stress environment is governed by the synergistic effects of elastic, plastic, and creep mechanisms. To accurately characterize its mechanical response, based on continuum mechanics theory, the total strain increment is decomposed into the following three components: elastic strain increment, plastic strain increment, and creep strain increment, with the following equation established:

$$d{\epsilon }_{ij}=d{\epsilon }_{ij}^{\mathrm{e}}+d{\epsilon }_{ij}^{\mathrm{p}}+d{\epsilon }_{ij}^{\mathrm{c}}$$

(1)

Herein, the elastic strain $d{\epsilon }_{ij}^{\mathrm{e}}$ denotes instantaneous reversible deformation governed by the generalized Hooke’s law. The deviatoric stress and volumetric responses are characterized by the shear modulus G and bulk modulus K, respectively, as expressed by the following equations:

$$d{\epsilon }_{ij}^{\mathrm{e}}={\displaystyle \frac{d{s}_{ij}}{\mathit{2}G}}+{\displaystyle \frac{d{\sigma }_{kk}}{\mathit{9}K}}{\delta }_{ij}$$

(2)

The plastic strain $d{\epsilon }_{ij}^{\mathrm{p}}$ represents the irreversible shear sliding of the material post-yielding. This study employs the Drucker–Prager criterion to determine the yield threshold. By integrating the liquid column pressure term and deviatoric stress term, this criterion accurately captures the sensitivity of salt-gypsum rock yielding to confining pressure and the dilatancy behavior during shear failure, making it more applicable to the complex stress conditions of deep soft rocks than the von Mises criterion. The plastic flow direction is defined by the gradient of a non-associated plastic potential function. Through the introduction of a dilatancy angle, the direction of plastic volumetric strain can be independently regulated, allowing for precise simulation of the compressional or dilatational behavior of salt-gypsum rock under triaxial stress:

$$f=\alpha I_1+\sqrt{J_2}-k=0$$

(3)

$$G=\sqrt{(\xi \overline{{\mathsf{\sigma }}_0}\tan \psi {)}^2+q^2}-p\tan \psi$$

(4)

$$d{\epsilon }_{ij}^{\mathrm{p}}={\displaystyle \frac{d{\overline{\epsilon }}^{\mathrm{p}\mathrm{l}}}{c}}{\displaystyle \frac{\partial G}{\partial {\sigma }_{ij}^{\cdot }}}$$

(5)

In the equation, $f$ is the yield function, and G is the plastic potential function; $\alpha$, $k$ are material constants, $I_1$ is the first invariant of stress, and $J_2$ is the second invariant of deviatoric stress; $\xi ,\overline{{\mathsf{\sigma }}_0},\psi$ are parameters related to material properties, respectively, q is the generalized shear stress, p is the mean stress; $d{\overline{\epsilon }}^{\mathrm{p}\mathrm{l}}$ is the plastic strain increment, c is a material constant, and ${\sigma }_{ij}^{\cdot }$ is the stress tensor.

As the time-dependent viscoplastic flow component, the creep strain increment $d{\epsilon }_{ij}^{\mathrm{c}}$ is constructed based on the power-law characteristics observed in experiments. The nonlinear effects of deviatoric stress and time on the creep rate are quantified by the stress exponent m and time exponent n. It should be emphasized that the plastic and creep strain increments share the same gradient direction of the potential function, an assumption that implies the consistency of the two under shear-dominated mechanisms:

$${\overline{\epsilon }}^{\mathrm{c}\mathrm{r}}=A{q}^m{t}^n$$

(6)

$$d{\epsilon }_{ij}^{\mathrm{c}}={\overline{\epsilon }}^{\mathrm{c}\mathrm{r}}{\displaystyle \frac{\partial G}{\partial {\sigma }_{ij}^{\cdot }}}$$

(7)

In the equation, ${\overline{\epsilon }}^{\mathrm{c}\mathrm{r}}$ is the equivalent creep strain, A is a material constant, q is the generalized shear stress, and t is time. Experimental observations show that the creep rate of salt-gypsum rock exhibits a distinct power-law growth trend under different stress and temperature conditions, providing a reliable basis for equation construction. The above theoretical framework achieves a coupled description of elastic rebound, plastic yielding, and long-term creep behavior, providing a solid mechanical foundation for predicting the spatio-temporal evolution of borehole shrinkage in deep salt-gypsum rock formations as described below.

3.2. Creep Data Fitting and Establishment of Constitutive Model

To establish the creep constitutive equation for deep salt-gypsum rock, three sets of strain-time data before creep test failure were selected for curve fitting. Equation (8) was adopted as the basic equation, where the time exponent n was set as a function of deviatoric stress q, with the specific form as follows:

$$n=f\left(q\right)=Bq+C$$

(8)

Fitting analysis was performed on a total of six groups of experimental data (LC1–LC6), with the results shown in Figure 6. All six groups of data exhibit good correlation. Through parameter optimization, the fitting equations for the six groups of data were finally determined, with specific parameter values listed in

Table 3. Specific fitting parameters.

Cores	Deviatoric Stress (MPa)	A (10−5)	m	n	Creep Equation Fitting
LC1	30	2.50 × 10−2	2	0.40793	$\begin{array}{c}\epsilon =1\times {10}^{-7}{q}^2{t}^n\\ n=-0.002q+0.474\end{array}$
	40	2.50 × 10−2	2	0.36466
	50	2.50 × 10−2	2	0.35985
LC2	70	9.00 × 10−10	5	0.54282	$\begin{array}{c}\epsilon =9\times {10}^{-15}{q}^5{t}^n\\ n=-0.003q+0.761\end{array}$
	80	9.00 × 10−10	5	0.51548
	90	9.00 × 10−10	5	0.48074
LC3	30	2.00 × 10−3	2	0.63683	$\begin{array}{c}\epsilon =2\times {10}^{-8}{q}^2{t}^n\\ n=-0.002q+0.689\end{array}$
	45	2.00 × 10−3	2	0.58782
	60	2.00 × 10−3	2	0.57883
LC4	135	2.70 × 10−9	4	0.59114	$\begin{array}{c}\epsilon =2.7\times {10}^{-14}{q}^4{t}^n\\ n=-0.001q+0.753\end{array}$
	150	2.70 × 10−9	4	0.54511
	180	2.70 × 10−9	4	0.53785
LC5	70	2.50 × 10−5	3	0.5177	$\begin{array}{c}\epsilon =8\times {10}^{-11}{q}^3{t}^n\\ n=-0.003q+0.7\end{array}$
	90	2.50 × 10−5	3	0.45917
	110	2.50 × 10−5	3	0.41222
LC6	50	9.00 × 10−7	4	0.39767	$\begin{array}{c}\epsilon =9\times {10}^{-12}{q}^4{t}^n\\ n=-0.004q+0.574\end{array}$
	60	9.00 × 10−7	4	0.35714
	80	9.00 × 10−7	4	0.28976

. The applicable conditions of this model are as follows: temperature 140–180 °C, confining pressure 60–100 MPa, and deviatoric stress 30–210 MPa. When beyond this range, parameters A and m need to be modified via the interpolation method.

4. Numerical Model for Borehole Shrinkage

4.1. Geometric Model and Material Parameters

To quantitatively study the borehole deformation law during drilling in deep salt-gypsum rock formations, a three-dimensional numerical model for borehole shrinkage (Figure 7) was constructed based on the geological characteristics of salt-gypsum rocks in the deep strata of the Bayan area. The model is composed of upper and lower sandstone-mudstone layers and a middle salt-gypsum rock layer, with the thickness of sandstone-mudstone layers both set to 4 m, the salt-gypsum rock formation to 16 m, the total model thickness to 24 m, corresponding to a well depth of 5700 m, and a borehole diameter of 190 mm.

The material parameters of the model are set as follows: the elastic modulus of sandstone-mudstone is 48 GPa, with a Poisson’s ratio of 0.3; the elastic modulus of salt-gypsum rock is 68 GPa, with a Poisson’s ratio of 0.3. The constitutive relation adopts a nonlinear model fitted based on creep experimental data, and the parameters of the LC2 rock sample are used as the basis for the simulation. This is because the LC2 rock corresponds to the well depth of the established model and the fitting curve. The specific parameter values are as follows: power-law creep coefficient A = 9 × 10⁻¹⁵, stress index m = 5, and time index n = −0.003. The model adopts the strain-hardening criterion, which can accurately describe the strength improvement characteristics of rocks caused by internal structure changes during deformation by introducing strain hardening parameters, thereby more realistically simulating the mechanical response of deep salt-gypsum rock formations.

4.2. Mesh Generation and Boundary Loads

The model is discretized using non-uniform mesh density, with local refinement in stress-concentrated zones (e.g., wellbore walls and layer interfaces) and sparser meshes in remote areas to optimize computational efficiency. Hexahedral elements are used, resulting in an optimized total mesh count of 340,200 elements. This meshing strategy balances numerical accuracy and computational cost, providing a robust foundation for borehole deformation simulation. At the interface between the salt-bearing gypsum mudstone and salt layers, displacement continuity constraints are imposed to prohibit relative slip during creep, reflecting the cooperative deformation behavior of real geological layers.

In situ stress boundary conditions are determined using logging data inversion results: a maximum horizontal stress of 127.49 MPa, a minimum horizontal stress of 123.58 MPa, and a vertical stress of 117.43 MPa. To investigate the effect of varying drilling fluid densities on borehole deformation, five representative densities (2.0 g/cm³, 2.1 g/cm³, 2.2 g/cm³, 2.3 g/cm³, and 2.4 g/cm³) were simulated by applying corresponding uniform pressure to the borehole inner wall. These densities cover the typical pressure regulation range in field drilling, enabling systematic analysis of borehole response characteristics under varying liquid column pressures. The numerical simulation analysis step runs for a total of 4 h to capture the early-stage dynamic evolution law of borehole deformation.

4.3. Analysis of Borehole Creep Simulation Results

Numerical simulation results (Figure 8) show that the deformation of the borehole surrounding rock under different drilling fluid density conditions exhibits significant stratification characteristics: the borehole diameter changes slightly in the salt layers on both sides, while the deformation in the middle salt-gypsum layer is significantly higher than that in other rock layers. When the drilling fluid density is 2.2 g/cm³, the peak radial displacement in the salt-gypsum layer is 0.074 mm, indicating borehole expansion. This phenomenon is attributed to the fact that a higher liquid column pressure suppresses the radial contraction creep of salt-gypsum rock, instead prompting it to expand outward under lateral stress, leading to an increase in borehole size.

To further analyze the impact of time scale on formation creep amount, in combination with actual on-site operating conditions, reaming operations must be conducted within 4 h during drilling. If a sticking phenomenon occurs, the drilling fluid density must be increased immediately, and it can be adjusted to the corresponding density within the 2 h drilling fluid circulation cycle to prevent sustained creep development. To explore the mechanism of action of this time scale, a simulation with a 6 h time scale was conducted, and the simulation results are shown in Figure 9. As time extends, the creep amount shows a slow upward trend: the creep amount at 4 h is 0.074 mm, consistent with the results in Figure 8; at 6 h, the creep amount increases to 0.09577 mm, with no sticking phenomenon occurring at this point.

To systematically analyze the effect of drilling fluid density on borehole deformation, simulations were conducted across a density gradient of 2.0–2.4 g/cm³. The results are shown in Figure 10. With the increase of the density of the drilling fluid, the wellbore diameter changes from contraction to expansion. At 2.0 g/cm³, the unilateral wellbore diameter shrinks by 1.40 mm. Compared with the original diameter of 190 mm, the overall shrinkage rate is 1.47%; at 2.2 g/cm³, the borehole diameter change becomes 0.015 mm, signifying the critical threshold for the transition from shrinkage to expansion; and at 2.4 g/cm³, borehole enlargement reaches 4.06 mm, indicating significant expansion.

Validation using field drilling data from Well Guangming-1 in the Bayan region shows that when the drilling fluid density was maintained at 2.2–2.3 g/cm³, drilling operations proceeded smoothly without sticking, whereas when the density dropped to 2.0 g/cm³, borehole wall sticking occurred during tripping within 4 h (without escalating to a pipe sticking incident). This closely matches the numerical simulation results, where borehole deformation or expansion remained minimal at 2.2–2.3 g/cm³ to ensure drilling safety, while bilateral shrinkage of 2.80 mm at 2.0 g/cm³ exceeded the contact stress limits between the drill string and borehole wall, posing a sticking risk. This comparison validates the numerical model’s effectiveness in predicting borehole deformation and drilling risks in salt-gypsum formations.

5. Optimization of Drilling Fluid Density Based on Creep Characteristics

Given the physico-mechanical properties of deep salt-gypsum strata in Bayan, optimizing the drilling fluid density is crucial for ensuring borehole stability. Experimental and numerical modeling reveal that borehole diameter variations transition from shrinkage to expansion as the drilling fluid density increases. This is due to liquid column pressure controlling the creep direction of salt-gypsum rock, inducing radial contraction or expansion deformation, and thus influencing borehole geometry. Through a systematic calculation of borehole diameter changes across a density range of 1.9–2.4 g/cm³, a drilling fluid density-borehole deformation control chart (Figure 11) was developed for this area, visually depicting borehole deformation within 4 h under various density scenarios.

Further analysis reveals that at drilling fluid densities of 1.9–2.0 g/cm³, borehole shrinkage is pronounced (2.8–6.5 mm), presenting a high risk of drill string sticking; at densities of 2.0–2.1 g/cm³, shrinkage persists but decreases to 0.6–2.8 mm, potentially causing drill string sticking without exceeding critical risk thresholds. At densities of 2.1–2.3 g/cm³, borehole diameter changes shift from shrinkage to minor expansion (−0.6 to 0.5 mm), where liquid column pressure and creep stress achieve dynamic equilibrium, effectively suppressing excessive shrinkage and preventing high-pressure-induced borehole collapse to ensure safe drilling. At densities exceeding 2.3 g/cm³, borehole enlargement exceeds 1.0 mm, eliminating sticking risks but increasing annular pressure losses and drilling costs. Research confirms that a drilling fluid density of 2.1–2.3 g/cm³ is optimal for deep salt-gypsum strata in Bayan, effectively managing shrinkage risks while avoiding excessive expansion-related hazards and offering quantitative guidance for field drilling fluid design.

6. Conclusions

(1)

Long-term creep tests on deep rocks revealed that salt-gypsum rock primarily exhibits brittle failure via single shear fracture at 140 °C, while multiple intersecting shear bands form at 180 °C, indicating a transition to plastic flow-dominated composite failure. The coupled effect of confining pressure and deviatoric stress is temperature-dependent: critical deviatoric stress is independent of confining pressure at 140 °C but decreases significantly with increasing confining pressure at 180 °C, suggesting that salt-gypsum rock easily enters a plastic flow state under high-temperature and high-confining-pressure conditions.

(2)

Total strain was decomposed into elastic, plastic, and creep components, with creep strain following a power-law relationship. Creep constitutive equations for LC1–LC6 rocks were developed, and parameter fitting revealed stress exponents m ranging from 2 to 5, while time exponents n decreased with increasing deviatoric stress.

(3)

A numerical model of borehole shrinkage demonstrated that salt-gypsum layer deformation is sensitive to drilling fluid density: there is a high shrinkage risk when the density is ≤2.0 g/cm³; dynamic equilibrium with diameter changes of −0.6 to 0.5 mm occurs at 2.1–2.3 g/cm³; and expansion is enhanced at ≥2.4 g/cm³. Field validation supports a recommended optimal density of 2.1–2.3 g/cm³, which effectively mitigates shrinkage, controls costs, and provides a quantitative framework for drilling fluid design in analogous strata.